## New Profit Sharing and Gaining Ratio: Calculations with Solved Examples

The compilation of these Retirement or Death of a Partner Notes makes students exam preparation simpler and organised.

## New Profit Sharing and Gaining Ratio

On the death or retirement of a partner, the partnership firm will be reconstituted. One major change will be the change in the profit-sharing ratios of the remaining partners. Let us see how the gaining ratio and sacrificing ratio will be calculated.

### New Profit Sharing Ratio

There are different cases when a partnership can have a new profit sharing ratio:

• Sometimes the partners may decide to change their existing profit sharing ratio, without any admission or retirement of a partner.
• At the time of admission of the new partner.
• At the time of retirement or death of an old partner.

This may result in again to a few partners and loss to others. The partners who are in profit due to this change in the profit-sharing ratio should compensate the sacrificing partner/partners.

New profit sharing ratio: Ratio in which the partners decide to share profits/losses in the future.

Gaining ratio: Ratio in which the partners have agreed to gain their share of profit from other partners.

Sacrificing ratio: Ratio in which the partners have agreed to sacrifice their share of profit in favour of other partners.
Sacrificing ratio = Old Ratio – New Ratio

### Gaining Ratio

The gaining ratio is calculated at the time of retirement or the death of a partner. It is the ratio in which the remaining partners acquire the outgoing partner’s share of profit.

When the partner retires, the profit-sharing ratio of the continuing partners gets changed. Continuing partners distribute the share of retiring partners among them.

Gaining ratio = New Ratio – Old Ratio (if positive)

Examples:

Question:
Various cases of new ratio and gaining ratio are explained as follows:

Case 1: When the share of retiring partner is acquired by old partners in an old ratio
Amit, Sumit, and Punit share profit and losses in the ratio of 3 : 2 : 1, respectively. Amit retires and the remaining partners decide to share to take Amit’s share in the existing ratio i.e. 2 : 1. Calculate the new ratio and gaining ratio.
Solution:
The existing ratio between Sumit and Punit = 2/6 and 1/6
Amit’s ratio (retiring partner) = 3/6
Amit’s share taken by Sumit and Punit in the ratio of 2 : 1
Sumit gets = 3/6 × 2/3 = 6/18
Punit gets = 3/6 × 1/3 = 3/18
New ratio between Sumit and Punit is = 6 : 3 = 2 : 1
Gaining ratio = New Ratio – Old Ratio
Sumit’s gain = 2/3 – 2/6 = 2/6
Punit’s gain = 1/3 – 1/6 = 1/6
Gaining ratio = 2 : 1
New Ratio = 2 : 1

Case 2: When the share of retiring partner is acquired by old partners in old specified proportions
Amit, Sumit, and Punit share profit and losses in the ratio of 2 : 3 : 1, respectively. Amit retires and the remaining partners decide to share to take Amit’s share equally. Calculate the new ratio and gaining ratio.
Solution:
The existing ratio between Sumit and Punit = 3/6 and 1/6
Amit’s ratio (retiring partner) = 2/6
Amit’s share taken by Sumit and Punit in the ratio of 1 : 1
Sumit gets = 2/6 × 1/2 = 1/6
Sumit’s new share = 3/6 + 1/6 = 4/6
Punit gets = 2/6 × 1/2 = 1/6
Punit’s new share = 1/6 + 1/6 = 2/6
New ratio between Sumit and Punit is = 4 : 2 = 2 : 1
Gaining ratio is given the question i.e. 1 : 1
Gaining ratio = 1 : 1
New Ratio = 2 : 1

Case 3: When the share of the retiring partner is acquired fully by one of the continuing partners
Amit, Sumit, and Punit share profit and losses in the ratio of 4 : 5 : 2, respectively. Amit retires and Punit acquires Amit’s share. Calculate the new ratio and gaining ratio.
Solution:
Punit’s new share = 2/11 + 4/11 = 6/11
Sumit share remains unchanged = 5/11
The new ratio between Sumit and Punit is = 5 : 6
The gaining ratio in this case between Sumit and Punit will be
Sumit’s gain = 5/11 – 5/11 = Nil
Punit’s gain = 6/11 – 2/11 = 4/11
This shows that the entire gain is taken by Punit.

## Methods of Calculating Depreciation Amount: SLM, Annuity Method

The compilation of these Depreciation, Provision and Reserves Notes makes students exam preparation simpler and organised.

## Methods of Calculating Depreciation Amount

Depreciation is a simple and interesting concept to study in accountancy. It holds the vital answer to the amount of expense which is charged to the profit and loss account during a period. The amount of depreciation, like other expenses, impacts the amount of profit earned or loss incurred during a year. Therefore, it is important to study the different methods, such as SLM, annuity method, etc. Let us study these methods.

### The Methods of Charging Depreciation

Straight Line Method (SLM)
Straight-line depreciation is the most commonly used depreciation method in accounts and is used mainly owing to its simplicity. For the application of the straight-line method, a firm charges an equal amount of the asset’s cost to each accounting period. The straight-line formula that is used to calculate depreciation expense is as follows:

Asset’s historical cost – the asset’s estimated salvage value / the asset’s useful life

Units of Production
The units of production depreciation method allocate an equal amount of expense to each unit produced or service rendered by the asset. This method is usually applied to assets used in the production line. The formula to calculate depreciation expense involves the following steps:

Determine the depreciation per unit:
(Asset’s historical cost – estimated salvage value) / estimated total units of production during the asset’s useful life

Determine the expense for the accounting period:
(Depreciation per unit X number of units produced in the period)

Sum of Year’s Digits
Sum of years’ digits is a depreciation method that results in a more accelerated write-off of the asset than the straight-line method, but less accelerated than that of the double-declining balance method. Under this method, annual depreciation is determined by multiplying the depreciable cost by a series of fractions based on the sum of the asset’s useful life digits. The sum of the digits can be determined by using the formula:
(n2 + n)/2, where n is equal to the useful life of the asset

Double Declining Balance
The double-declining balance method is a type of accelerated depreciation method that calculates a higher depreciation charge in the first year of an asset’s life and gradually decreases depreciation expense in subsequent years. This method is used if the organization wants to increase the expenses for the year, to reduce tax liability.

Annuity Method
Annuity depreciation methods are usually not based on time, but on a level of Annuity. This could be miles driven for a vehicle, or a cycle count for a machine. When the asset is acquired, its life is estimated in terms of the level of activity or annuity. Assume a vehicle above is estimated to go 50,000 miles in its lifetime. The per-mile depreciation rate is calculated as follows:

(INR 17,000 cost – INR 2,000 salvage) / 50,000 miles = INR 0.30 per mile

Each year, the depreciation expense is then calculated by multiplying the number of miles driven by the per-mile depreciation rate.

Example:

Question:
Discuss the group depreciation method.
We use the group depreciation method for depreciating multiple assets using a similar type of depreciation method. The assets must be similar in nature and also have approximately the same useful lives for using this method.

Must Follow:

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## Operating Profit: Meaning, Significance, Calculation with Solved Examples

The compilation of these Financial Statements Notes makes students exam preparation simpler and organised.

## Operating Profit

When it comes to the financials of a business, the operating profit is regarded to be a very pivotal element in analyzing the revenue earned for a period. There is a lot more to the term than just some returns on trade. Let us find out what operating profits means and why they hold ample value for a business.

### What is Operating Profit?

Operating profit is the income earned from the performance of core operations of a business, excluding any financing or tax-related issues. The concept is used to investigate the profit-making potential of a business, excluding all unusual factors. This information is particularly valuable when monitored on a trend line, to see how a business is performing over a long period of time. If operating income is negative, a business will likely require additional outside funding to remain in operation.

Operating profit is stated as a subtotal on a company’s income statement after all general and administrative expenses and before the line items for interest income and expense, as well as income taxes.

Operating profit does not necessarily equate to the cash flows generated by a business since the accounting entries made under the accrual basis of accounting can result in operating profits being reported that are substantially different from cash flows.

### How to calculate Operating Profits?

For calculating the operating profits of a business, the following formula can be used:

Operating Profit = Revenue – (Labour + cost of goods sold + Expenses incurred in the normal course of business)

Operating profits are important because it is an indirect measure of efficiency. The higher the operating profit, the more profitable a company’s core business is.

Several factors can affect the operating profit. These include the pricing strategy of the business, prices for raw materials, or labour costs. This is because these items directly relate to the day-to-day decisions that managers make. Operating profit is also a measure of managerial flexibility and competency, particularly during tough economic times.

While the elimination of production costs from the overall operating revenue, along with any costs that may be associated with depreciation and amortization, are permitted when determining the operating profit, the calculation does not account for any debt obligations that must be met even if those obligations are directly tied to the company’s ability to maintain normal business operations.

Operating income usually does not include any investment income generated through a part stake in another company. This also includes the investment income that may be associated directly with the core business operations of the secondary company. Additionally, the sale of assets such as real estate and production equipment is not included. This is because these sales are not a part of the core operations of the business.

Example:

Question:
Consider the following figures and calculate EBIT.

• Revenue – 10,00,000 INR
• Cost of goods sold – 5,00,000 INR
• Labour – 3,00,000 INR
• General & administrative expenses – 50,000 INR

EBIT is Earnings before Interest and Taxes. So EBIT, in this case, will be Operating Profits
Operating Profit = INR 1,000,000 – INR 500,000 – INR 300,000 – INR 50,000 = INR 150,000

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## Circular Flow of Income and Methods of Calculating National Income: Guides

The compilation of these National Income Accounting Notes makes students exam preparation simpler and organised.

## Circular Flow of Income and Methods of Calculating National Income

What goes around comes around right? Have you ever wondered where the money your parents earn comes from? And after you have spent it, where will this money end up? As you may have figured it out, money in our economy flows in circles. We call this the circular flow of income. Let us learn more.

### Flow of Money

In the course of your academic year, you are in constant need of textbooks, notebooks, and stationery. And your family members usually fulfill these basic demands. But have you ever wondered how they are able to do this? You must have seen your parents go to work every day and receive salaries in return for their services. And this salary is what they use to pay for your education and your basic needs.

Now in addition to your education, they also account for numerous other expenses like household groceries, rent, and so on. And these expenses, although small, affect the economy in some way or the other. Let’s see how.

Now let’s take groceries as an example. When your parents purchase groceries, it creates a demand for the same. An increase in demand translates into an increase in the production of goods and services. And to meet this demand, manufacturers and industries hire more people in exchange for their skills and services.

In this process of providing services, people earn more spendable income. If you observe closely, there is a continuous flow of money from households to industries and back to households. And that’s exactly what is referred to as circular flow of income.

### Circular Flow of Income

Let’s now understand this concept in economic terms. The circular flow of income is a model that represents how money moves around in an economy. In a simple economy, we have only two components—households and industries. But it isn’t that simple.

In an open economy, there are a lot more factors that affect the circular flow of income. In addition to household consumption and business production, an open economy also takes into account the government spending and foreign trade.

Money is injected into the economy when the government invests money in infrastructure and welfare schemes. Similarly, industries and businesses also earn income when they export goods. However, when we import goods and services and pay taxes to the government, we reduce our spendable income.

Now government spending, exports, and investments together with household income (wages) constitute the influx of money into an economy. Similarly, business investments, taxes, and imports constitute the total outflow. The national income will increase when the total influx of money is more than the outflow of money. And the circular flow of income will be in balance when the total influx matches the total outflow.

### Methods of Calculating National Income

Now that you are familiar with the concept of the circular flow of income, let’s understand the methods of calculating national income. Calculating and measuring national income is important because that’s how we can assess an economy’s growth rate. There are several methods of calculating national income. Let’s briefly look at each method.

Income Method
The income method of calculating national income focuses on the production perspective. Now production of goods and services involves the use of land, labour, capital, and so on. And if we consider these factors of production, income is generated via rent, wages and salaries, profits, and interest.

We can then calculate the national income by adding all these types of income. Another important source of income is mixed-income. Mixed-income refers to the income generated by self-employed professionals and sole proprietors.

According to the income method:

National Income = Rent + Wages + Interest + Profit + Mixed-Income

The income method, however, does not consider transfer payments, prize money (lotteries), illegal money, profit tax, and the sale of second-hand goods.

Expenditure Method
The expenditure method of calculating national income focuses on expenditures. Now expenditure refers to all the purchases made by residents, government, or business enterprises. The expenditure method takes the following elements into consideration:

• Purchase of consumer goods and services by residents and households (C)
• Government expenditure on goods and services (G)
• Business enterprises’ expenditure on capital goods and stocks (I)
• Net exports (exports-imports) (NX)

Hence, according to the expenditure method:

National Income = C + G + I + NX

However, the expenditure method excludes expenditure on second-hand goods and the purchase of shares and bonds.

The value-added method of calculating national income focuses on the value added to a product at each stage of production. To calculate the national income using this method, we will have to first calculate the net value added at factor cost (NVAFC). And to calculate the (NVAFC), we will have to deduct the net indirect taxes.

Usually, this method involves dividing the economy into various industries such as agriculture, fishing, transport, communication, and so on. Then by calculating the value-added ((NVAFC) at each stage, we can derive the national income. Now since this method concentrates on the net value added by each component, we would need to exclude or subtract the following elements from the output of each enterprise:

• Consumption of raw materials
• Consumption of capital
• Net indirect taxes

Now if we add the NVAFC of all enterprises of an industry, we get the net value added at factor cost for that industry. And by adding the NVAFC of all industries, we get the net domestic product at factor cost, which is represented as NDPFC. And to this, if we add the net factor income from abroad, we get the national income.

Hence, according to the value-added method:

National Income = (NDPFC) + Net Factor Income from abroad

Example:

Question:
Which of the following sources is an exception while calculating national income using the income method.
A. Salaries
B. Rent
C. Profit from the sale of second-hand goods
D. Mixed-income
C. Profit from the sale of second-hand goods
The income method concentrates on the income generated from the various factors of production such as land and labour. This method does not consider the income generated from the sale of second-hand goods.

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## Price Elasticity of Supply: Calculation Methods, Types, Factors, Examples

The compilation of these The Theory of Firm Under Perfect Competition Notes makes students exam preparation simpler and organised.

## Price Elasticity of Supply

We have studied that price and supply go hand in hand i.e. they are directly related to each other. But using this can you answer how much will the supply change if the price changes by 10%? Definitely not. Thus it’s time to answer such questions using the price elasticity of supply.

### Price Elasticity of Supply

We have been studying the impact of price on supply. However, all these definitions have been qualitative. With this in mind, the price elasticity of supply came into existence. The price elasticity of supply tackles the quantitative side of the price and supply relationship.

It refers to the degree of responsiveness of supply of a commodity with reference to change in the price of such commodity. Note that the price elasticity of supply is always positive. This happens because of the positive or direct relationship between price and supply, unlike demand.

### Measurement of Price Elasticity of Supply

We can measure price elasticity of supply using the following two methods:

Percentage Method
The percentage method is the most frequently used method to calculate the price elasticity of supply, as was in the case of demand. This method is also known as the proportionate method. According to this method, elasticity is measured as the ratio of the percentage change in the quantity supplied to a percentage change in the price. The formula to calculate the price elasticity of supply using the percentage method is as follows:

Es = Percentage change in quantity supplied/Percentage change in price

Here, Es = The price elasticity of supply,

Percentage change in quantity supplied = [Change in quantity supplied/Initial quantity supplied] × 100

Percentage change in price = [Change in price/Initial price] × 100

The Proportionate Method: The percentage method rightly also known as the proportionate method as the formulas for both are interchangeable and one can easily derive the other. Considering and putting the following values in the formula for percentage method: Let change in quantity supplied = ΔQ, initial quantity = Q, change in price = ΔP, initial price = P, we get:

Es = {[ΔQ/Q) × 100] ÷ [(ΔP/P) × 100]} = (ΔQ/ΔP) × (P/Q)

Geometric Method
The geometric method helps in the calculation of the price elasticity of supply from the supply curve itself. This method is based on the viewpoint that elasticity can be calculated at a point on the supply curve. It is also known as the point method or the arc method. The formula to calculate elasticity using this method is as below:

Es = Intercept of supply curve on the X-axis/Quantity supplied at that price

### Kinds of Elasticities of Supply

According to the market for commodities, they respond differently to changes in price. These different reactions are mapped using the concept of price elasticity if supply. According to the different kinds of responsiveness of commodities, the price elasticities of supply are categorized into five types.

Perfectly Elastic Supply
A commodity is said to have a perfectly elastic supply if it has an infinite supply at a particular price and even a slight change in this price brings the supply down to zero. This further means that any quantity of the commodity can be supplied at this price and suppliers refuse to supply even one unit at any rate different from this price.

Under these circumstances, the price elasticity of supply Es is equal to ∞. Further in geometric terms, a supply curve with a horizontal straight line parallel to the X-axis exhibits the behaviour of a perfectly elastic supply.

Perfectly Inelastic Supply
A perfectly inelastic supply remains unmoved in response to any change in the price. In other words, the supply of such a commodity always remains constant no matter what the price is. A perfectly inelastic supply is represented as Es = 0. Further, a perfectly inelastic supply curve is a vertical straight line parallel to the Y-axis.

Highly Elastic Supply
When the percentage change in quantity supplied is more than the percentage change in price then the supply is said to be highly elastic. Alternatively, the supply of such a commodity has a high degree of responsiveness or is volatile. The supply responds by a big factor for even a small change in the price. The price elasticity of supply for such a case is greater than 1, i.e. Es > 1, and the supply curve has an intercept on the Y-axis or a negative intercept on the X-axis.

Less Elastic Supply
For a less elastic supply, the percentage change in quantity supplied is smaller than the percentage change in price. The supply for such a commodity tends to change by a small factor and has a small degree of responsiveness to a change in the price. In this case, the price elasticity of supply or Es<1 and the supply curve has an intercept on the X-axis.

Unitary Elastic Supply
When the percentage change in quantity supplied is equal to the percentage change in price such that the price elasticity of a supply is equal to one, then supply for such a commodity is said to be unitary elastic. As mentioned, in such a case Es= 1. Further, the supply curve is a straight line passing through the origin. Note that any supply curve that passes through the origin, irrespective of its slope, tends to have a unitary elastic supply.

### Time Period and Supply

The change in the supply of a commodity also depends on our perception of the timeframe. This means, that in many cases the change in supply tends to differ when considered over different time periods. Such an observation leads to a classification of time into three time periods.

Market Period: A market period is a very short interval of time. On the other hand, supply cannot change in the blink of an eye. Producers need time to adjust to the changes in the price of a commodity. Observe that such statements are similar to the conditions of a perfectly inelastic supply. Thus, in a market period, the supply is perfectly inelastic.

Short Period: A Short-period is a small period of time. In such a timeframe, only the variable factors of production can be played with. Hence the change in supply is limited to a small degree of response. Evidently, for a short period, the supply tends to be less elastic.

Long Period: A long period of time is a time interval sufficiently long, in which all the factors of production can be altered. Thus for a long period, the supply responds in a high manner.

### Factors that Govern Price Elasticity of Supply

Nature of the Commodity
On the basis of nature of commodities can be classified into durable or perishable goods. Definitely, their response to a change in price also varies. Durable good has long lifetimes and can be stored for long periods. Examples are furniture, TV, etc. Hence such goods have a high elastic supply as producers can manipulate their supply to earn greater profits.

On the other hand, perishable goods have short lifetimes and cannot be stored. Vegetables, milk, etc are some perishable goods. Such goods need to be disposed of and hence have an inelastic supply.

Cost of Production
As a firm looks to expand production, it needs to employ more factors of production. As a result of this, the cost of production rises. This rise varies from one factor to another factor of production. If the cost of adding more factors of production rises rapidly then the firm refrains from expanding supply.

Conversely, a slow rise in the cost of production with the addition of factors proves to be a good incentive for change in supply. Thus, the supply is inelastic in the former various it tends to be elastic in the latter.

Time Period
As already discussed, in the market period supply is inelastic, in short, time period supply is less elastic whereas in a long time period supply tends to be more elastic.

Nature of Inputs Used
The elasticity of supply depends on the nature of inputs. Inputs can be divided as easily available and scarcely available. If the inputs are easily available then the supply is elastic as it can be changed easily. On the other hand, if the availability of inputs is scarce then the supply tends to be inelastic.

Natural Factors
The commodities, whose production is dependent on natural factors, as in the case of seasonal crops, have an inelastic supply. On the contrary, goods whose production is independent of natural factors for example manufactured goods, have an elastic supply.

Example:

Question:
Why is the price elasticity of supply always positive?
The price elasticity of supply is always positive because of the direct relationship between price and quantity of a commodity supplied. In other words price and supply move in the same direction.

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## Calculation of Mean, Median and Mode: Formulas and Solved Examples

The compilation of these Measures of Central Tendency Notes makes students exam preparation simpler and organised.

## Calculation of Mean, Median, and Mode

When working on a given set of data, it is not possible to remember all the values in that set. But we require inference of the data given to us. This problem is solved by mean median and mode. These, known as measures of central tendency, represent all the values of the data. As a result, they help us to draw an inference and an estimate of all the values. Let us learn about the measures of central tendency and the calculation of Mean Median and Mode.

### The Measures of Central Tendency – Mean Median and Mode

As already discussed, the mean median and mode are known as measures of central tendency. They are also known as statistical averages. Their simple function is to mathematically represent all the values in a particular set of data. Hence, this representation shows the general trend and inclination of all the values.

An average provides a simple way of representing all the individual data. It also aids in the comparison of different groups of data. In addition to this, an average in economic terms can represent the direction an economy is headed towards. Hence, it can be easily used to formulate policies and bring about reform for a better economy.

For example, a low per capita income is an indication for the government to formulate policies focused on the increase in income of people. We will learn about three measures of central tendency- Mean Median and Mode.

### Arithmetic Mean

The first concept to understand from Mean Median and Mode is Mean. Mean is simply defined as the ratio of the summation of all values to the number of items. Note that there are two types of arithmetic mean which are simple arithmetic mean and weighted arithmetic mean.

Mean = ∑X ÷ N

Here, ∑X = Sum of all the individual values and
N = Total number of items

The simple arithmetic mean considers all the values in data as equal and grants equal importance to each value. Whereas, in weighted arithmetic mean weights or importance is assigned to the values. Without further delay let us study methods of constructing mean.

### Mean Calculation for Individual Series

1. Direct Method
In this method, the formal definition of mean is used. The values of items are simply summed and divided by the number of observations.

Mean = ∑X ÷ N

2. Assumed Mean Method
In the assumed mean method, a value is randomly selected as an assumed mean. Generally, the value is around the centre of the series as this facilitates calculations( the calculated deviations are both negative and positive around the assumed value, hence they cancel out or sum up to a very small value).

The assumed mean is found by dividing the maximum and minimum values by 2. Now deviation of each value from the assumed mean is calculated as deviation = value of the item – assumed value of mean in a separate column. The summation of these deviations are calculated and the actual mean is derived using the given formula:

Mean = A + (∑d ÷ N)

Here, A = Assumed value of the mean
∑d = Summation of deviations and
N = Number of observations

### Mean Calculation for Discrete Series

Again in the case of discrete series, the mean can be calculated by three approaches as follows:

1. Direct Method
The formula for the direct method is as follows:

Mean = ∑fX/∑f

Here, ∑fX = Summation of the product of values of items with their corresponding frequencies
∑f = Summation of all the frequencies

2. Assumed Mean Method
The basic idea behind the assumed mean method remains the same for discrete series too, but the overall formula changes a bit to incorporate the addition of frequencies assigned to observations as follows:

Mean = A + ∑fd/∑f

Here, A = Assumed mean value
∑fd = Summation of the product of deviations and corresponding frequencies
∑f = Summation of the frequencies

3. Step Deviation Method
Similar to the assumed mean method, the concept behind step deviation method is to make calculations easier. It is a simpler variant of the assumed mean method and is used when there is a common factor among all the deviations by which they can be divided to reduce their values.

The factor is indicated by ‘C’. The deviation, when reduced by this factor, is known as a step-deviation. The formula is as follows:

Mean = A + (∑fd’/∑f) × C

C = The common factor using which deviations are converted to step-deviations

Note: In this method step-deviation denoted by d’ is used and not d.

d’ = (X – A)/C

Here, X = The value of the item
A = Assumed value of mean and
C = Common factor chosen

### Mean Calculation for Frequency Distribution

The three approaches towards calculating mean for frequency distribution series are as follows:

1. Direct Method
In a frequency distribution, instead of individual values of observations, classes are mentioned. Hence to find the mean we need a single value that can represent the interval.

Such a value is found by adding the upper and lower class values and dividing the sum by 2. This value is known as mid-value. It is usually represented by m or Xi. Therefore the formula for calculating mean by direct method for frequency distribution is:

Mean = ∑fXi/∑f
OR
Mean = ∑fm/∑f

Here, ∑fXi or ∑fm = Summation of the product of mid values and corresponding frequencies
∑f = Summation of the frequencies

2. Assumed Mean Method
The overall idea of the assumed mean method here also remains the same except the fact that the concept of mid values is incorporated. The formula remains the same as the following:

Mean = A + ∑fd/∑f

Here, A = assumed mean value
∑fd = Summation of the product of deviation and corresponding frequency
∑f = Summation of the frequencies

Note: Here mid-values of the classes are used for all calculation purposes.

3. Step-Deviation Method
Since the assumed mean method, in this case, is almost the same, likewise, the step deviation method also remains almost the same as it is a simpler version of the former. The only change incorporates the concept of mid-values. The formula is as follows:

Mean = A + (∑fd’/∑f) × C

### Weighted Arithmetic Mean

As already mentioned weighted arithmetic mean assigns weights to observations depending on their importance. Different items of the series are weighted according to their relative importance and the mean is hence called weighted arithmetic mean. The formula for calculation of weighted mean is mentioned below:

Mean = ∑WX/∑W

Here, ∑WX = Summation of the product of items and the corresponding weights assigned to them
∑W = Summation of the weights

### Median

Another measure of central tendency i.e. (Mean Median and Mode) is median which is essentially known as the central value of a series. Median is a value in series such that it divides the series exactly in halves. This means one half of the series above-median contains all values greater than it and the other half contains all values smaller than the median. Hence median is the mid-value.

### Calculation of Median

Median for Individual series
In individual series, where data is given in the raw form, the first step towards median calculation is to arrange the data in ascending or descending order. Now calculate the number of observations denoted by N. The next step is decided by whether the value of N is even or odd.

1. If the value of N is odd then simply the value of (N+1)/2 th item is median for the data.
2. If the value of N is even, then use this formula:
Median = [size of (N+1)/2 term + size of (N/2 + 1)th term] ÷ 2

Median for Discrete Series
The first step for calculation of median here also involves arranging the data in ascending or descending order. This is followed by the conversion of simple frequencies into cumulative frequencies. Hence another column for cumulative frequency needs to be constructed, wherein the last value is labeled as the value of N (i.e ∑f).

Next, we need to find the value of (N+1)/2. Lastly, the value corresponding to the cumulative frequency just greater than (N+1)/2 is termed as the median for the data.

Median for Frequency Distribution
As in all other types of distributions, here also initially we arrange the classes in either ascending or descending order. Next, we need to find the cumulative frequencies. The last value in the cumulative frequency column which is ∑f is labeled as N. This is followed by the calculation of the value of N/2.

Further, the class corresponding to the cumulative frequency just greater than this value is known as the median class. Lastly, the median value is calculated by applying the following formula:

Median = l/2 + h/f[N/2 – C]

Here, l = The lower limit of the median class
h = size of the class
f = Frequency corresponding to the median class
N = Summation of frequencies
C = The cumulative frequency corresponding to the class just before the median class

### Mode

Now we come to the third concept of Mean Median and Mode. It is the measure of central tendency aims at pointing out the value that occurs most frequently in a series. This value, when it represents the data is known as the mode of the series. Mode simply refers to the value that occurs the maximum number of times in a distribution.

### Calculation of Mode

Mode for Individual Series
In the case of individual series, we just have to inspect the item that occurs most frequently in the distribution. Further, this item is the mode of the series.

Mode for Discrete Series
In discrete series, we have values of items with their corresponding frequencies. In essence, here the value of the item with the highest frequency will be the mode for the distribution.

Mode for Frequency Distribution
Lastly, for frequency distribution, the method for mode calculation is somewhat different. Here we have to find a modal class. The modal class is the one with the highest frequency value. The class just before the modal class is called the pre-modal class. Whereas, the class just after the modal class is known as the post-modal class. Lastly, the following formula is applied for the calculation of mode:

Mode = l + h [(f1 – f0)/(2f1 – f0 – f2)]

Here, l = The lower limit of the modal class
f1 = Frequency corresponding to the modal class
f2 = Frequency corresponding to the post-modal class
and f0 = Frequency corresponding to the pre-modal class

Example:

Question:
Calculate mode for the following data:

As the frequency for class 30 – 40 is maximum, this class is the modal class.
Classes 20 – 30 and 40 – 50 are pre-modal and post-modal classes respectively.
The mode is:
Mode = 30 + 10 × [(15 – 10)/(2 × 15 – 10 – 10)]
= 30 + 5
= 35

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## Packaging: Introduction, Importance as a Marketing Tool, Concepts

The compilation of these Marketing Notes makes students exam preparation simpler and organised.

## Packaging

We know about the four very important P’s of a marketing mix, namely Product, Price, Place, and Promotion. But did you know that many consider another P that is equally important- Packaging. That’s right, the packaging of a product is a very important factor in marketing. Let us see why.

### Packaging

As we know first impressions go a very long way in how people perceive anything. This is the same idea that companies implement via their packaging. The outer appearance of the product (the package) is the first thing a potential customer will see, and so it can be a great marketing tool for the product.

In fact, the package of a product serves multiple practical purposes as well. Let us take a look at some of the uses and functions that it serves.

Protection: The first and the most obvious use of packaging is protection. It physically protects the goods from damage that may be caused due to environmental factors. It is the protection against breaking, moisture, dust, temperature changes, etc.

Information Transmission: Packaging and labelling are essential tools to inform the customer about the product. They relay important information about directions for use, storage instructions, ingredients, warnings, helpline information, and any government-required warnings.

Convenience: Goods have to be transported, distributed, stored, and warehoused during their journey from production to consumption. Packaging will make the process of handling goods more convenient for all parties involved.

Security: To ensure that there is no tampering with the packaging of the goods is crucial. The package of a product will secure the goods from any foreign elements or alterations. High-quality packages will reduce the risk of any pilferage.

### Packaging as a Marketing Tool

Effective packaging can actually help a company attract consumers to its product. It can be the tool that sets apart their product in a vast sea of options that the consumer has at their disposal. Good packaging can actually add to the perceived value of a product.

There are some effective techniques one can use to ensure that your product package is a great marketing tool for your product. Let us take a look at some elements that you can incorporate into a package to make it more effective.

Capturing Attention
One important aspect of a package is that it must draw the attention of a potential customer when it is sitting on a shelf. It does not have to be the loudest or brightest package, but it must be unique in some way. Sometimes simplicity could be what sets it apart. Other factors could be the shape, the colour scheme or even the texture of the package.

Brand and Product Names should be very Clear
It is of absolute attention that your packaging draws maximum attention to your brand name. The customer will not buy a product if they do not know whose product they are buying. And clearly displaying your brand name is also a good branding strategy.

Point out to Benefits
Your product may have certain unique elements or benefits. Your packaging should draw attention to such benefits, it is a huge selling point. For example, if the product is ‘organic’ or has ‘no preservatives’ it should say so on the package and be displayed prominently.

Designed with the Target Audience in Mind
The company must be clear on whom the packaging is designed to attract and impress. Say the target audience is youth, then the design can be abstract and modernistic. But say the target customers are senior citizens, then the design should be clear and specific. Designing your packaging for a target audience is not always easy but certain criteria can be followed.

Example:

Question:
What are some environmental considerations to keep in mind while designing the package of a product?
In this era, while designing the packaging there are certain environmental factors all companies must keep in mind. This is one way to be environmentally conscious and avoid pollution.

• Make sure the package is easily disposable, and provide instructions for such disposal.
• Avoid using excess material while packaging the product. We must restrict our use of excessive plastic if there is no necessary requirement for it.
• The materials we use for the packaging should be recyclable or reusable.

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## Marketing: Branding, Labelling, Publicity, Sales Promotion, Product etc.

The compilation of these Business Studies Notes makes students exam preparation simpler and organised.

## Marketing

In the modern world, marketing is an important part. Marketing helps the consumer to get aware of the product. But what is Branding? What is Labeling? What is Personal Selling? and what is Promotion? How do Sales Promotion and Publicity work? Let’s find out more about Marketing.

Bank Nifty Pivot Point Calculator is playing an important role in marketing now. Best platform to learn marketing and their products, pricing, selling, promotion, and publicity.

## Frequency Distribution: Frequency Series, Types of Series with Examples

The compilation of these Organisation of Data Notes makes students exam preparation simpler and organised.

## Frequency Distribution

Assume you are collecting the data about the weights of all students in your class. Definitely, there will be many students that share the same weight. In such a case, we can say that some weight values occur frequently. Thus we can construct a statistical frequency series out of this data according to a frequency distribution.

### Frequency Series

A frequency distribution is the part of a broader type of statistical series, which is frequency series. A frequency series is simply a series that contains frequency. Before discussing a frequency series, there are certain terms of absolute importance which are as follows:

Frequency
Frequency is basically the number of times a data item occurs in the series. In other words, it deals with how frequent a data item is in the series. For example, if the weight of 5 students in a class is exactly 65 kg, then the frequency of data item 65kg is 5.

Class Frequency
Generally, we construct various classes that have a range of values from the data. The class frequency is the number of times the items corresponding to a class interval repeat in the series. In simple words, it is the frequency of a class. For example, if there are 10 students weighing 50-60 kg, then the class frequency for the class 50-60 is 10.

Tally Bars
We generally use tally bars to count the frequency in a series. Whenever an item occurs in a series, it is represented by a ‘|’. This is an item that occurs 4 times then it is represented as ||||. One important point to remember is that we represent the fifth occurrence by crossing the four tally bars. This is the four and cross method.

Discrete Series or Frequency Array: In this type, there are no class intervals with a specific range of data items. Instead, there are data items with their exact value and corresponding frequency. Definitely, we use this when the data collected is very small.

Frequency Distribution: Here, we mention various class intervals with a range of values for data intervals with their respective class frequencies. We will be studying further about below.

### Frequency Distribution

In a frequency distribution series, we make use of various class intervals to represent the range of values of the data under consideration. The class intervals are framed according to the lowest and maximum values of the given data. Also, these class intervals have an upper and lower values.

Whenever an item occupies the range between upper and lower values of a class interval, it is written against the corresponding class interval using a tally bar.

Further, a major difference between frequency array and frequency distribution series is that in frequency array the X-variable or the basis of classification (weight of students in our example) generally assumes discrete values. Whereas, in a frequency distribution, the X-variable or the basis of classification assumes continuous values.

### Types of Frequency Distribution

The frequency distribution is further classified into five. These are:

Exclusive Series
In such a series, for a particular class interval, all the data items having values ranging from its lower limit to just below the upper limit are counted in the class interval. In other words, we do not include the items that have values less than the lower limit, equal to the upper limit, and greater than the upper limit.

Note that here the upper limit of a class repeats itself in the lower limit of the next interval. This is the most used type of frequency distribution.

Inclusive Series
On the contrary to exclusive series, an inclusive series includes both its upper and lower limit. Of course, this means that we do not include the items with values less than the lower limit and greater than the upper limit.

Open End Series
In an open-end series, the lower limit of the first class in the series and the upper limit of the last class in the series is missing. Instead, there is ‘below the lower limit’ of the first class and ‘lower limit and above the lower limit’ of the last class.

Cumulative Frequency Series
In a cumulative frequency series, we either add or subtract the frequencies of all the preceding class intervals to determine the frequency for a particular class. Further, the classes are converted into either ‘less than the upper limit’ or ‘more than the lower limit’.

Mid-Values Frequency Series
A mid-value frequency series is one in which we have the mid values of class intervals and the corresponding frequencies. In other words, the mid values represent the range of a particular class interval. To determine the upper and lower limits of a class represented by its mid-value we can use the following formulas:

Lower Limit = m – (1\2) × i
Upper Limit = m – (1\2) × i

Here, m = The mid-value of the class
i = Difference between the mid-values

Example:

Question:
List the different types of frequency distribution series.
The various types of the frequency distribution are:

1. Exclusive series
2. Inclusive series
3. Open-end series
4. Cumulative frequency series
5. Mid-value frequency series

## Accounting Treatment of Dissolution: Realisation Account, Capital Account

The compilation of these Dissolution of Partnership Firm Notes makes students exam preparation simpler and organised.

## Accounting Treatment of Dissolution

Let us learn about the accounting treatment in case of a dissolution of the partnership firm. There is a special account to be made known as the realisation account, along with the necessary changes to the capital accounts. Let us study this.

### Accounting Treatment

On dissolution, the books of the firm are to be closed. The dissolution process starts by opening the following accounts in the firm’s books:

1. Realisation Account
2. Partner’s Loan Account
3. Partners’ Capital Accounts
4. Bank or Cash Account

1. Realisation Account
The object of preparing Realisation account is to close the books of accounts of the dissolved firm and to determine profit or loss on the Realisation of assets and payment of liabilities. It is prepared by:

• Transferring all the assets except Cash or Bank Account to the debit side of the account.
• Transferring all the liabilities except Partner’s Loan Account and Partners’ Capital Accounts to the credit side of the account.
• Crediting the Receipt on the sale of assets to the account.
• Debiting the payment of Liabilities to the account.
• Debiting the dissolution expenses of the firm.

The balance in the account may be either profit or loss. We transfer this balance to the Capital Accounts of the Partners in their profit-sharing ratio.

Realisation Account

2. Partner’s Loan Account
We do not transfer the loan by a partner to the firm to the Realisation account, it remains in its account itself. At the time of settlement, i.e., payment of liabilities, we pay the partner’s loan after paying the outside liabilities but before payment of capital.

Following entry is the entry on payment of Partner’s loan:

3. Partners Capital Accounts
If partners take over the firm’s assets, we debit it to their Capital Accounts at the agreed value being payment against their capital. If a partner takes over the liability of the firm, we credit it to their Capital Accounts. In addition, we also transfer undistributed profits/losses, reserves, and Realisation profit/loss to capital accounts in their profit-sharing ratio. Entries are:

i. On transfer of undistributed profits/losses and reserves:

ii. Transfer of Realisation profit/ loss

iii. For final settlement with partners:
a. The partner brings Cash to meet the deficiency in capital

b. On payment to partners or closing partners’ capital accounts

4. Bank or Cash Account
On the debit side, we show the opening balance, the amount received from the sale of assets, and the amount brought by partners. And on the credit side, we show payment of liabilities, expenses, and amounts paid to partners. After settling the claims of the partners, there is no balance in the Bank/Cash Account.

Example:

Question:
P and Q were sharing profits and losses in the ratio of 3: 2. The balance sheet of a firm as of 31st March 2018 is:

On the above date, the firm dissolves. Following is the additional information. Prepare the necessary Accounts.

• P took over 50% of the furniture at 20% less than book value. The remaining furniture was sold for ₹ 1,05,000.
• Debtors realised at ₹ 26,000.
• Q took over the stock for ₹ 29,000.
• Q’s sister’s loan was paid off along with an interest of ₹ 2,000.
• Expenses on realisation amounted to ₹ 5,000.

Solution:
Realisation Account

Partner’s Capital Accounts

Bank Account