Frequency Distribution: Frequency Series, Types of Series with Examples

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 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.

Tally Bars

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.

Discrete Series or Frequency Array

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.

Frequency Distribution

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.

Exclusive Series

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.

Inclusive Series

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.

Open End Series

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


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

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
Realisation Account

Realisation Account 1

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:
Partner’s Loan Account

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:
Partners Capital Accounts

ii. Transfer of Realisation profit/ loss
Partners Capital Accounts 1

iii. For final settlement with partners:
a. The partner brings Cash to meet the deficiency in capital
Partners Capital Accounts 2

b. On payment to partners or closing partners’ capital accounts
Partners Capital Accounts 3

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.


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:
Accounting Treatment of Dissolution
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.

Realisation Account
Accounting Treatment of Dissolution 1

Partner’s Capital Accounts
Accounting Treatment of Dissolution 2

Bank Account
Accounting Treatment of Dissolution 3

Water Resources: Conservation and Management of Water, Examples

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

An Introduction to Water Resources

Water – a must for all life forms on earth and the most important natural resource. We all know that about three-fourths of the earth’s surface is covered with water. But about 96.5% of the global water resources come from the oceans and seas. In India, the water resources amount to an estimated 1897 square kilometers per annum. However, we all know about the shortage of Water we are facing as a country. Let us learn more about the conversation of the water resource.

Some quick Facts and Figures

  • The total volume of water on the earth’s surface – 96.5%
  • The total volume of usable freshwater – 2.5%
  • The volume of freshwater in ice-sheets and glaciers – 70%
  • Stored groundwater – 30%
  • Precipitation (rainfall) in India – 4% of earth’s total
  • India’s rank in the world for water availability per person (per annum) – 133

Conservation & Management of Water Resources

‘Water water everywhere, not a drop to drink.’ It is a very old saying in a different reference to the situation. But, this is exactly what we fear will happen very soon, if we do not wisely use and conserve our water resources.

Research shows that by 2025, India, along with many other countries will face a serious scarcity of water. Many regions in our country are currently undergoing the process of ‘water stress’. According to research by Falken Mark, a Swedish expert on water, ‘water stress’ happens when the water availability falls below 1000 cubic meters per person per day.

How did we reach here?

An Introduction to Water Resources

Though blessed with large rivers like the Ganga, Yamuna, Godavari, Narmada, and others, India’s socio-economic development has a lot to contribute to decreasing water resources. Rising population, industrialization, urbanization and modernization of agriculture, are some of the main reasons for water shortages in many parts of the country. As a result, most of our prominent rivers, especially the smaller ones have become toxic with waste products and pollution.

Saving Our Water Resources

Water is indeed an essential resource for life on earth and it must be conserved. In fact, historically, humans had learned to conserve the available water resource by building dams.


An Introduction to Water Resources 1

Dams are simply hydraulic structures that act as a barrier between the source and destination of flowing water. Earlier, these dams were small and hand-made. In our modern society, engineering techniques and methods are used to construct most of these dams.

Depending on its need, the water flow can be obstructed, redirected, or slowed down using a dam. The barrier often creates a small reservoir or a lake, collecting the excess flow of water. People use most dams for irrigation. While some dams are used for generating electricity, which we know as ‘hydropower’ or ‘hydro energy.

Dams can be of different types and of various sizes. While timber dams are made from wood, the masonry or embankment dams are made with stones and concrete. Dams can also be low, medium, or high in height, depending on their location and usage. Though dams can be helpful in conserving water resources, too many of them can also cause over sedimentation of the river beds.

Also, over usage of dams can reduce the aquatic life of the river, on which they flow. That is why we also have more natural and long-lasting methods of saving our water resources. The two most widely used methods are:

Rainwater Harvesting

An Introduction to Water Resources 2

You must have come across this term from multiple media sources. Rainwater harvesting is one of the most efficient and effective ways of conserving water. It is more like the recycling of natural water. In this, rooftop rainwater harvesting is a common practice in states like Rajasthan, West Bengal, Meghalaya, and major parts of South India, where rainfall is usually heavy. People connect PVC pipes to a drain on their roof and the rainwater is collected below in large storage tanks.

This water is then utilized for daily needs even after rains are over. Mostly, people do not collect the water off first rainfall but thereafter. In Shillong and other parts of Meghalaya and rain-prone regions of the North East, water from rooftop rainwater harvesting covers about 15-25% of household water requirements.

DIY: You can try a home experiment for your learning exercise. Collect the rainwater and store it. You can even filter the water for a clean output. Now, use this water for your household needs or plants. Did you know? In the state of Tamil Nadu, it is compulsory for every house/residential building to have a rooftop rainwater harvesting system!

Bamboo Drip Irrigation System

An Introduction to Water Resources 3

This is an indigenous method that has been in practice for about 200 years in the north-eastern states of India. While this practice helps conserve the region’s water resources, it also helps in the irrigation of local farms and fields. People use bamboo pipes for tapping the waters of streams and springs. About 18020 liters of water flow through a network of pipes and end up as drips on the farmlands.


Question 1.
What is water stress?
According to research by Falken Mark, a Swedish expert on water, ‘water stress’ happens when the water availability falls below 1000 cubic meters per person per day.

Question 2.
What are the different methods of water conservation?
We can conserve water resources using different methods:

  • Dams: These are hydraulic structures that can either control, redirect or obstruct the flow of water from a water body. Dams are made from wood, stone, or concrete.
  • Rainwater Harvesting: Rainwater is collected from rooftops or ground and stored in large tanks for later use. Rainwater harvesting is popular in Rajasthan, West Bengal, Meghalaya, and Tamil Nadu.
  • Drip Irrigation: This method is most practiced in North-Eastern states, for irrigation of farms as well as save the local water resources. Bamboo pipes flow water over a long distance and end up in drips when they reach the plants.

Water Resources: Methods of Water Conservation, Dams, Rain Harvesting

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

Water Resources

They say that when the well is dry only then do you know the worth of water. And how true! Three-fourths of our planet is covered in water, and yet we face a global crisis of water shortage and water pollution. This is why it is very important that we learn more about water conversation. Let us get started.

What is Water?: Sea Waves, Tides, Ocean Waves and Solved Examples

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

What is Water?

What is Water? Can you imagine surviving without water? No, right? It is impossible to live without water. It is the most basic necessity of all living creatures. No living creature can survive without it. Earth is the only planet that has water in it. Let’s find out more about it.

Sea Waves

The up and down movements of water in the sea are known as sea waves. The lower part is called wave trough whereas, the upper part of the wave is called wave crest. The distance between two adjacent crests is the wavelength and the vertical distance between the crest and the trough is the wave height.

Sea Waves


Tides are the rise and fall of sea levels caused by the combined effects of the gravitational forces exerted by the Moon and the Sun and the rotation of Earth. The rise of water level in the sea indicates high tide and lower water level indicates low tide. The types of tides are spring tides and neap tides.


Ocean Tides

The continuous flow of seawater from one direction to another is called ocean tides, It is caused by forces acting upon this mean flow, such as breaking waves, wind, the Coriolis effect, cabbeling, temperature, and salinity differences. They are classified as warm currents and cold currents.

Ocean Tides

Warm currents are currents that come from tropical or subtropical regions and flow towards the polar or subpolar regions. The water is warm here hence it is called warm currents. Similarly, cold currents are the currents that flow in from the polar or subpolar regions towards the tropical or subtropical regions. The water is cold here hence it is called cold currents.


Question 1.
Which of the following is a type of wave?
a. Ripples
b. Swells
c. Sea
d. All are the types of waves
The correct answer is the option “d”.
Ripples are the instant effect of wind on the water and they die down as quickly as they form, as the surface tension of the water dampens their efforts. Waves always travel in the same direction as the wind is blowing: if the wind changes then the waves change with it.

Wave size is determined by the strength of the wind, the length of time it has been blowing and the distance it has blown over or the ‘fetch’. When strong winds blow for longer than a few hours, it gives the water sufficient energy that it then takes on a character of its own. This character and movement are known as a swell, and it will march across open areas of water independent of the wind.

Question 2.
Which factors influence ocean currents?
a. Earth’s rotation
b. Winds across ocean
c. The density of water
d. All of the above
The correct answer is the option “d”.

Factors Influencing Nature and Movement of Ocean Currents are:

  • The earth’s rotation: Gravitational force and force of deflection.
  • The sea: Atmospheric pressure, winds, precipitation, evaporation, and insolation. It also includes pressure gradient, temperature difference, salinity, density, and melting of ice.
  • Modified ocean currents: Direction and shape of the coast, seasonal variations, and bottom topography.

Water: Importance of Water, Uses, Consumption, Prevention

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


How could one live without water? Water has many uses. However, seawater can’t be used for drinking. Seawater has waves, tides, and currents. Do you know the phenomena behind it? Let’s find out more about it and know the importance of water.

Solar System: Sun, Stars, Earth, Moon, Asteroids, Meteors

The compilation of these The Earth in the Solar System Notes makes students exam preparation simpler and organised.

Solar System

If you look at the sky above you, during the nighttime, you’ll notice that it is full of tiny shining objects. Some of these objects are bright while others are dim. Most of them, seem to be twinkling. The reality is not all of the objects in the sky can be seen with the naked eye. It is our solar system that is full of these objects. So let’s study the solar system in detail.

Celestial Bodies

The sun, the moon, and all the objects, shining in the night sky are known as the Celestial Bodies. This includes every natural object that is located outside the Earth’s atmosphere, such as the Moon, the Sun, an asteroid, planet, or star. The Kuiper belt contains many celestial bodies. Even an asteroid in space is a celestial body.

Features of a Celestial Body
Some of the celestial bodies are very big and hot. They are composed of gas and have their own light and heat. These emit heat in large amounts. Such celestial bodies are known as stars. The sun is also a star.

Further, when you look at the night sky, you’ll see different patterns formed by the different groups of stars. These are called constellations. Ursa Major is one such constellation. In archaic times, people used stars to determine directions during the night. The North Star known as the Pole Star indicates the north direction.

A pole star is a visible star. It is approximately aligned with the Earth’s axis of rotation. This means, that the apparent position of the Pole Star is close to one of the celestial poles, and it lies approximately directly overhead when viewed from the Earth’s North Pole or the South Pole.

The Pole Star always remains in the same position in the Sky. You can locate it with the help of Saptarishi. On the other hand, there are some celestial bodies that do not have their own heat and light. They are lit by the light of the stars. Such bodies are called planets.

The Solar System

The sun, eight planets, satellites, stars, and some other celestial bodies known as asteroids and meteoroids form the solar system.

The Solar System

Stars are celestial bodies having their own heat and light, which they emit in large amounts. Example: The Sun is a Star.


The Sun
The sun is the centre of the solar system. It is huge and is made up of extremely hot gases. The sun is the primary source of light and heat for the entire solar system.

The Sun

The word planet is acquired from the Greek word, ‘Planetai’ which means wanderers. Our solar system has eight planets. These are Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune. All of these eight planets of our solar system move around the sun in fixed paths. These paths are elongated. They are called orbits.


Until August 2006, Pluto was also a planet. But now it is called only a celestial body (dwarf planet).

The Earth
The Earth is our home and the third nearest planet to the Sun. The shape of the earth is called Geoid since it is slightly flattened at the poles. Certain conditions which are necessary to support life are found only on earth. This is also the reason, why life is existing only on Earth at the moment.

If one looks from outer space, the earth appears blue. This is because, a 2/3rds surface of the earth, is covered by water. Therefore, Earth is also known as the blue planet.

The Earth

The Moon
Our planet Earth only has one natural satellite which is the moon. The moon appears to be extremely big to us. This is because it is nearer to our planet in comparison to the other celestial bodies. The moon moves around the earth in about 27 days and 8 hours. On the moon, the atmospheric conditions are not favourable to support life.

The moon always moves in a synchronous rotation with Earth. This means that the same side is always facing the Earth. Every once a month, you’ll see a full moon night. It is known as Poornima. A fortnight later, you’ll not be able to see any moon at all. It is a new moon night also known as new moon night or ‘Amavasya’.

The Moon

There are several tiny bodies that also move around the sun. These bodies are known as asteroids. Asteroids can be seen between the orbit of Mars and Jupiter.


There are several tiny pieces of rocks that orbit around the sun. These are known as meteoroids. Our galaxy is a huge system of billions of stars, and clouds of dust and gases. There are several millions of such galaxies that make the universe.



Which planet is known as ‘Earth’s Twin?
Venus is known as Earth’s twin because its shape and size are similar to that of Earth.

The Earth in the Solar System: Celestial Bodies, Sun, Planets

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

The Earth in the Solar System

Have you ever just admired the sky in the night? It looks so beautiful that we just can’t take our eyes off. There are so many beautiful objects outside the earth in space that we can’t see through naked eyes. What are these objects? Why do they shine at night and not in the day? Let’s learn about these objects and the earth in the solar system.

Resources and Development: Types, Planning, Conservation, Examples

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

An Introduction to Resources and Development

Have you ever thought about what it takes for us to live? Of course, we use food, clothing, shelter, and other necessities to make life comfortable. But where do they come from? Resources of all kinds- natural and man-made, help us live the life that we live. Let us find out more about various kinds of resources and development of the same.

Types of Resources

To simply define, resources are everything available in our environment which satisfies our needs. In fact, human beings themselves are a part of the natural resources. They develop the available natural elements and transform them into ‘resources’ for use. These are the different types of resources based on various factors:

Based on their Origin: Biotic & Abiotic Resources

  • Biotic resources comprise any life form that lives in nature. Like us-human beings, other animals, plants, and all flora and fauna.
  • Whereas, abiotic resources are available in nature too, but have no life. Like metals, rocks, and stones.

Based on their Exhaustibility: Renewable & Non-renewable

  • Renewable resources are elements of nature that renew themselves. Solar energy, wind, water, forests, etc.
  • On the other hand, non-renewable resources, as the name suggests are limited for use by humans. Like fossil fuels and minerals. Though they would take millions of years to form, eventually, they would get over with continuous use.

Based on Ownership: Individual, Community, National, and International

  • Individual resources mostly refer to land, property, plantations, farms, etc. that people own. The resources that all community members use are Community-owned resources. Like farmlands, properties, pastures, public parks, playgrounds, burial grounds, picnic spots, etc.
  • National resources are simply everything in nature or man-made that belong to the country. This includes the territory of oceans and seas. The government of the country has the right to keep, develop or utilize any or all of these resources according to their requirements.
  • On the other hand, institutions control and regulate international resources. For using any resource beyond a country’s own, the respective government would need to take permission from these institutions.

Based on the Status of Development: Potential, Developed, Stock

  • Potential resources are those which are already available in nature. Also, we have already discovered them but are not completely utilized. Solar and wind energy are two of such resources. Despite their current usage, we can explore these resources more.
  • Developed resources are quite the opposite. We take years to develop most of the water, fossil fuel, minerals, plants, and animals that we use for our needs today.
  • Stock Resources are ones that have the potential but we do not have the adequate knowledge or technology to develop them. Hydrogen and Oxygen gases can be used as rich sources of energy but we are yet to discover how.

Development of Resources

Resources and Development

Nature has blessed us with so many natural resources. And, to add it, humans have learned to develop the gifts of nature and create man-made resources. But none of these come for free. Even though you might think that it occurs in nature, each of these resources will have to be developed, maintained, and conserved so our future generations can get benefits from them, as we did.

Hence resource planning is essential to bring about sustainable existence, which is a part of sustainable development. Sustainable economic development refers to the ‘development of resources without causing any harm to the environment. Also, such development should not compromise with the needs of the future generations.’

Resources and Development Planning

So, how do we plan the resources and development of the same? India is a land of rich natural resources and diversely so. However, while some regions are ahead in their resources and development, other regions lag behind. For example, states like Rajasthan, Bihar, Jharkhand, and Chhattisgarh, are blessed with minerals and metal ores.

However, they largely lack proper infrastructure and urban resources. In such cases, we need to consider resource planning at the national, state, regional, and even local levels. Resource planning involves 3 steps:

  • Identifying and documenting the available resources across different regions
  • Designing a structured plan supported by innovation and technology
  • Matching the resources and development plans with those of the nation

Conservation of Resources

Land Utilization and Planning
Land is the most important natural resource. Over the years, to make optimum utilization of our natural resources, human beings have caused a lot of damages to our land resources. About 95% of our basic needs –food, clothing, shelter come from the land. Hence conservation of land resources and development of land is extremely crucial to our future generations can survive. There are different land planning and conservation measures we can take to protect this natural resource-

  • Planting shelter belts for plants
  • Controlling over-grazing in open pastures
  • Stabilizing sand dunes
  • Proper management of wastelands
  • Controlling mining activities
  • Proper disposal of industrial waste
  • Reducing land and water degradation in industrial areas

Soil Conservation
India’s natural landscape and geographical location make it blessed with a different variety of soils in different regions. Moreover, each of these soils yields plants endemic to the region they are found in. However, drastic farming and mass production lead to heavy soil erosion and reduced fertility of the soil. There are different methods of controlling soil erosion-

  • Contour ploughing to reduce the flow of water during irrigation
  • Terrace farming to reduce soil erosion
  • Planting shelter belts for plants


When people are considered as a resource, it is termed as _____?
a. Renewable Resource
b. Non-renewable Resource
c. Human Resource
d. None of the Above
The correct answer is option “c”.
When people are considered as a resource they are called Human Resources. They are one of the most important resources because any resource can turn into a useful resource through a human resource.

Resource and Development: Planning, Types of Resources and Examples

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

Resources and Development

India is considered to be a land rich with resources, be it natural, human or technological. However, any resource is not useful until we utilize and develop it. And not all resources are infinite, so we must preserve them too. This is why we must learn about the development and conversation of resources.