The DAV Maths Class 7 Solutions and **DAV Class 7 Maths Chapter 12 Worksheet 3** Solutions of Data Handling offer comprehensive answers to textbook questions.

## DAV Class 7 Maths Ch 12 WS 3 Solutions

Question 1.

Find the mode of the following observations:

(z) 25, 14, 28, 17, 18, 14, 25, 14, 17, 14

(ii) 0, 6, 1, 5, 6, 2, 0, 4, 6, 3, 4, 6, 3, 1

Answer:

(i) The given observations are

25, 14, 28, 17, 18, 14, 25, 14, 17, 14

Here the observation 14 repeats 4 times

∴ Modal observation = 14

(ii) The given observations are

0, 6,1, 5, 6, 2, 0, 4, 6, 3, 4, 6, 3,1

Here the observation 6 comes 4 times

∴ Modal observation is 6.

Question 2.

The following table shows the weight of 15 students. Find the mode.

Weight (in kg) | Number of students |

46 | 3 |

51 | 1 |

53 | 5 |

56 | 2 |

60 | 4 |

Answer:

The frequency of 53 kg is more i.e. 5

Mode is 53 kg.

Question 3.

The following table shows sale of shirts having different sizes from a certain shop in a month. Find the mode.

Answer:

Number of shirts of size 39 is 31, which is maximum frequency.

Hence the Mode is 39.

Question 4.

In January 2015, the number of children in 10 families of a locality are:

4, 3, 4, 0, 2, 2, 5, 2, 1, 3 Find the mean, median and mode.

At the end of the year, two families having children 0 and 1 vacated the house. As a result, two more families having children 2 and 5 got the vacant accommodation. Find the new mean, median and mode.

Answer:

The given observations are 4, 3, 4, 0, 2, 2, 5, 2, 1, 3

Mean = \(\frac{\text { Sum of the observations }}{\text { Number of observations }}\)

= \(\frac{4+3+4+0+2+2+5+2+1+3}{10}=\frac{26}{10}\)

= 2.6

Hence mean = 2.6

Arranging the observations in the increasing order,

0, 1, 2, 2, 2, 3, 3, 4, 4, 5

Number of observations = 10 (even)

Median = \(\frac{\frac{10^{\text {th }}}{2} \text { observation }+\left(\frac{10}{2}+1\right)^{\text {th }} \text { observation }}{2}\)

= \(\frac{5^{\text {th }} \text { observation }+6^{\text {th }} \text { observation }}{2}=\frac{2+3}{2}\)

= 2.5

Hence Median = 2.5

Mode: In the given observations 0,1, 2, 2, 2, 3, 3, 4, 4, 5

2 occurs 3 times the most. Therefore mode = 2

Now in the end of the year, the two observations 0 and 1 have been replaced by 2 and 5 respectively.

∴ New observations are 2, 5, 2, 2, 2, 3, 3,4, 4, 5

New Mean = \(\frac{2+5+2+2+2+3+3+4+4+5}{10}=\frac{32}{10}\) = 3.2

New Median: Arranging the new observations in increasing order, 2, 2, 2, 2, 3, 3, 4, 4, 5, 5

Number of observation is 10(even)

New Median = \(\frac{\frac{10^{\text {th }}}{2} \text { observation }+\left(\frac{10}{2}+1\right)^{\text {th }} \text { observation }}{2}\)

= \(\frac{5^{\text {th }} \text { observation }+6^{\text {th }} \text { observation }}{2}=\frac{3+3}{2}\) = 3

New Mode : Given observations are 2, 2, 2, 2, 3, 3, 4, 4, 5, 5

Here 2 repeats 4 times, the most

∴ Mode = 2.