Well-designed AP Board Solutions Class 7 Maths Chapter 3 Data Handling Exercise 3.2 offers step-by-step explanations to help students understand problem-solving strategies.

## Data Handling Class 7 Exercise 3.2 Solutions – 7th Class Maths 3.2 Exercise Solutions

Question 1.

The scores in mathematics test (out of 25) of 15 students is as follows :

19,25,23,20,9,20,15,10,5,16,25 20,24,12,20

Find the mode and median of this data. Are they same?

Solution:

Given scores in mathematics test (out of 25) of 15 students is as follows : 19,25,23,20,9,20,15,10,5,16,25,20,24,12,20

Ascending order of the above is 5,9,10,12,15,16,19,20,20,20,20,23,24,25,25

Number of observations = 15

Median = \(\frac{15+1}{2}\)th observation = 8th observation = 20

Most repeated value = 20

∴ Mode = 20

∴ Here median and mode are same.

Question 2.

The runs scored in a cricket match by 11 players is as follows : 6,15,120,50,100,80,10,15,8,10,15 Find the mean, mode and median of this data. Are the three same ?

Solution:

The runs scored by 11 players in a cricket match is as follows: 6,15,120,50,100,80,10,15,8,10,15

Ascending order of the above is 6,8,10,10,15,15,15,50,80,100,120

Mean = \(\frac{6+8+10+10+15+15+15+50+80+100+120}{11}\) = \(\frac{429}{11}\) = 39.

Most repeated value = 15

∴ Mode = 15

Number of items in the data = 11.

∴ Median = \(\frac{11+1}{2}\)th observation

= \(\frac{12}{2}\) = 6th observation

Mean, median and mode are not same.

Question 3.

The weights (in kg.) of 15 students of a class are : 38,42,35,37,45,50,32,43,43,40,36,38,43,38,47

i) Find the mode and median of this data.

ii) Is there more than one mode?

Solution:

The weights (in kg) of 15 students of a class are : 38,42,35,37,45,50,32,43,43,40,36,38,43,38,47.

Ascending order of the given number is 32,35,36,37,38,38,38,40,42,43,43,43,45,47,50.

i) Most repeated values = 38 and 43

Mode = 38 and 43

Number of items = 15

Median = \(\frac{15+1}{2}\)th observation

= \(\frac{16}{2}\) = 8th observation = 40

ii) Yes, there are two modes for the given data.

Question 4.

Find the mode and median of the data:

13,16,12,14,19,12,14,13,14

Solution:

Given data is

13,16,12,14,19,12,14,13,14

Ascending order is

12,12,13,13,14,14,14,16,19

Most repeated value = 14

Mode = 14.

Number of items = 9

Median = \(\frac{9+1}{2}\)th observation

= \(\frac{10}{2}\) = 5th observation

∴ Median = 14

Question 5.

Tell whether the statement is true or false :

i) The mode is always one of the numbers in a data.

ii) The mean is one of the numbers in a data.

iii) The median is always one of the numbers in a data.

iv) The data 6,4,3,8,9,12,13,9 has mean 9.

Solution:

i) True

ii) False

iii) False

If there are odd number of observation, then median is one of the number of the data.

If there are even number of observation, then the average of middle number is the median of the data.

iv) False

Given data 6,4,3,8,9,12,13,9.

Mean = \(\frac{6+4+3+8+9+12+13+9}{8}\) = \(\frac{64}{8}\) = 8.

Given mean = 9