**Data Handling Class 7 Ex. 3.2;**

**New Ncert Solution for Class 7 Maths Chapter 3 Data Handling Free Solution;**

**Exercise 3.2**

**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 1:-**

Given scores-data:

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

Taking arrangement of the given data in increasing order

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

The-mode (a set of observations), is the observation that occurs, most-often.

Since, 20 occurs 4-times (highest)

So, Mode = 20

n = 15 (odd) [ where, n = number of observation.]

the median, gives us the middle observation.

∴ Median = (n+1)/2 th term = (15+1)/2 = 8th term = 20

So, median = 20 and mode = 20

Finally, Mode and median are same as 20.

**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 2:-**

Given data:

6, 15, 120, 50, 100, 80, 10, 15, 8, 10, 15

Taking arrangment of the given data in increasing order, we get

6, 8, 10, 10, 15, 15, 15, 50, 80, 100, 120,

Here, 15 occurs 3 times (highest)

∴ Mode = 15

n = 11 (odd)

∴ Median = (11+1)/2 th term = 6th term = 15

Thus mean = 39, mode = 15 and median = 15

No, the mean, mode and median are not given the same data.

**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 3:-**

Given data: 38, 42, 35, 37, 45, 50, 32, 43, 43, 40, 36, 38, 43, 38, 47

Arranging in increasing order, we get

32, 35, 36, 37, 38, 38, 38, 40, 42, 43, 43, 43, 45, 47, 50,

(i) Here, 38 and 43 occur 3 times (highest)

Thus mode = 38 and 43

Since, n = 15(odd) [where, n = number of observation data.]

Median = (n+1)/2 th term =(15+1)/2 th term = 8th term = 40

Thus mode 38 and 43 and median = 40

(ii) Yes, the given data has two modes i.e. 38 and 43.

**Question 4 :- Find the mode and median of the data:**

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

**Solution 4:-**

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

Arranging the given data in increasing order, we get

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

Here, 14 occur 3 times (highest)

Thus, mode = 14

n = 9(odd) [where, n = number of observation.]

∴ Median = (n+1)/2 th term = (9+1)/2 th term = 5th term = 14

Hence, mode = 14 and median = 14.

**Question 5 :- Tell whether the statement is true or false.**

**(i) The mode is always one of the number 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 5:-**

(i) True

(ii) False

(iii) True

(iv) False.