The mean of 25 observations is 36. Out of these observations if the mean of first 13 observations is 32 and that of the last 13 observations is 40, the 13th observation is :
a. 23
b. 36
c. 38
d. 40

Solution:

It is given that

Mean of 25 observations = 36

Sum of 25 observations = 36 × 25 = 900

Mean of first 13 observations = 32

Sum of first 13 observations = 13 × 32 = 416

Mean of last 13 observations = 40

Sum of last 13 observations = 40 × 13 = 520

We know that

13th observation = [Sum of last 13 observations + Sum of first 13 observations] - Sum of 25 observations

Substituting the values

= 520 + 416 - 900

= 936 - 900

= 36

Therefore, the 13th observation is 36.

✦ Try This: The mean of 50 observations is 26. Out of these observations if the mean of first 12 observations is 23 and that of the last 12 observations is 30, the 12th observation is :

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 14

NCERT Exemplar Class 9 Maths Exercise 14.1 Problem 20

The mean of 25 observations is 36. Out of these observations if the mean of first 13 observations is 32 and that of the last 13 observations is 40, the 13th observation is : a. 23, b. 36, c. 38, d. 40

Summary:

The mean of 25 observations is 36. Out of these observations if the mean of first 13 observations is 32 and that of the last 13 observations is 40, the 13th observation is 36

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