Question

The mean of 25 observations is 36. If the mean of the first 13 observations is 32 and that of the last 13 observations is 39, find the 13th observation.

Answer 1

Answer:

sum of first 13 observation = 32×13= 416

sum of last 13 observation = 39×13= 507

13th observation = 507 - 416= 91

Answer 2

13th observation is 23.

Step-by-step explanation:

We are given that the mean of 25 observations is 36 and also the mean of first 13 observations is 32 and that of the last 13 observations is 39.

As we know that Mean formula, $\bar X$ = $\frac{\sum X}{n}$

where, $\sum X$ = Total Sum of n observation

                 n = Number of observation

So, Total Sum of n observation ($\sum X$) = $\text{Mean} (\bar X) \times \text{Number of observation} (n)$

So, Total Sum of all 25 observations = $36 \times 25 = 900$

Total Sum of first 13 observations = $32 \times 13=416$

Total Sum of last 13 observations = $39 \times 13=507$

Note: Total Sum of first 13 observations + Total Sum of last 13 observations = Total Sum of all 25 observations + 13th observation in data

So,  416 + 507 = 900 + 13th observation

Therefore, 13th observation = 923 - 900 = 23 .