Question

The mean of 17 observations is 20. If the mean of the first 9 observation is 23 and that of last 9 observations is 18, find the 9th observation.

Answer 1

9th observation is 29.

Step-by-step explanation:

We are given that the mean of 17 observations is 20 and also the mean of first 9 observations is 23 and that of the last 9 observations is 18.

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 17 observations = $20 \times 17 = 340$

Total Sum of first 9 observations = $23 \times 9=207$

Total Sum of last 9 observations = $18 \times 9=162$

Note: Total Sum of first 9 observations + Total Sum of last 9 observations = Total Sum of all 17 observations + 9th observation in data

So,  207 + 162 = 340 + 9th observation

Therefore, 9th observation = 369 - 340 = 29 .