Question

The mean of 13 observations is 14. If the mean of the first 7 observations is 12 and that of the last 7 observations is16.Find the 7th observation

Answer 1

Answer:

7th observation is 14 .

Step-by-step explanation:

We are given that the mean of 13 observations is 14 and also the mean of first 7 observations is 12 and that of the last 7 observations is 16.

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

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

              n = Number of observation

So, Total Sum of n observation ($\sum X$) = Mean (X bar) * Number of observation (n)

So, Total Sum of all 13 observations = 14 * 13 = 182

Total Sum of first 7 observations = 12 * 7 = 84

Total Sum of last 7 observations = 16 * 7 = 112  

Note: Total Sum of first 7 observations + Total Sum of last 7 observations = Total Sum of all 13 observations + 7th observation in data

So,  112 + 84 = 182 + 7th observation

Therefore, 7th observation = 196 - 182 = 14 .