Question

(7) The mean of 10 observations is calculated as 22.7. It
was later noticed that one observation was taken as
15 instead of 51 by mistake. Then, the correct mean of
the data is....... .
A 25.3 B. 26.3 C. 25 D. 26​

Answer 1

Answer:

Correct Mean = 26.3

Step-by-step explanation:

We are given that the mean of 10 observations is calculated as 22.7. It  was later noticed that one observation was taken as  15 instead of 51 by mistake.

Mean of the data = $\frac{\sum X}{n}$ , where $\sum X$ = Total sum of all values in the data

                                                        n = Total no. of observations in data

               22.7  =  $\frac{\sum X}{10}$

So, Incorrect $\sum X$ = 22.7 * 10 = 227

Now, it is given that one observation was taken as  15 instead of 51 by mistake ;

Correct  $\sum X$ = 227 - Incorrect value + Correct value

                      = 227 - 15 + 51 = 263

Correct n = 10 - 1 + 1 = 10

Therefore, Correct Mean = $\frac{Correct \sum X}{ n}$ = 263/10 = 26.3 .