Question

The mean of 16 observations is 24.5. On checking, it was found that two observations were

wrongly copied as 3 and 6. If wrong observations are replaced by correct values 8 and 9, then

find the correct mean.

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Answer 1

Answer:

Correct Mean = 25

Step-by-step explanation:

We are given that the mean of 16 observations is 24.5 . Also, on checking, it was found that two observations were  wrongly copied as 3 and 6.

Firstly, Mean formula is given by, X bar = $\frac{\sum X}{n}$

where, n = number of observations in data

          $\sum X$ = Sum of all values in the data

So, Original Mean = $\frac{\sum X}{n}$

Incorrect $\sum X$ = 24.5 * 16 = 392

Now, it is given that wrong observations are replaced by correct values 8 and 9;

So, Correct  $\sum X$ = 392 - 3 - 6 + 8 + 9 = 400

     Correct n = 16 - 2 + 2 = 16

Therefore, Correct Mean = (Correct  $\sum X$) ÷ (Correct n)

                                          = 400 ÷ 16 = 25 .