Question

The mean of 100 observations is 50 if observation 50 is replaced by 150 find the resulting mean

Answer 1

New Mean = 51

Step-by-step explanation:

We are given that the mean of 100 observations is 50.

Firstly, Mean = Sum of all values ÷ Total number of observations

      or    Mean, $\bar X$ = $\frac{\sum X}{n}$

So, According to our question;

      Mean of 100 obs. = Sum of all 100 obs. ÷ 100

                   50             = $\frac{\sum X}{100}$

So, Sum of all 100 obs., $\sum X$ = $50 \times 100$ = 5000

Now, as we are given that observation 50 is replaced by 150, which means;

New Sum of all 100 obs., $\sum X$ = 5000 - 50 + 150 = 5100

Total no. of observations, n = 100 - 1 + 1 = 100

Therefore, New resulting mean = $\frac{New \sum X}{n}$ = $\frac{5100}{100}$

                                                       = 51.

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