Question

The mean of 100 observations is 50. If one of the observations which was 50 is replaced by 150, the resulting will be

(a) 50.5
(b) 51
(c) 51.5
(d) 52

Answer 1

We know

Mean = $\frac{\mathrm{Sum}\mathrm{of}\mathrm{observations}}{\mathrm{Number}\mathrm{of}\mathrm{observations}}$

⇒ Sum of observations = Mean × Number of observations

Mean of 100 observations = 50 (Given)

∴ Sum of 100 observations = 50 × 100 = 5000

If one of the observations which was 50 is replaced by 150, then

New sum of 100 observations = Sum of 100 observations − 50 + 150

⇒ New sum of 100 observations = 5000 − 50 + 150 = 5100

∴ New mean of 100 observations = $\frac{\mathrm{New}\mathrm{sum}\mathrm{of}100\mathrm{observations}}{100}=\frac{5100}{100}=51$

Thus, the new mean of 100 observations is 51.

Hence, the correct answer is option (b).