Question

If the mean of 25 observations is 27 and each observation is decreased by 7, what will be the new mean?

Answer 1

​Mean of given observations = $\frac{\mathrm{Sum}\mathrm{of}\mathrm{given}\mathrm{observations}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{observations}}$

Mean of 25 observations = 27

∴ Sum of 25 observations = 27 × 25 = 675

If 7 is subtracted from every number, then the sum = 675 − (25 × 7)
= 675 − 175
= 500

Then, new mean = $\frac{500}{25}=20$

Thus, the new mean will be 20.