Question

Fill In the Blanks

The mean of a set of 12 observations is 10 and another set of 8 observations is 12. The mean of all 20 observations is _______.

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 a set of 12 observations = 10 (Given)

∴ Sum of a set of 12 observations = 10 × 12 = 120 .....(1)

Mean of another set of 8 observations = 12 (Given)

∴ Sum of another set of 8 observations = 12 × 8 = 96 .....(2)

Now,

Sum of all 20 observations

= Sum of a set of 12 observations + Sum of another set of 8 observations

= 120 + 96 [From (1) and (2)]

= 216

∴ Mean of all 20 observations = $\frac{\mathrm{Sum}\mathrm{of}\mathrm{all}20\mathrm{observations}}{20}=\frac{216}{20}$ = 10.8

Thus, the mean of all 20 observations is 10.8.

The mean of a set of 12 observations is 10 and another set of 8 observations is 12. The mean of all 20 observations is ___10.8___.