Question

If the mean of first 10 observations is 15 and the mean of first 15 observations is 10. Find the mean of all observations

Answer 1

Given:

The mean of first 10 observations = 15

The mean of another 15 observations = 10

To find:

The mean of all observations

Solution:

The formula to find the mean of the observations is given as follows:

$\boxed{Mean\:=\:\frac{Sum\:of\:observations}{No.\:of\:observations} }$

For the first 10 observations

Using the formula, we get

15 = $\frac{Sum\:of\:10\:observations}{10}$

⇒ Sum of first 10 observations = 15 × 10

⇒ Sum of first 10 observations = 150

For the 15 observations

Using the formula, we get

10 = $\frac{Sum\:of\:15\:observations}{15}$

⇒ Sum of another 15 observations = 10 × 15

⇒ Sum of another 15 observations = 150

Now,

The sum of all (15 + 10 =) 25 observations will be,

= [Sum of first 10 observations] + [Sum of another 15 observations ]

= 150 + 150

= 300

∴ Mean of all 25 observations = $\frac{Sum\:of\:25\:observations}{No.\:of\: observations} = \frac{300}{25}$ = 12

Thus, the mean of all observations is 12.

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