Question

Question 6
10 is the mean of 6 observations. 20 is the mean of 4 observations. The mean of a combined set is given by

Answer 1

Answer:

14

Step-by-step explanation:

10*6=60 20*4=80

mean of combined = 60+80/10=14

Answer 2

The mean of the combined set is equal to 14.

Given,

10 is the mean of 6 observations. 20 is the mean of 4 observations.

To Find,

The mean of a combined set is given by?

Solution,

We can solve the question as follows:
The mean of 6 observations is 10 and the mean of 4 observations is 20. We have to find the mean of the combined set.

$Mean\: of\: 6\: observations =10\\Mean\: of\: 4\: observations =20$

The formula for finding the mean of a set of observations is:

$Mean = \frac{Sum\: of\: all\: observations}{Total\: no.\: of\: observations}$

Now, we will find the sum of all observations in both cases.

In the first case,

$10 = \frac{Sum\: of\: observations}{6}$

$Sum\: of\: observations = 10*6 = 60$

In the second case,

$20 = \frac{Sum\: of\: observations}{4}$

$Sum\: of\: observations = 20*4 = 80$

Now, the mean of the combined set will be equal to the sum of observations of both the cases divided by the total observations in both the cases.

$Total\: sum\: of\: observations = 80 + 60 = 140$

$Total\: observations = 6 + 4 = 10$

The mean will be:

$Mean = \frac{140}{10}= 14$

Hence, the mean is equal to 14.