The mean of a set of 6 observations is 10 and that of a set of 4 observations is 5. What will be the mean of the mixed sets ?

Correct option is B

Given:
Mean of first set of 6 observations = 10
Mean of second set of 4 observations = 5

Formula Used:

$$\text{Mean} = \frac{\text{Sum of observations}}{\text{Total number of observations}}$$

Solution:

For the first set (6 observations, mean = 10):

Sum = 6 $$\times$$​ 10 = 60

For the second set (4 observations, mean = 5):

Sum = 4 $$\times$$​ 5 = 20

Total sum of mixed sets = 60 + 20 = 80
Total number of observations = 6 + 4 = 10
​$$\text{Mean} = \frac{\text{Total sum of mixed sets}}{\text{Total number of observations}}$$​​

Mean = $$\frac{80}{10}$$​

Mean = 8

So, the mean of the mixed sets is 8.

Thus, the correct answer is (b).