10 is the mean of a set of 7 observations and 5 is the mean of another set of 3 observations. The mean of the combined set is:

Correct option is A

Given:

The mean of the first set of 7 observations is 10.

The mean of the second set of 3 observations is 5.

Formula Used:

Mean of combined set =$$\frac{\text{Sum of all observations in the first set} + \text{Sum of all observations in the second set}}{\text{Total number of observations in both sets}}$$​

Solution:

Sum of the first set of 7 observations: Since the mean of the first set is 10 and there are 7 observations, the sum of the first set is:

Sum of first set = 10 × 7 = 70

Sum of the second set of 3 observations: Since the mean of the second set is 5 and there are 3 observations, the sum of the second set is:

Sum of second set = 5 × 3 = 15

Total sum of all observations: The total sum of all observations in both sets is:

Total sum = 70 + 15 = 85

Total number of observations = 7 + 3 = 10

Mean of combined set =$$\frac{85}{10} =$$​ 8.5