The mean of x, x + 3, x + 5, x + 7, x + 10 is 9. What is the mean of the first 3 observations?

Correct option is B

Given:

The observations are (x), (x + 3), ( x + 5 ), ( x + 7 ), and ( x + 10 ).

The mean of these observations is 9.

Formula Used:
The mean of a set of observations is given by:

​$$\text{Mean} = \frac{\text{Sum of observations}}{\text{Number of observations}}$$​​

Solution:
The sum of the observations is:

x + (x + 3) + (x + 5) + (x + 7) + (x + 10) = 5x + 25

Using the formula for the mean:

​$$\frac{5x + 25}{5} = 9$$​​

Simplifying this equation:

5x + 25 = 45

5x = 20

x = 4

Now, the first three observations are x , x + 3 , and x + 5.

Substituting x = 4 :

4, 4 + 3 = 7, 4 + 5 = 9

The mean of these three observations is:

​$$\frac{4 + 7 + 9}{3} = \frac{20}{3} = 6.67$$​​