Question

If the mean of 2, 9, x + 6, 2x + 3, 5, 10, 5 is 7, then the value of x is ______.

Options

• 9

• 6

• 5

• 3

Answer 1

If the mean of 2, 9, x + 6, 2x + 3, 5, 10, 5 is 7, then the value of x is 3.

Explanation:

The formula for the mean of a set of numbers is:

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

We are given the numbers:
2, 9, (x + 6), (2x + 3), 5, 10, 5
The mean is given as 7.

${\displaystyle \frac{2+9+(x+6)+(2x+3)+5+10+5}{7}=7}$

Sum of all terms:

= 2 + 9 + x + 6 + 2x + 3 + 5 + 10 + 5

= (2 + 9 + 6 + 3 + 5 + 10 + 5) + (x + 2x)

= 40 + 3x

Now, using the mean formula:

${\displaystyle \frac{40+3x}{7}}$

= 7

Multiply both sides by 7:

40 + 3x = 49

Subtract 40 from both sides:

3x = 9

x = ${\displaystyle \frac{9}{3}}$

x = 3