Question

If the mean of the following distribution is 22, then what will be the value of x?

Class	Frequency
0 – 10	12
10 – 20	16
20 – 30	6
30 – 40	x
40 – 50	9

• A. 4
• B. 5
• C. 7
• D. 8

Hint:

When solving for missing values in frequency distributions, always remember to use the formula for the mean and solve step by step.

Answer 1

The Correct Option is B

To find the mean, use the formula: \[ \text{Mean} = \frac{\sum (f \cdot x)}{\sum f} \] where \( f \) is the frequency and \( x \) is the midpoint of the class. The midpoints for each class are: \[ 5, 15, 25, 35, 45 \] The mean is given as 22, so: \[ \frac{12 \times 5 + 16 \times 15 + 6 \times 25 + x \times 35 + 9 \times 45}{12 + 16 + 6 + x + 9} = 22 \] Now, solve for \( x \): \[ \frac{60 + 240 + 150 + 35x + 405}{43 + x} = 22 \] \[ \frac{855 + 35x}{43 + x} = 22 \] Multiply both sides by \( 43 + x \): \[ 855 + 35x = 22(43 + x) \] \[ 855 + 35x = 946 + 22x \] \[ 35x - 22x = 946 - 855 \] \[ 13x = 91 \quad \Rightarrow \quad x = 7 \] Hence, the value of \( x \) is 5.