Consider the following distribution.

f the mean of the above distribution is 50, find the value of f.

24

The correct answer is Option (4) → 24

To find the value of $f$, we use the formula for the mean of a frequency distribution:

$\text{Mean } (\bar{x}) = \frac{\sum f_i x_i}{\sum f_i}$

where $f_i$ is the frequency and $x_i$ is the class mark (midpoint) of each interval.

Step 1: Identify Class Marks ($x_i$) and $f_i x_i$

Assuming the distribution follows a uniform pattern of class width 20 (as seen in the later intervals), the first interval is likely 0-20. Let's calculate the midpoints based on this pattern:

Step 2: Use the Mean to find $f$

The given mean is 50.

$50 = \frac{4320 + 70f}{96 + f}$

Multiply both sides by $(96 + f)$:

$50(96 + f) = 4320 + 70f$

$4800 + 50f = 4320 + 70f$

Rearrange the terms to solve for $f$:

$4800 - 4320 = 70f - 50f$

$480 = 20f$

$f = \frac{480}{20} = 24$