Consider the following distribution.

Class Interval	0-20	20-40	40-60	60-80	80-100
Frequency	17	28	32	f	19

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

The class mark (midpoint) of each interval is the average of the lower and upper limits.

Class Interval	Class Mark (x)	Frequency (f)
0-20	10	17
20-40	30	28
40-60	50	32
60-80	70	f
80-100	90	19

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The mean formula for grouped data is:

Mean $= \dfrac{\Sigma(f \times x)}{\Sigma f}$

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Calculating $f \times x$ for each class:

Class Mark (x)	Frequency (f)	f × x
10	17	170
30	28	840
50	32	1,600
70	f	70f
90	19	1,710
Total	96 + f	4,320 + 70f

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Given that the mean is 50:

$50 = \dfrac{4,320 + 70f}{96 + f}$

$50(96 + f) = 4,320 + 70f$

$4,800 + 50f = 4,320 + 70f$

$4,800 - 4,320 = 70f - 50f$

$480 = 20f$

$f = 24$

Therefore, the value of $f = 24$.