If the mean of the above distribution is 50, what is the value of f

Consider the following distribution:

If the mean of the above distribution is 50, what is the value of f?

  1. 24
  2. 34
  3. 56
  4. 96

Answer

Mean of grouped data = (Sum of (Interval midpoint × Frequency)) / (Sum of Frequency)

Mean = ∑(fx) / ∑f

Midpoint of interval = ½(Lower class limit + Upper class limit)

Midpoints of intervals are 10, 30, 50, 70 and 90.

∑(fx) = 17×10 + 28×30 + 32×50 + 70f + 19×90

∑(fx) = 10(17 + 84 + 160 + 7f + 171) = 4320 + 70f

∑f = 17 + 28 + 32 + f + 19 = 96 + f

Mean = 50 = (4320 + 70f)/(96 + f)

5(96 + f) = 432 + 7f

480 + 5f = 432 + 7f

2f = 48

f = 24

The correct option is A.