Find the missing frequency of the following incomplete frequency distribution if the median is 46 and find the mean of the complete distribution.

Given Median =46

Then, median Class = 40 – 50

the lower limit (l) = 40

cumulative frequency of the class preceding 40 – 50 (cf) = 42 + x

frequency of the median class 40 – 50 = 65,

class size (h) = 10

Total frequencies (n) = 229

So, 150 + x + y = 229

⇒ x + y = 229 – 150

⇒ x + y = 79 …(i)

Using the formula,,we have

⇒39 = 72.5 – x

⇒ x = 33.5

Putting the value of x in eq. (i), we get

⇒ 33.5 + y = 79

⇒ y = 79 – 33.5

⇒ y = 45.5