An incomplete distribution is given below: Variable: 10 - 20, 20 - 30, 30 - 40, 40 - 50, 50 - 60, 60 - 70, 70 - 80

Question

An incomplete distribution is given below:

You are given that the median value is 46 and the total number of items is 230. 

(i) Using the median formula fill up missing frequencies. 

(ii) Calculate the AM of the completed distribution.

Answer 1

Given, 

Median = 46

Then, median class = 40-50 

Therefore, 

l = 40, h = 10, f = 65, F = 42 + x

Median = l + \(\frac{\frac{N}{2}-F}{f}\)

\(46=40+\frac{115-(42+x)}{65}\times 10\)

\(\frac{6\times65}{10}=73-\times\)

39 = 73 – x 

x = 73 – 39 

x = 34 

Given, 

N = 230 

= 12 + 30 + 34 + 65 + y + 25 + 18 = 230 

= 184 + y = 230

= y = 230 – 184 = 46

Mean = \(\frac{\sum fx}{N}\)

\(=\frac{10550}{230}=45.87\)