Paper 4: Fundamentals of Business Mathematics & Statistic

5.26 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Measures of Central Tendency and Measures of Dispersion

Calculation of median from cumulative frequency distribution

In this case at first cumulative frequency is to be converted into general group frequency distribution. Then

applying usual formula median is to be calculated.

Example 31 : Compute median from the table given below :

Marks No. of students(f)

less than 10 3

less than 20 8

less than 30 17

less than 40 20

less than 50 22

Solution : The general group frequency distribution is as follows : ––

Table : Calculation of Median

Marks Students(f) c.f

0–10 3 3

10–20 5(=8-3) 8

20–30 9 (=17-8) 17

30–40 3 (= 20-17) 20

40–50 2 (=22–20) 22 (N)

median = value of

Nth

2 term = value of

22 th

2 term = value of 11th term

∴median class is ( 20 – 30)

∴median = (^12) m^1
l l l
f

• −
  (m – c),
  20 10
  = + 9 (11 – 8), here l 1 = 20 l 2 = 30, fm = 9, m = 11, c = 8
  =^20 +^109 = 20 + 3.33 = 23.33 marks.
  Note : If the cumulative frequency distribution is given in ‘more than type’ form then also the same procedure
  is to be followed.
  Example 32 : Calculate the median of the frequency distributions
  Marks : 1–20 21–40 41–60 61–80 81–100
  No. of students : 3 5 9 3 2