FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 5.25= 20 + 30 20 6 − (10–9)
= 20 +^106 = 20 + 1.67 = 21.67
5.1.5.2. Calculation of Median from Discrete Grouped Distribution
If the class intervals of grouped frequency distribution are in discrete form, at first they are to be converted
into class-boundaries and hence to find median by applying usual formula. The idea will be clear from the
following example.
Example 30 : Marks obtained by 62 students in English are as follows:––
Marks No. of students
10–19 5
20–29 8
30–39 14
40–49 20
50–59 11
60–69 4
Total 62Compute median class and median.
Solution :
The class intervals are in discrete form. They are to be converted to class boundaries first, which is shown below :
Table : Calculation of Median
Class boundaries frequecy Cumulative Frequency
9.5 – 19.5 5 5
19.5–29.5 8 13
29.5–39.5 14 27
39.5–49.5 20 47
49.5–59.5 11 58
59.5–69.5 4 62 (N)
Median = value of
Nth
2 term = values of
62 th
2 term or value of 31st term
∴ Median lies in (39.5 – 49.5)
Now median = (^12) m^1
l l l
f
- −
(m – c), here l 1 = 39.5, l 2 = 49.5, fm = 20, m = 31, c = 27
Median = 39.5 +^1020 (31 – 27) = 39.5 +^12 × 4 = 39. 5 + 2 = 41.5 marks.