# 7.1c Median

7.1c Median

1. The median of a group of data refers to the value which is at the
middle of the data after the data has been arranged according to
grouped data and ungrouped data.

(A) Ungrouped Data

Example 1:
Find the median for each of the sets of data given below.
(a) 15, 18, 21, 25, 20, 18
(b) 13, 6, 9, 17, 11

Solution:
(a) Arrange the data in the ascending order
15, 18, 18, 20, 21, 25
$\text{Median}={T}_{\frac{n+1}{2}}={T}_{\frac{6+1}{2}}={T}_{3\frac{1}{2}}=\frac{18+20}{2}=19$
(b) 6, 9, 11, 13, 17
$\text{Median}={T}_{\frac{n+1}{2}}={T}_{\frac{5+1}{2}}={T}_{3}=11$

(B) Grouped Data (without Class Interval)

Example 2:
The frequency table shows the marks obtained by 40 students in a
biology test.

 Marks 50 55 60 65 70 Number of students 6 8 15 10 1

Solution:

(C) Grouped Data (with Class Interval)

m = median
L = Lower boundary of median class
N = Number of data
F = Total frequency before median class
fm = Total frequency in median class
c = Class size = (Upper boundary – lower boundary)

1. The median can be determined from an accumulative frequency
table and the ogive.

2. The ogiveis an accumulative graph; the median, quartiles and the
range between quartilescan be determined from it.

Example 3:
The grouped frequency distribution was obtained from 100 students regarding the scores in their test shown as below.
 Scores Frequency 5 – 9 4 10 – 14 10 15 – 19 19 20 – 24 26 25 – 29 21 30 – 34 12 35 – 39 8
Find the median.

Solution:
Method 1: using formula

 Scores Frequency Cumulative Frequency 5 – 9 4 4 10 – 14 10 14 15 – 19 19 33 20 – 24 26 59 25 – 29 21 80 30 – 34 12 92 35 – 39 8 100