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
Median = T n + 1 2 = T 6 + 1 2 = T 3 1 2 = 18 + 20 2 = 19
(b) 6, 9, 11, 13, 17
Median = T n + 1 2 = T 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:
Median = T n + 1 2 = T 40 + 1 2 = T 20 1 2 = 60 ( 20 1 2 th term is 60)


(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










S t e p   1 Median class is given by  T n 2 =   T 100 2 = T 50  Median class is the class  20 24 S t e p   2 m = L + ( N 2 F f m ) c m = 19.5 + ( 100 2 33 26 ) 5 m = 19.5 + 3.269 = 22.77

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