Median
The median is the middle value in a set of
quantities. It separates an ordered set of data
into two equal parts. Half of the quantities
found above the median and the other half is
found below it.
In finding the median of grouped data, we use the formula:
where 𝑥̃ = median
𝑋𝑙𝑏 = the lower boundary of true lower limit of the median class
N = total frequency
𝑐𝑓𝑏 = cumulative frequency before the median class
𝑓𝑚 = frequency of the median class
𝑖 = size of the class interval
To compute the median (𝑥̃) of grouped data, we proceed as follows:
1. Compute the cumulative frequencies by adding the
frequencies to the cumulative frequencies.
2. Determine one-half of the total number of cases:N/2.
3. Get the cf of the class immediate below the median class.
4. Determine the frequency (fm) of the median class.
5. Find the class interval in which the median class falls and
determine the exact lower limit of this interval.
6. Apply the formula by substituting the given values.
Class
Interval
47 - 52
41 – 46
35 – 40
29 – 34
23 - 28
17 – 22
11 – 16
5 – 10
i = 6
True
Limits
Frequency
<cf
46.6 – 52.5
40.5 – 46.5
34.5 – 40.5
28.5 – 34.5
22.5 – 28.5
16.5 – 22.5
10.5 – 16.5
4.5 – 10.5
1
0
4
2
9
9
4
1
N = 30
30
29
29
25
23
14
5
1
N =
N/2 =
cf b =
fm =
i
=
Xlb =
Use the formula in finding the mean
The ages of the residents along Fortaliza street in Hingatungan,
Silago, Southern Leyte is given below. Find the median age.
Ages
63 - 69
56 – 62
49 – 55
42 – 48
35 – 41
28 – 34
21 – 27
14 – 20
7 – 13
Frequency
3
11
18
26
21
15
12
7
2
Assignment
Direction: Using 10 as the size of class interval, make a frequency
distribution of the scores obtained by 50 students in a college entrance
test. Find the Median.
80
90
100
70
90
110
80
100
120
80
100
100 100
60
80
80
100
100
120
80
90
90
90
70
80
70
100
100
120
100