2. Median
• The median is usually defined as that value which divides a distribution so that equal
number of items occur on either side of it.
• In other words 50 percent of the observations will be smaller than the median and
50 percent of the observations will be greater than the median.
1. Calculation of median in a series of individual observations:
• Arrange the data in the ascending or descending order
• Median is located by finding the size of the (n+1/2)th item.
𝑴 =
𝒏 + 𝟏
𝟐
𝒕𝒉 𝒊𝒕𝒆𝒎
M= Median
n= number of observations
Example 1. Find out the median from the data recorded on the number of clusters per
plant in a pulse crop: 10,18, 17, 19, 10, 15, 11, 17, 12
3. S. No. Data arranged in
ascending order
1 10
2 10
3 11
4 12
5 15
6 17
7 17
8 18
9 19
Median = Size of (n+1)/2 th item
= (9+1)2 th item
=5th item
Median = 15
2. Calculation of median in a discrete series
• Data should be arranged in ascending or
descending order of magnitude
• Find out the cumulative frequencies
• Median= size of the (n+1)/2 th item
• Find out the (n+1)/2 th item. It can be found by first
locating the cumulative frequency which is equal to
(n+1)/2 or the next higher to this and then
determine the value corresponding to it. This will
be the value of median.
4. Example 1. Find out the median of the following data
No. of angular seeded plants 12 8 17 10 11 16 18 14 6 7
No. of plants 39 33 42 40 47 42 60 50 22 25
No. of angular
seeded plants
No. of plants Cumulative
Frequency
6 22 22
7 25 47
8 33 80
10 40 120
11 47 167
12 39 206
14 50 256
16 42 298
17 42 340
18 60 400
Median = (400+1)/2 th item
=200.5th item
Median=12
5. 3. Calculation of median in a continuous series
• While computing the value of the median in a continuous series, first determine the
particular class in which the value of the median lies.
• Use n/2 as the rankof the median and not (n+1)/2
𝑴𝒆𝒅𝒊𝒂𝒏 = 𝑳 +
𝒏
𝟐 − 𝒄𝒇
𝒇
× 𝒊
L= lower limit of the median class
cf= cumulative frequency of the class preceding the median class
f=frequency of the median class
i= class interval
6. No. of grains per
earhead classes
Frequency Cumulative
frequency
5-10 2 2
10-15 27 29
15-20 52 81
20-25 118 199
25-30 57 256
30-35 27 283
35-40 13 296
40-45 4 300
Example 1. Calculate the value of the
median from the data recorded on the
number of grains per earhead on 300
wheat earhead.
Solution:
Median= Size of (n/2)th item= 300/2= 150
Median lies in the class=20-25
L=20; n/2= 150; cf=81; i=5; f=118
Median=20+(69/118)*5
=20+2.92
=22.92
7. 4. Calculation of median in unequal class-
intervals
• In unequal class-interval frequencies need not
be adjusted to make the class intervals equal
and the formula can be used here.
𝑴𝒆𝒅𝒊𝒂𝒏 = 𝑳 +
𝒏
𝟐
− 𝒄𝒇
𝒇
× 𝒊
n/2=70/2= 35
Median= 30+ ((35-21)/10)*10
= 30+(140/10)*10
=30+14
=44
Classes Frequency Cumulative
Frequency
0-10 5 5
10-30 16 21
30-60 30 51
60-80 12 63
80-90 6 69
90-100 1 70
Classes Frequency Cumulative Frequency
0-10 5 5
10-20 8 13
20-30 8 21
30-40 10 31
40-50 10 41
50-60 10 51
60-70 6 57
70-80 6 63
80-90 6 69
90-100 1 70
8. 5. Calculation of median in open-end classes
• Since the median is not affected by the values of extreme ends we are not concerned
with the extreme values for the calculation of median in open-end classes.
Size of item
classes
Frequency Cumulative
Frequency
Less than 10 4 4
10-20 8 12
20-30 14 26
30-40 6 32
40 and
above
4 36
Example 1. Calculate the median in
open –end series.
Solution:
𝑴𝒆𝒅𝒊𝒂𝒏 = 𝑳 +
𝒏
𝟐
− 𝒄𝒇
𝒇
× 𝒊
n/2= 36/2= 18th item
Median lies in the class 20-30
Median= 20+((18-12)/14)*10
=24.29
9. 6. Graphic Location of Median:
• Draw two ogives one by less than method and the other by more than method.
• From the point where the two curves intersect draw a perpendicular line to the X-
axis. The point on the X-axis will give the median value.
