A measure of central tendency that determines the centrally positioned worth of a given collection is named the Median. The variety of values of the collection under and above the given collection is at all times equal. To find out the median worth of a given collection, it’s first managed in rising or lowering order, then the worth within the center is taken because the central worth or median of the collection. For instance, to find out the Median of the collection 2, 20, 14, 18, 4, 11, 15, it will likely be first written in ascending order, i.e., 2, 4, 11, 14, 15, 18, 20. Now the center worth of this collection is the quantity at 4th place, i.e., 14. Subsequently, the median of the given collection is 14. The Median is denoted by M.
In accordance with Connor, “The Median is that worth of the variable which divides the group into two equal components, one half comprising all values higher than the median worth and the opposite half comprising all of the values smaller than the median worth.”
Graphic Willpower of Median
The median of a given collection will also be calculated by means of its graphical illustration within the type of lower than or greater than ogive. By ogives, the median may be decided in two methods:
1. Presenting the information of given collection on a graph within the type of lower than ogive or greater than ogive.
2. Presenting the information of given collection on a graph, concurrently within the type of each lower than ogive and greater than ogive. The purpose the place these two ogives meet is the median worth of the given collection.
1. Lower than Ogive or Greater than Ogive Method
In accordance with the ‘Lower than’ or ‘Greater than’ Ogive Method, to find out the median of a given collection, it’s, to begin with, transformed into both lower than or greater than cumulative collection. After that, the cumulative collection are introduced graphically for the presentation of lower than or greater than ogive. Within the subsequent step, the N/2th time period of the collection is set. From the N/2th time period on the graph’s Y-axis, a perpendicular to the proper is drawn. This perpendicular cuts the cumulative frequency curve giving the median worth of the collection.
For instance,
Decide median worth of the next collection with the assistance of each Lower than Ogive Method and Greater than Ogive Method:
Class Measurement 0-10
10-20
20-30
30-40
40-50
50-60
60-70
70-80
Frequency 4
6
5
10
20
18
27
10
Resolution:
Utilizing Much less Than Ogive Method
Class Measurement Frequency Cumulative Frequency Lower than 10
4
4
Lower than 20
6
10
Lower than 30
5
15
Lower than 40
10
25
Lower than 50
20
45
Lower than 60
18
63
Lower than 70
27
90
Lower than 80
10
100
N/2th time period = 100/2 = 50
Now, mark 50 on the Y-axis of graph and make a perpendicular from this level to the proper to chop the ogive at level A.
From level A, draw a perpendicular on X-axis. The purpose on X-axis at which the perpendicular cuts, is the median worth.
The perpendicular from level A cuts the X-axis at level 52.7 .
Subsequently, the Median (M) = 52.7
Utilizing Extra Than Ogive Method
Class Measurement Frequency Cumulative Frequency Greater than 0
4
100
Greater than 10
6
96
Greater than 20
5
90
Greater than 30
10
85
Greater than 40
20
75
Greater than 50
18
55
Greater than 60
27
37
Greater than 70
10
10
N/2th time period = 100/2 = 50
Now, mark 50 on the Y-axis of graph and make a perpendicular from this level to the proper to chop the ogive at level A.
From level A, draw a perpendicular on X-axis. The purpose on X-axis at which the perpendicular cuts, is the median worth.
The perpendicular from level A cuts the X-axis at level 52.7 .
Subsequently, the Median (M) = 52.7
2. Lower than Ogive and Greater than Ogive Method
In accordance with the ‘Lower than’ and ‘Greater than’ Ogive Method, to find out the median of a given collection, each lower than and greater than, ogives are introduced on a graph concurrently. The perpendicular on the X-axis drawn from the purpose at which each the ogive curves lower one another, is the median worth of the given collection.
For instance,
Decide the median worth of the next collection utilizing the Lower than and Greater than Ogive Method:
Marks 0-5
5-10
10-15
15-20
20-25
25-30
30-35
No. of College students 3
10
15
7
4
6
5
Resolution:
Class Measurement (Lower than) Cumulative Frequency Class Measurement (Greater than) Cumulative Frequency Lower than 5
3
Greater than 0
50
Lower than 10
13
Greater than 5
47
Lower than 15
28
Greater than 10
37
Lower than 20
35
Greater than 15
22
Lower than 25
39
Greater than 20
15
Lower than 30
45
Greater than 25
11
Lower than 35
50
Greater than 30
5
The lower than and greater than ogive cuts one another at level B, and the purpose at which the perpendicular drawn on X-axis from level B is the median worth of the given collection.
Subsequently, the Median (M) = 14
