Median
Median
The median is a variate value which divides the given data into two equal parts. If the data are arranged either in ascending or descending order, the middlemost number is median.
For example,
1, 3, 8, \(\underline{10}\), 13, 16, 20
The middle number 10 is median.
Calculation of median for individual series:
The formula for calculating median for individual series is given by;
Median (Md) = Position of \((\frac{N + 1}{2})\)^{th} item
where, N = No. of observation or items.
The steps for calculation of median for individual series:
 Arrange the data in ascending or descending order.
 Count the number of terms (n).
Median for a discrete data:
Let, x_{1}, x_{2}, x_{3..................}x_{n} be the variable values and f_{1}, f_{2}, f_{3},............ f_{n} be their corresponding frequency respectively.
Then, Median (Md) = Position of \((\frac{N + 1}{2})\)^{th} item
where, N = total sum of a frequency
Median for a continuous data:
To calculate the median for a continuous data, the following steps are applied:
 Prepare cumulative frequency table
 Find the value of \((\frac{N}{2})\)^{th} items which gives the median class.
 Use the formula, Median = l + \(\frac{\frac{N}{2}− c.f}{f}\) × i
where,
l = lower limit of median class
c.f = cumulative frequency
f = frequency
i = class interval
 Calculation of median for individual series = Position of \((\frac{N + 1}{2})\)^{th} item
 Median for a discrete data = Position of \((\frac{N + 1}{2})\)^{th} item
 Median for a continuous data = L + \(\frac{\frac{N}{2}− c.f}{F}\) × i

In the data set below, what is the median?
1, 2. 4, 4, 5, 6, 6, 6 , 7, 7, 8
5
6
4
7

In the data set below, what is the median?
2, 2, 2, 2, 3 , 5, 5, 5, 7, 8, 9, 97
5
8
3

In the data set below, what is the median?
19 37 41 43 83 85 94
41
43
37
83

In the data set below, what is the median?
2, 4, 5, 6, 6, 7, 8, 8, 8, 9
8
6
7
5

Find the median.
64, 60, 70, 72, 68, 80, 85, 56
41
75
69
68

Find the median.
47, 61, 13, 34, 56, 22, 8
34
56
54
45

Find the median.
8, 1, 3, 3, 1, 7, 4, 1, 4, 4
45
8
32
3.5

x1, 2x+1, x+5 and 3x+1are ascending order. If its median is18, find the value of x.
12
1
45
3

12, 17, 2x+3, 3x+5, 36, 43 are in ascending order. If its median is 29, find the value of x.
20
10
15
12

6, 8, 10, 12, 2x, 2x+2, 18, 20, 22, 24 are in ascending order. If its median is 15, find the value of x.
7
12
8
5

Find median. 12, 1, 10, 1, 9, 3, 4, 9, 7, 9
2
5
1
8

Find median.
85, 77, 60, 89, 91, 89, 78
85
45
60
47

What is value of x if its median is 12. x+1, 2x1, x+7 and 3x+4
4
6
2
13

Find median. 15, 10, 11, 9, 14
15
11
12
20

Find median. 14, 16, 12, 6, 8,10
12
4
15
11

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