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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.
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:
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
To calculate the median for a continuous data, the following steps are applied:
First, arrange the numbers from least to greatest. Remember that with negative numbers, larger numbers like -9 (if you ignore the minus sign) are less than smaller numbers.
-9 | -8 | -5 | -5 | -5 | -4 | -3 | 0 |
There is an even number of numbers, so there are two numbers in the middle.
-9 | -8 | -5 | -5 | -5 | -4 | -3 | 0 |
The median is the mean of the two middle numbers. Find the mean of -5 and -5.
First, arrange the numbers from least to greatest:
9.1 | 9.1 | 9.3 | 9.3 | 9.3 | 9.5 | 9.8 | ||||||
9.8 | 9.9 |
Now find the number in the middle.
9.1 | 9.1 | 9.3 | 9.3 | 9.3 | 9.5 | 9.8 | ||||||
9.8 | 9.9 |
The number in the middle is 9.3.
Hence, The median voltage was 9.3 volts.
Solution:
Here, Given data is 10 ,14, 16,. 20, 22, 25, 28
Numbers of terms(n) = 7
We have, Median =( \(\frac{n+1}{2}\))^{th }item
( \(\frac{7+1}{2}\))^{th }item
= (\(\frac{8}{2}\))^{th} item
= 4^{th} item
\(\therefore\) The median of the given data is 20.
Solution:
Arranging the data in ascending order
10, 12, 16, 20, 24, 28 , 30, 32
Number of terms(n) = 8
We have,
Median = (\(\frac{n+1}{2}\))^{th} item
= (\(\frac{8+1}{2}\))^{th} item
= (\(\frac{9}{2}\))^{th} item
= (4.5)^{th} item
Now,
Median = mean of 4^{th} item and 5^{th} item
= \(\frac{20+24}{2}\)
= \(\frac{44}{2}\)
= 22
\(\therefore\) Median = 22
Find the median of the given data:
x | 10 | 15 | 20 | 25 | 30 |
f | 2 | 4 | 6 | 5 | 4 |
Solution:
x | f | c.f |
10 | 2 | 2 |
15 | 4 | 6 |
20 | 6 | 12 |
25 | 5 | 17 |
30 | 4 | 21 |
N = 21 |
We have,
Median = value of (\(\frac{n+1}{2}\))^{th} item
= value of (\(\frac{21+1}{2}\))^{th} item
= value of 11^{th} item
In c.f. just greater than 11 is 12 and its corresponding value is 20.
\(\therefore\) Median is 20.
Find the median from the given data:
x |
10 |
16 |
20 |
25 |
30 |
35 |
50 |
f |
4 |
6 |
10 |
15 |
20 |
12 |
8 |
Solution:
x | f | c.f. |
10 | 4 | 4 |
16 | 6 | 10 |
20 | 10 | 20 |
25 | 15 | 35 |
30 | 20 | 55 |
35 | 12 | 67 |
50 | 8 | 75 |
N=75 |
We have, = value of (\(\frac{N+1}{2}\))^{th} item
= value of (\(\frac{75+1}{2}\))^{th} item
= value of 38^{th} item
In c.f. column, c.f. just greater then 38 is 55 and its corresponding value is 30.
\(\therefore\) Median = 30
Find the median from the given data:
Marks |
80 |
75 |
60 |
55 |
50 |
40 |
35 |
no. of students |
3 |
7 |
10 |
6 |
4 |
2 |
1 |
Solution:
Marks | f | c.f. |
80 | 3 | 3 |
75 | 7 | 10 |
60 | 10 | 20 |
55 | 6 | 26 |
50 | 4 | 30 |
40 | 2 | 32 |
35 | 1 | 33 |
N=33 |
We have, = value of (\(\frac{N+1}{2}\))^{th} item
= value of (\(\frac{33+1}{2}\))^{th} item
= value of 17^{th} item
In c.f. column, c.f. just greater then 17 is 20 and its corresponding value is 60.
\(\therefore\) Median = 60
Find the median from the given data:
height (cm) |
110 |
115 |
120 |
124 |
128 |
130 |
no. of girls |
3 |
5 |
10 |
7 |
3 |
2 |
We have, = value of (\(\frac{N+1}{2}\))^{th} item
= value of (\(\frac{40+1}{2}\))^{th} item
= value of 20.5^{th} item
In c.f. column, c.f. just greater then 20.5 is 28 and its corresponding value is 120.
\(\therefore\) Median = 120
Find the median from the given data:
x |
10 |
20 |
30 |
40 |
50 |
f |
4 |
6 |
10 |
8 |
5 |
Solution:
x | f | c.f. |
10 | 4 | 4 |
20 | 6 | 10 |
30 | 10 | 20 |
40 | 8 | 28 |
50 | 5 | 33 |
N=33 |
We have, = value of (\(\frac{N+1}{2}\))^{th} item
= value of (\(\frac{33+1}{2}\))^{th} item
= value of 17^{th} item
In c.f. column, c.f. just greater then 17 is 20 and its corresponding value is 30.
\(\therefore\) Median = 30
In the data set below, what is the median?
1, 2. 4, 4, 5, 6, 6, 6 , 7, 7, 8
In the data set below, what is the median?
2, 2, 2, 2, 3 , 5, 5, 5, 7, 8, 9, 9
In the data set below, what is the median?
19 37 41 43 83 85 94
In the data set below, what is the median?
2, 4, 5, 6, 6, 7, 8, 8, 8, 9
Find the median.
64, 60, 70, 72, 68, 80, 85, 56
Find the median.
47, 61, 13, 34, 56, 22, 8
Find the median.
8, 1, 3, 3, 1, 7, 4, 1, 4, 4
x-1, 2x+1, x+5 and 3x+1are ascending order. If its median is18, find the value of x.
12, 17, 2x+3, 3x+5, 36, 43 are in ascending order. If its median is 29, find the value of x.
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.
Find median. 12, 1, 10, 1, 9, 3, 4, 9, 7, 9
Find median.
85, 77, 60, 89, 91, 89, 78
What is value of x if its median is 12. x+1, 2x-1, x+7 and 3x+4
Find median. 15, 10, 11, 9, 14
Find median. 14, 16, 12, 6, 8,10
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The median of x-4,x,2x and 2x 12 is 9,wherex is a positive intenger. find the value of x.
The median of x-4,x,2x and 2x 12 is 9,wherex is a positive intenger. find the value of x.
Mar 03, 2017
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