Introduction to median in math:-
Median is another measure of central tendency. It is the middle value of a series of numbers. It divides the series into two equal parts. One half contains values less than the median and the other half contains values more than the median. So we arrange the series in ascending or descending order to find the median. If the series contains 'n' numbers and if 'n' is odd, then the median is found by the formula `(n+1)/2` . If n is even then we must find the mean value of the `(n/2)` th and `(n + 1)/2` th numbers to find the median.
If we have many frequencies of the given numbers in a grouped data, then we use the formula
Median =` l +((N/2-m)/f)xxc` f
where l is the lower limit of the median class,
m is cumulative frequency up to l,
f is the frequency of the median class,
N is total frequency and
c is the length of the class interval.
To Find Median when Frequency is not Given.
Let us find the median of the following numbers 25,29, 32, 46, 73, 25, 28
Solution:
Step 1: We must arrange the numbers in order. So let us arrange them in ascending order 25,25,28,29,32,46,73
Step 2: Here n=7 so it is odd
Step 3: So median is `(7+1)/2` th number = 4th number = 29
Step 4: Let us count the numbers before 29. There are 3 numbers. 25, 25, 28
Step 5: Let us count the numbers after the median. There are 3 numbers 32,46,73
Step 6: Hence we find that 29 is the middle number.
Answer: Median is 29
Find the median of the numbers 12,29, 24, 36, 32,48,59,73
Solution:
Step 1: Let us arrange them in ascending order .12, 24, 29, 32,36,48,59, 73
Step 2 : Let us count the numbers. They are 8. n = 8 is even
Step 3 : The formula is to find the median of `n/2` th number and `(n +1)/2` th number . That is `8/2` th number and `(8+1)/2` th number
That means we must find the median of 4th number and 5th number.
4th number is 32 and 5th number is 36
Hence median is` (32+36)/2` = `68/2` = 34
Answer: Median of the 8 given numbers is 34.Between, if you have problem on these topics adding exponents, please browse expert math related websites for more help on cbse model question papers for class 9.
To Find Median when Grouped Data is Given:
A grouped data is given. Let us find the median using the formula for the grouped data.
The income of the people in a factory is as follows:-
__________________________________________________________________
Income $ 80 - 100 100- 150 150- 180 180-200 200-250 250-300
__________________________________________________________________
Number of persons 16 24 26 30 20 7
__________________________________________________________________
Find the median.
Solution:-
Step 1 : We must find the cumulative frequency first. CI is class Interval
_____________________________________________
Income $ Number of persons Cumulative frequency
CI f cf
_____________________________________________
80 -100 16 16
100 - 150 24 40 m
(l) 150 - 180 26 (f) 66
180 - 200 30 96
200 - 250 20 116
250 - 300 7 123 -> N
Step 3 : N=123 is odd
Hence we must find `(N+1)/2` th item = `(123 + 1)/2` th number = `124/2` th number = 62
Step 4 : The 62nd number lies in the Class Interval 150-180 . Hence l is the lower limit 150,so l = 150
Step 5 : The frequency of f is 150-180 is 26 f = 26
Step 6 : C is the length of the class interval = 150-180 = 30
so C = 30
Step 7 : m is the cumulative frequency up to l that is the previous Class Interval cf m = 40
Step 8 : Median =` l + ((N/2 - m)/f )C `
=`150 + (62-40)/26 xx 30 `
= `150 + 22 xx 30 `
= `150 + 25.38 `
= `175.38`
Answer : Median of the grouped data is 175.38
Hence we can find the median by finding the middle value of a grouped data.
Median is another measure of central tendency. It is the middle value of a series of numbers. It divides the series into two equal parts. One half contains values less than the median and the other half contains values more than the median. So we arrange the series in ascending or descending order to find the median. If the series contains 'n' numbers and if 'n' is odd, then the median is found by the formula `(n+1)/2` . If n is even then we must find the mean value of the `(n/2)` th and `(n + 1)/2` th numbers to find the median.
If we have many frequencies of the given numbers in a grouped data, then we use the formula
Median =` l +((N/2-m)/f)xxc` f
where l is the lower limit of the median class,
m is cumulative frequency up to l,
f is the frequency of the median class,
N is total frequency and
c is the length of the class interval.
To Find Median when Frequency is not Given.
Let us find the median of the following numbers 25,29, 32, 46, 73, 25, 28
Solution:
Step 1: We must arrange the numbers in order. So let us arrange them in ascending order 25,25,28,29,32,46,73
Step 2: Here n=7 so it is odd
Step 3: So median is `(7+1)/2` th number = 4th number = 29
Step 4: Let us count the numbers before 29. There are 3 numbers. 25, 25, 28
Step 5: Let us count the numbers after the median. There are 3 numbers 32,46,73
Step 6: Hence we find that 29 is the middle number.
Answer: Median is 29
Find the median of the numbers 12,29, 24, 36, 32,48,59,73
Solution:
Step 1: Let us arrange them in ascending order .12, 24, 29, 32,36,48,59, 73
Step 2 : Let us count the numbers. They are 8. n = 8 is even
Step 3 : The formula is to find the median of `n/2` th number and `(n +1)/2` th number . That is `8/2` th number and `(8+1)/2` th number
That means we must find the median of 4th number and 5th number.
4th number is 32 and 5th number is 36
Hence median is` (32+36)/2` = `68/2` = 34
Answer: Median of the 8 given numbers is 34.Between, if you have problem on these topics adding exponents, please browse expert math related websites for more help on cbse model question papers for class 9.
To Find Median when Grouped Data is Given:
A grouped data is given. Let us find the median using the formula for the grouped data.
The income of the people in a factory is as follows:-
__________________________________________________________________
Income $ 80 - 100 100- 150 150- 180 180-200 200-250 250-300
__________________________________________________________________
Number of persons 16 24 26 30 20 7
__________________________________________________________________
Find the median.
Solution:-
Step 1 : We must find the cumulative frequency first. CI is class Interval
_____________________________________________
Income $ Number of persons Cumulative frequency
CI f cf
_____________________________________________
80 -100 16 16
100 - 150 24 40 m
(l) 150 - 180 26 (f) 66
180 - 200 30 96
200 - 250 20 116
250 - 300 7 123 -> N
Step 3 : N=123 is odd
Hence we must find `(N+1)/2` th item = `(123 + 1)/2` th number = `124/2` th number = 62
Step 4 : The 62nd number lies in the Class Interval 150-180 . Hence l is the lower limit 150,so l = 150
Step 5 : The frequency of f is 150-180 is 26 f = 26
Step 6 : C is the length of the class interval = 150-180 = 30
so C = 30
Step 7 : m is the cumulative frequency up to l that is the previous Class Interval cf m = 40
Step 8 : Median =` l + ((N/2 - m)/f )C `
=`150 + (62-40)/26 xx 30 `
= `150 + 22 xx 30 `
= `150 + 25.38 `
= `175.38`
Answer : Median of the grouped data is 175.38
Hence we can find the median by finding the middle value of a grouped data.
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