Solve Math Median

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.