Question

A survey regarding the height (in cm) of 51 girls of class X of a school was conducted and the following data was obtained:

Height in cm	Number of Girls
Less than 140	4
Less than 145	11
Less than 150	29
Less than 155	40
Less than 160	46
Less than 165	51

Find the median height.

Answer 1

To calculate the median height, we need to find the class intervals and their corresponding frequencies

The given distribution being of thee less than type 140, 145, 150,…..,165 give the upper limits of the corresponding class intervals. So, the classes should be below 140, 145, 150,......, 160, 165 observe that from the given distribution, we find that there are 4-girls with height less than 140 is 4. Now there are 4 girls with heights less than 140. Therefore, the number of girls with height in the interval 140, 145 is 11- 4=7, similarly. The frequencies of 145 150 is 29-11=18, for 150-155 it is 40-29=11, and so on so our
frequencies distribution becomes.

Class interval	Frequency	Cumulative frequency
below 140	4	4
140-145	7	11
145-150	18	29
150-155	11	40
155-160	6	46
160-165	5	51

Now N = 51

So, N/2=51/2=25.5

Now, the cumulative frequency just greater than 25.5 is 29 and the corresponding class is 145 - 150.

Therefore, 145 - 150 is the median class.

l = 145, f = 18, F = 11 and h = 5

We know that

Median `=l+(N/2-F)/fxxh`

`=145+(25.5-11)/18xx5`

`=145+14.5/18xx5`

`=145+72.5/18`

= 145 + 4.03

= 149.03

Hence, the median height is 149.03