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 interval and their corresponding frequencies. 

The given distribution being of the less than type 140, 145, 150,….165 give the upper limit of the corresponding class intervals. So, the classes should be below 140, 140-145, 145-150,….160-165. Observe that from the given distribution, we find that there are 4 girls with height less than 145 and 4 girls with height less than 140. Therefore, the number of girls with height in the interval 140-145 is 11 – 4 = 7 

Similarly, the frequency of 145-150 is 29 – 11 = 19, for 150-155 it is 40 – 29 = 11 and so on so our frequency distribution table with the given cumulative frequency becomes:

Now,

N = 51

So,

 \(\frac{N}{2}=\frac{51}{2}=25.5\)

This observation lies in the class 145 – 150

Then, 

l (lower limit) = 145

f = 11 and h = 5

Median = 145 + \(\frac{25.5-11}{18}\times5\)

= 145 + 4.03 = 149.03 

So, the median height of the girls is 149.03 cm. This means that the height of the about 50% of the girls is less than this height and 50% are taller than this height.