Following is the distribution of I.Q. of 100 students. find the median I.Q.
I.Q.: 55-64 65-74 75-84 85-94 95-104 105-114 115-124 125-134 135-144
No. of students: 1 2 9 22 33 22 8 2 1

Academic Mathematics NCERT Class 10

Given:

The distribution of 100 students.

To do:

We have to find the median I.Q.

Solution:

Arranging the classes in exclusive form and then forming its cumulative frequency table as below, we get,

Here,

$N = 100$

$\frac{N}{2} = \frac{100}{2} = 50$

The cumulative frequency just greater than $\frac{N}{2}$ is 67 and the corresponding class is 94.5 – 104.5.

This implies, 94.5 – 104.5 is the median class.

Therefore,

$l = 94.5, f = 33, F = 34$ and $h = (104.5 - 94.5) = 10$

Medain $=\mathrm{l}+\frac{\frac{\mathrm{N}}{2}-\mathrm{F}}{\mathrm{f}} \times \mathrm{h}$

$=94.5+\frac{50-34}{33} \times 10$

$=94.5+\frac{16}{33} \times 10$

$=94.5+\frac{160}{33}$

$= 94.5 + 4.85$

$= 99.35$

The median I.Q. is 99.35.

Updated on: 10-Oct-2022

54 Views

Kickstart Your Career

Get certified by completing the course

Advertisements