The median for the data is IQ 60 − 70 70 − 80 80 − 90 90 − 100 100 − 110 110 − 120 120 − 130 No. of pupils 2 3 5 16 14 13 7 Options: A . &nbsp 102.86 B . &nbsp 98.46 C . &nbsp 97.47 D . &nbsp 103.26

Answer: Option A : A C l a s s I n t e r v a l Frequency C u m u l a t i v e F r e q u e n c y 60 − 70 2 2 70 − 80 3 5 80 − 90 5 10 90 − 100 16 26 100 − 110 14 40 110 − 120 13 53 120 − 130 7 60 n 2 = 30 . So, the median class is the one whose cumulative frequency is closest to and greater than 30. ∴ the median class is 100-110 M e d i a n = l + ( n 2 − c f f ) × h Where l is lower class limit of median class. n is total number of observations. c f is the cumulative frequency of the class preceding the median class. f is the frequency of the median class and h is the class size. ⟹ M e d i a n = 100 + 30 − 26 14 × 10 ∴ M e d i a n = 102.86

The median for the data is IQ 60−7070−8080−9090

Question

The median for the data is

$\begin{matrix} IQ & 60 - 70 & 70 - 80 & 80 - 90 & 90 - 100 & 100 - 110 & 110 - 120 & 120 - 130 No. of pupils & 2 & 3 & 5 & 16 & 14 & 13 & 7 \end{matrix}$

Options:

A . 102.86

B . 98.46

C . 97.47

D . 103.26

Answer: Option A
:
A

$\begin{matrix} C l a s s I n t e r v a l & Frequency & C u m u l a t i v e F r e q u e n c y 60 - 70 & 2 & 2 70 - 80 & 3 & 5 80 - 90 & 5 & 10 90 - 100 & 16 & 26 100 - 110 & 14 & 40 110 - 120 & 13 & 53 120 - 130 & 7 & 60 \end{matrix}$

$\frac{n}{2} = 30$ .
So, the median class is the one whose cumulative frequency is closest to and greater than 30.
$∴$ the median class is 100-110
$M e d i a n = l + (\frac{\frac{n}{2} - c f}{f}) \times h$
Where $l$ is lower class limit of median class.
$n$ is total number of observations.
$c f$ is the cumulative frequency of the class preceding the median class.
$f$ is the frequency of the median class and h is the class size.
$⟹ M e d i a n = 100 + \frac{30 - 26}{14} \times 10$
$∴ M e d i a n = 102.86$