Question

Below is given frequency distribution of I.Q. (Intelligent Quotient) of 80 candidates.

I.Q.	70 - 80	80 - 90	90 - 100	100 - 110	110 - 120	120 - 130	130 - 140
No. of Candidates	7	16	20	17	11	7	2

Find median I.Q. of candidates

• A. $100.5$
• B. $98.5$
• C. $94.5$
• D. None of these

Answer 1

The correct option is B $98.5$

There are total 80 candidates. Hence, the median will be the mean of 40th and 41st candidate. Both of which lie in the interval 90-100
The median of grouped data is given by:
Median $L+\left(\frac{\frac{n}{2}-c{f}_b}{f_m}\right)\times w$
where:
L is the lower class boundary of the group containing the median
n is the total number of data
$c{f}_b$ is the cumulative frequency of the groups before the median group
$f_m$ is the frequency of the median group
w is the group width
Hence,
Median = $90+\left(\frac{\frac{80}{2}-23}{20}\right)\times 10$
Median = $90+\left(\frac{17}{20}\right)\times 10$
Median = $90+8.5$
Median = $98.5$