Question

The median for the data is

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

• A. 102.86
• B. 98.46
• C. 97.47
• D. 103.26

Answer 1

The correct option is A 102.86

$$\begin{array}{ccc}ClassInterval& Frequency& CumulativeFrequency\\ 60-70& 2& 2\\ 70-80& 3& 5\\ 80-90& 5& 10\\ 90-100& 16& 26\\ 100-110& 14& 40\\ 110-120& 13& 53\\ 120-130& 7& 60\end{array}$$

$\frac{N}{2}=30$
$\therefore$ the median class is 100-110
$\text{Median}=\text{LRL}+\left(\frac{\frac{N}{2}-f_c}{f_m}\right)\times i$,
where LRL stands for the lower real limit, $f_m$=frequency of median class, $f_c$=cumulative frequency above the median class and $i$=size of the class interval
$⟹\text{Median}=100+\frac{30-26}{14}\times 10=102.86$