Question

The mode for the given data is ___ .

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

Answer 1

$$\begin{array}{cc}\text{Class Interval}& \text{Frequency}\\ 60-70& 2\\ 70-80& 3\\ 80-90& 5\\ 90-100& 16\\ 100-110& 14\\ 110-120& 13\\ 120-130& 7\end{array}$$

Modal class is the class with the highest frequency.
$\therefore$ Modal class = 90 - 100

$\text{Using Mode}=l+\left(\frac{f_1-f_0}{2f_1-f_0-f_2}\right)\times h$
where $f_1$ represents the frequency of the modal class.
Also,
$l=$ lower boundary of the modal class
$h=$ size of the modal class interval
$f_0=$ frequency of the class preceding the modal class
$f_2=$ frequency of the class succeeding the modal class

$\therefore Mode=90+\frac{16-5}{32-5-14}\times 10=98.46$