Mathematics - Statistics Question with Solution | TestHub

$$\text{ Frequency distribution is given as }$$
Clearly, modal class is $100-150$, as the maximum frequency occurs in this class. Given, Mode $=140$ We have $$\text{ Mode }=\ell +\frac{f_0-f_{-1}}{2f_0-f_{-1}-f_1}\times i$$ where $$\begin{array}{rl}& \ell =100,f_0=37,f_{-1}=33,f_1=\mathrm{b}\\ & i=50\end{array}$$ Thus, we get $$140=100+\left[\frac{37-33}{2(37)-33-b}\right]\times 50$$ $$\begin{array}{rl}& =100+\left[\frac{4}{74-33-b}\right]\times 50\\ & =100+\frac{200}{41-b}\\ \Rightarrow & 5740=4300+40b\Rightarrow b=36\end{array}$$