The frequency distribution of daily working expenditure of families...

The frequency distribution of daily working expenditure of families in a locality is as follows:

If the mode of the distribution is

₹ 140

, then the value of

b

Options

Correct answer

D. 36

Step-by-step solution

\text{ Frequency distribution is given as } The frequency distribution of daily working expenditure of families in a locality is as follows: If the mode of the

\\ 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}}{2 f_0-f_{-1}-f_1} \times

i where

\begin{aligned}& \ell=100, f_0=37, f_{-1}=33, f_1=\mathrm{b}\\ & i=50 \end{aligned}

Thus, we get 140=100+

\left[\frac{37-33}{2(37)-33-b}\right] \times

50

\begin{aligned}& =100+\left[\frac{4}{74-33-b}\right] \times50 \\ & =100+\frac{200}{41-b}\\ \Rightarrow & 5740=4300+40 b \Rightarrow b=36 \end{aligned}

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