Question

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

Expenditure in ₹ (x):	0 – 50	50 – 100	100 – 150	150 – 200	200 – 250
No. of families (f):	24	33	37	b	25

If the mode of the distribution is ₹ 140 then the value of b is ______.

Options

• 34

• 31

• 26

• 36

Answer 1

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

Expenditure in ₹ (x):	0 – 50	50 – 100	100 – 150	150 – 200	200 – 250
No. of families (f):	24	33	37	b	25

If the mode of the distribution is ₹ 140 then the value of b is 36.

Explanation:

Frequency distribution is given as

Expenditure	No. of families (f)
0 – 50	24
50 – 100	33
100 – 150	37
150 – 200	b
200 – 250	25

Clearly, modal class is 100 – 150, as the maximum frequency occurs in this class.

Given, Mode = 140

We have

Mode = `ℓ + (f_0 - f_-1)/(2f_0 - f_-1 - f_1) xx i`

where

ℓ = 100, f₀ = 37, f_–1 = 33, f₁ = b

i = 50

Thus, we get

140 = `100 + [(37 - 33)/(2(37) - 33 - b)] xx 50`

= `100 + [4/(74 - 33 - b)] xx 50`

= `100 + 200/(41 - b)`

⇒ 41 – b = 5

⇒ b = 36