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Given below is the distribution of total household expenditure

Question

Given below is the distribution of total household expenditure of $200$ manual workers in a city:
Expenditure (in Rs) $1000 - 1500$ $1500 - 2000$ $2000 - 2500$ $2500 - 3000$ $3000 - 3500$ $3500 - 4000$ $4000 - 4500$ $4500 - 5000$
No. of manual workers $24$ $40$ $31$ $28$ $32$ $23$ $17$ $5$
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Given below is the distribution of total household expenditure of

200

manual workers in a city:

Expenditure (in Rs)	$1000 - 1500$	$1500 - 2000$	$2000 - 2500$	$2500 - 3000$	$3000 - 3500$	$3500 - 4000$	$4000 - 4500$	$4500 - 5000$
No. of manual workers	$24$	$40$	$31$	$28$	$32$	$23$	$17$	$5$

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Text solutionVerified

Here:
Maximum class frequency

= 40

The class corresponding to Maximum class frequency is the modal class.
So, Modal class

= 1500 - 2000

Lower limit

= L = 1500

Modal class size

= h = 500

Frequency of class preceding the modal class

= f 0 = 24

Frequency of the modal class

= f 1 = 40

Frequency of class succeeding the modal

= f 2 = 31

Mode formula is given by.

Mode

= L + (\frac{f _{1} - f _{0}}{2 f _{1} - f _{0} - f _{2}}) \times h

Mode

= 1500 + (\frac{40 - 24}{2 ( 40 ) - 24 - 31}) \times 500

= 1500 + 16/25 \times 500

= 1820

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Question Text	Given below is the distribution of total household expenditure of $200$ manual workers in a city: Find Mode.
Answer Type	Text solution:1
Upvotes	150