A survey showed that the average daily expenditures (in rupees) of 30 households in a city were:
11, 12, 14, 16, 16, 17, 18, 18, 20, 20, 20, 21, 21, 22, 22, 23, 23, 24, 25, 25, 26, 27, 28, 28, 31, 32, 32, 33, 36, 36.
(a) Prepare a frequency distribution using class intervals:

10-14, 15-19, 20-24, 25-29, 30-34 and 35-39.

(b) What percent of the households spend more than ₹ 29 each day?
(c) Draw a frequency histogram for the above data.

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Solution

(a)

Class Interval Tally Marks Frequency

10 − 14
15 − 19
20 − 24
25 − 29
30 − 34
35 − 39

3
5
10
6
4
2

30

(b) Households that spend more than 29 each day $= \frac{6}{30} \times 100 = 20 %$

(c) To construct histogram, we first need to convert the given inclusive series into an exclusive series using the following formula.

The value of adjustment as calculated is then added to the upper limit of each class and subtracted from the lower limit of each class.
$Here, the value of adjustment = \frac{15 - 14}{2} = 0.5$

Therefore, we add 0.5 to the upper limit and subtract 0.5 from the lower limit of each class.

Class Interval Frequency

9.5 − 14.5
14.5 − 19.5
19.5 − 24.5
24.5 − 29.5
29.5 − 34.5
34.5 − 39.5 3
5
10
6
4
2

30

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Class Interval	Tally Marks	Frequency
10 − 14 15 − 19 20 − 24 25 − 29 30 − 34 35 − 39		3 5 10 6 4 2
		30

Class Interval	Frequency
9.5 − 14.5 14.5 − 19.5 19.5 − 24.5 24.5 − 29.5 29.5 − 34.5 34.5 − 39.5	3 5 10 6 4 2
	30