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Exercises · Q5
Q.

Use the data in Table 3.2 that relate to monthly household expenditure (in Rs) on food of 50 households and

(i) Obtain the range of monthly household expenditure on food.

(ii) Divide the range into appropriate number of class intervals and obtain the frequency distribution of expenditure.

(iii) Find the number of households whose monthly expenditure on food is

  1. less than Rs 2000
  2. more than Rs 3000
  3. between Rs 1500 and Rs 2500 Table 3.2 — Monthly Household Expenditure (in Rupees) on Food of 50 Households:
19041559347317352760
20411612175318554439
50901085182323461523
12111360111021521183
12181315110526282712
42481812126411831171
10071180195311372048
20251583132426213676
13971832196221772575
12931365114632221396
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With 50 raw expenditure figures, the range is Rs 4083. Choosing a convenient class width of Rs 500 gives a nine-class exclusive frequency distribution. From it: 33 households spend less than Rs 2000, 6 spend more than Rs 3000, and 19 spend between Rs 1500 and Rs 2500.

(i) Range

The range is the difference between the largest and the smallest observation:

Range=L−S=5090−1007=4083\text{Range} = L - S = 5090 - 1007 = 4083

So the range of monthly household food expenditure is Rs 4083.

(ii) Frequency distribution

A range of 4083 divided into classes of a convenient width of Rs 500 needs about 4083/500≈94083/500 \approx 9 classes. Using the exclusive method (upper limit excluded), we tally the 50 figures into the classes below.

Expenditure (Rs)Tally count (frequency)
1000 – 150020
1500 – 200013
2000 – 25006
2500 – 30005
3000 – 35002
3500 – 40001
4000 – 45002
4500 – 50000
5000 – 55001
Total50

The frequencies add up to 50, confirming that every household has been counted once.

(iii) Reading the distribution

(a) Less than Rs 2000 = households in 1000–1500 and 1500–2000: …

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