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
- less than Rs 2000
- more than Rs 3000
- between Rs 1500 and Rs 2500 Table 3.2 — Monthly Household Expenditure (in Rupees) on Food of 50 Households:
| 1904 | 1559 | 3473 | 1735 | 2760 |
| 2041 | 1612 | 1753 | 1855 | 4439 |
| 5090 | 1085 | 1823 | 2346 | 1523 |
| 1211 | 1360 | 1110 | 2152 | 1183 |
| 1218 | 1315 | 1105 | 2628 | 2712 |
| 4248 | 1812 | 1264 | 1183 | 1171 |
| 1007 | 1180 | 1953 | 1137 | 2048 |
| 2025 | 1583 | 1324 | 2621 | 3676 |
| 1397 | 1832 | 1962 | 2177 | 2575 |
| 1293 | 1365 | 1146 | 3222 | 1396 |
You're viewing a preview — the full solution, concept, methods & PYQ mapping are locked.
Start your 14-day free trial to unlock the full solution →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:
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 classes. Using the exclusive method (upper limit excluded), we tally the 50 figures into the classes below.
| Expenditure (Rs) | Tally count (frequency) |
|---|---|
| 1000 – 1500 | 20 |
| 1500 – 2000 | 13 |
| 2000 – 2500 | 6 |
| 2500 – 3000 | 5 |
| 3000 – 3500 | 2 |
| 3500 – 4000 | 1 |
| 4000 – 4500 | 2 |
| 4500 – 5000 | 0 |
| 5000 – 5500 | 1 |
| Total | 50 |
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: …
Unlock everything free for 14 days
- Full step-by-step solutions
- Concept-first explanations
- Methods, shortcuts & mistakes
- PYQ mapping + timed mock tests
Full access for 14 days. No credit card required.