Discussion
The following table presents the number of families in a village earning a certain level of monthly income from their factory job in the nearby town :
| Number of Families | Income band (in Rupees) |
|---|---|
| 42 | 5,000-9,999 |
| 40 | 10,000-14,999 |
| 36 | 15,000-19,999 |
| 18 | 20,000-24,999 |
| 5 | 25,000-30,000 |
Which of the following statements are correct ?
(i) Approximately 54% of the families earn between Rs. 10,000 and Rs. 20,000.
(ii) There are 70% families who earn more than Rs. 10,000.
(iii) A family with highest income earns Rs. 29,500.
(iv) Median income is between Rs. 10,000 and Rs. 14,999.
Answer: C
The correct statements are (i), (ii) and (iv).
The total number of families is 42 + 40 + 36 + 18 + 5 = 141.
\[ \begin{aligned} \text{(i)}\ \frac{40 + 36}{141} &= \frac{76}{141} \approx 53.9\% \\ \text{(ii)}\ \frac{40 + 36 + 18 + 5}{141} &= \frac{99}{141} \approx 70.2\% \end{aligned} \]
So (i), about 54 per cent between Rs. 10,000 and Rs. 20,000, and (ii), 70 per cent earning more than Rs. 10,000, are both correct. For (iv), the median is the 71st family in order of income; the first band holds 42 families and the first two hold 82, so the 71st falls in the band Rs. 10,000-14,999, and (iv) is correct.
Statement (iii) cannot be known: the table says only that the highest band runs from Rs. 25,000 to Rs. 30,000, not what the richest family earns. Every code containing (iii) is therefore wrong.
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