The age distribution of 40 children is as follows: | Age (in years) | 5–6 | 6–7 | 7–8 | 8–9 | 9–10 | 10–11 | | No. of children | 4 | 7 | 9 | 12 | 6 | 2 |. Consider the following statements in respect of the above frequency distribution:
- 1The median of the age distribution is 7 years.
- 270% of the children are in the age group 6–9 years.
- 3The modal age of the children is 8 years.
Which of the above statements are correct?
- A1 and 2 only
- B2 and 3 only
- C1 and 3 only
- D1, 2 and 3
Explanation
Cumulative frequencies are 4, 11, 20, 32, 38, 40; the median class is 7–8, giving median 7+(20−11)/9 = 8, so statement 1 is false. Ages 6–9 account for (7+9+12)/40 = 70% (statement 2 true), and the modal class is 8–9, i.e. modal age 8 (statement 3 true). Hence 2 and 3 only, option B. (One published transcription of the official key shows (a) here, but the computation and an independent key both give (b).) Note: key disputed — verify against the official UPSC key.