Question

A socio-economic survey of a city is planned with a sample size of 1250 persons, having the same proportion of age and sex distribution of the city population, as given in the table below. The required number of representative female respondents of the age group 19 to 40 years, is (rounded off to nearest integer).

Age group (in years)	City Population Distribution (in %)
	Male	Female
0 to 6	2	1.5
7 to 18	8.5	6
19 to 25	14.5	13.5
26 to 40	14.5	11
41 to 50	12	8
51 to 60	2.5	2.5
60 +	1.5	2

Hint:

Add the female percentages for the "19 to 25" and "26 to 40" rows, then apply that combined percentage to the 1250 sample size.

Answer 1

Correct Answer: 306

Step 1: Understanding the Question.
The survey sample of 1250 persons is spread across age and sex groups in the same proportion as the whole city. We need the number of FEMALE respondents falling in the combined age band 19 to 40 years, which covers two rows of the table: "19 to 25" and "26 to 40".

Step 2: Add up the relevant female percentages.
Female share for 19 to 25 years = 13.5%
Female share for 26 to 40 years = 11%
\[ \text{Total female share (19 to 40 years)} = 13.5\% + 11\% = 24.5\% \]

Step 3: Apply this share to the sample size.
\[ \text{Number of respondents} = 1250 \times \frac{24.5}{100} = 1250 \times 0.245 = 306.25 \]

Step 4: Round off to the nearest integer.
\[ 306.25 \approx 306 \]

Final Answer:
The required number of representative female respondents aged 19 to 40 years is 306. \[ \boxed{306} \]