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
Show 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.
Step 1: Find each age band's female respondents separately.
Rather than adding the percentages first, we can find the sample count for each row on its own and then add the counts.
Step 4: Add the two counts.
$$168.75 + 137.5 = 306.25$$
This matches the count found by adding the percentages first, since sampling is a linear operation on the percentage shares.
Step 5: Round to the nearest whole respondent.
$$306.25 \approx 306$$
Final Answer:
306 female respondents in the 19 to 40 year age group are needed for the survey sample.