Discussion
Among the women who gave birth in that hospital last year, the percentage of women who had their first child was :
80% for age group 20 - 24,
60% for age group 25 - 29,
30% for age group 30 - 34, and
2% for age group 35 - 40.
In the whole cohort, what percentage of women had their first child ?
Answer: C
The percentage having their first child was 61.6.
Apply each group's percentage to the number of women in it and add:
\[ \begin{aligned} 0.80 \times 450 &= 360 \\ 0.60 \times 350 &= 210 \\ 0.30 \times 150 &= 45 \\ 0.02 \times 50 &= 1 \end{aligned} \]
That is 616 first-time mothers out of 1000 women, or 61.6%.
43 is the simple average of the four percentages, (80 + 60 + 30 + 2)/4, which ignores that the groups differ greatly in size. 52.9 and 65.8 do not match the weighted total of 616.
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