How do I merge two age groups per 10k from an abortion rate table?

[samlag]

• I would like to find the 12 to 19 abortion rate per 10,000 women from the following table:

View attachment 7193
This would be the merging of age groups "12-17" with "18-19" to some how get the 12-19 abortion rate.
EDIT: "Distribution of abortion age" was translated from "Répartition des ges l'avortement" in French. It appears to me to be the percentage each age group's abortions are of the total amount of abortions.

The answer I came up with is 125.67 per 10,000. Not sure if that is correct.
I multiplied the rate per individual woman by the number of abortions for each group which I think gave the number of women. I added both of these groups together. I added both groups number of abortions and then divided the amount of women by amount of abortions and multiplied it by 10,000.

If you would like to answer, its probably best to focus on the math, and not politics :)

 

[Evgeny.Makarov]

Let us introduce some notations. Let age 12-17 be denoted by index 1 and age 18-19 by index 2. Let $a_i$ be the number of abortions and $r_i$ be rates for $i=1,2$. Let us express rates as absolute fractions (abortions per woman) rather than numbers per 10,000. Thus, $r_1=60.7/10,000=0.00607$. Let $w_i$ be the total number of women surveyed in each age group. Then $w_i\cdot r_i=a_i$ from where $w_i=\frac{a_i}{r_i}$. We get the following values.
\begin{align}
a_1&=10428 & r_1&=0.00607 & w_1&=a_1/r_1\approx 1,717,627\\
a_2&=13654 & r_2&=0.02409 & w_2&=a_2/r_2\approx 566,791
\end{align}

I multiplied the rate per individual woman by the number of abortions for each group which I think gave the number of women.

From the above, it seems that one must divide the number of abortions by the rate.

I added both of these groups together. I added both groups number of abortions and then divided the amount of women by amount of abortions and multiplied it by 10,000.

Here I agree. The combined rate is \(\displaystyle \frac{a_1+a_2}{w_1+w_2}=\frac{a_1+a_2}{a_1/r_1+a_2/r_2}\approx 0.01054\), or 105.4 per 10,000 women.

However, I am not sure what the third column, "Distribution of abortion age", means. Let us denote it by $d_i$ so that $d_1=6.4$ and $d_2=8.3$. If it is the fraction of total women surveyed in the given age bracket, then these numbers contradict our findings. In this case $w_2/w_1$ should equal $d_2/d_1$, which is not the case for the numbers above. If, however, this is true, then the combined rate equals \(\displaystyle \frac{d_1r_1+d_2r_2}{d_1+d_2}\approx162.4\) per 10,000.

 

[I like Serena]

However, I am not sure what the third column, "Distribution of abortion age", means. Let us denote it by $d_i$ so that $d_1=6.4$ and $d_2=8.3$.

Note that 10426 / 163652 = 6.4%.
It's the distribution of the abortions over the age groups as a percentage.

 

[samlag]

However, I am not sure what the third column, "Distribution of abortion age", means. Let us denote it by $d_i$ so that $d_1=6.4$ and $d_2=8.3$. If it is the fraction of total women surveyed in the given age bracket, then these numbers contradict out findings. In this case $w_2/w_1$ should equal $d_2/d_1$, which is not the case for the numbers above. If, however, this is true, then the combined rate equals \(\displaystyle \frac{d_1r_1+d_2r_2}{d_1+d_2}\approx162.4\) per 10,000.

"Distribution of abortion age" was translated from French "Répartition des ges l'avortement" which also translates to "Распределение мест абортов" and "Zetelverdeling abortus" in Dutch. It appears to me to be the percentage each age group is of the total amount of abortions.