How to combine monthly rates?

Question

I have a Google Analytics report that gives certain monthly values as percentages or fractions:

         Bounce    Pages per 
Month    Rate      Session
-----    ------   ---------
March     70%      5.16 
April     34%      6.25
May       21%      5.88

I've been tasked with coming up with a single value of each value for this date range; in other words, what's the overall Bounce Rate and Pages/Session for these three months?

I suspect that will involve the standard "combined rate" formula:

1/70 + 1/34 + 1/21 = 1/(overall Bounce Rate)

But I don't really know. And I'm not sure that applies to the Pages/Session version of the question.

(PS: I'm going to ask my boss if Google Analytics can just give him the aggregate scores he wants, but I need to be ready in case he says "no"!)

Answer 1

For each month $i$, let

• $r_i$ be the bounce rate
• $v_i$ be the number of visits
• $b_i$ be the number of bounces

We have $b_i=r_iv_i$, so if you want the bounce rate over three months ($i=1,2,3$), just calculate:

$$\frac{r_1v_1+r_2v_2+r_3v_3}{v_1+v_2+v_3}.$$

Notice that this weights each bounce rate $r_i$ by the proportion of visits in month $i$, $\frac{v_i}{v_1+v_2+v_3}$.