# Calculating average - How to interpret

I am currently looking into a dataset, and have a question about calculating average.

Assume I have the following data of the number of dogs in four different cities over the course of 4 weeks:

        London    NYC    Berlin    Tokyo
mon1    2         4      2         2
tue1    3         5      10        2
....
sat4    3         3      1         1
sun4    2         4      2         3


Now, I try to calculate the average number of dogs in each city.

Why do I get a different average if I calculate average for all four weeks at once (e.g. average(mon1:sun4)), compared to if I calculate the average for each week, and then find the total average from there?

For instance, if calculating the entire average all at once, I London stands out as having the highest average, whereas if I calculate the average for each week, and then find the total average from there, Berlin has the highest average.

Furthermore; what is the "correct" average?

• There must be a mistake in your formula. The average is actually the same. You can easily prove it algebraically – b00n heT Sep 20 '17 at 6:04
• Does this also apply for the average numbers of dogs over a period of several years? (Seeeing that some years have more weeks than others). – aprilrocks92 Sep 20 '17 at 6:10
• No. In that case there is a difference because, as you said, some years have more weeks than others and so their averages are weighted differently. – b00n heT Sep 20 '17 at 9:03