# Is it incorrect to calculate the mean and standard deviation of percentages?

My data is some percentages on how many transactions from a whole are missed each month. The percentages are for 13 months and ranging from 97 to 99 percent. I was asked to calculate the mean and standard deviation, but I am unsure if the result would be meaningful and if the mean could be calculated for percentages in the traditional sense (e.g., in Excel doing AVERAGE(percent array)) vs. some other method (weighted averaged) since I do not have any other information other than the percentages.

1. If the mean and standard deviation for percentages can be calculated,
2. What conditions are needed in order to calculate the mean and standard deviation for percentages,
3. Alternatives determining spread and central tendency for percentages over a period of time.

For example, would the following be incorrect to do assuming that the percentages represent # transactions missed / # total transactions for each different months with the same calculation being used for each month:

Month   Data
Feb-15  98.0%
Mar-15  98.7%
Apr-15  97.0%
May-15  99.9%
Jun-15  98.7%
Jul-15  97.9%

Mean
98.4%

SD (Population)
0.90%


From this post is seems like it should be done with weighted averages since the totals are different, and that calculating the mean and standard deviation is possible for percentages only if they come from the same total, meaning the above would be incorrect and that I would need additional information to determine the weight to multiple the percentages by, if that is correct.

• Of course you can calculate mean and SD of percentages: just plug them into the formula. What should be of concern is how the resulting values will be interpreted. Could you explain why you have been asked to perform this calculation and what will be done with the results? – whuber Oct 30 '15 at 2:35
• @whuber is right here. After all, a percentage is just a mean of 0's and 1's. What is most important is not whether a mean and standard deviation can be calculated, but what you want to do with them and if it makes sense in that context. – StatsStudent Oct 30 '15 at 2:41
• It was a blanket request to calculate the mean and standard deviation of a set of metrics to set thresholds for them. So in this example, the 98.4% average would be used to measure the current month against, with the assumption that the more standard deviations away it is from the mean, the more of a concern it would be. – daneshjai Oct 30 '15 at 5:02
• As you can see, two standard deviations away from the mean is already in a territory of over 100%. If your task is to see how extreme a new observation is as compared to the historical data, you could consider using some rank statistic. E.g. just see how many months out of the total number of months have been worse or better than the current month. You will get scores like 2/13 or 1/13, or even 0/13. – Richard Hardy Oct 30 '15 at 11:05