# Useful averages!

As I work in the fundraising world, the averages I tend to come across aren’t very useful for describing the data due to the natural skewness involved in raw money given through charitable donations.  I’d like to talk about one particular kind of average that is quite useful: that of the logged times when my daughter has woken up, gone for a nap, or gone to sleep.

As you can see, the wonderful thing about the averages depicted in the above R graph is that the lines showing her sleep schedule each day go equally as much above as below the line, and they don’t deviate too far.  So, when describing what time she wakes up, goes for her second nap, and goes to sleep, the average is a fairly accurate description.

Of course we can go a step further and calculate the standard deviation of the morning wakeups and second nap times to say that she wakes up at 6:56am plus or minus 53 minutes, and goes to her second nap at 2:15pm plus or minus 1 hour 27 minutes, and then we have an even better idea what her behaviour is.

You can in fact see a baseline shift in her bed times after the 10 mark on the X axis.  This was when we started trying to get her to bed a bit early.  So from day 1 to 10, she was going to sleep at about 9:38pm, whereas from day 11 to 20, she was going to sleep at about 8:39pm.  Overall of course, this balances out to an average bedtime of 9:09pm.  Assuming of course we stick to her early sleep schedule, her sleep times will continue to vary near that 8:30pm mark.