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My wife is a server at a restaurant and I've been tracking her tips over the last 9-10 months. The domain of her set is $[\$75,\$702]$ with a mean of \$236.7 and a standard deviation of \$106.64. Because of the small amount of data (206 total days of tips) in comparison to the number of possibilities she could make, I plotted the data in histogram form with classes of \$20.

My thoughts on this is that the data is approximately distributed skewed normally because of the type of data. With 206 data points, I wanted to try graphing a trendline over the histogram in order to match the histogram to an actual function and see if the distribution's pdf holds over another year of income. The problem is I have no idea how to do this. I've been looking over the internet all morning, and the more I read, it seems that a skewed normal distribution in excel is difficult with a real data set. Also, the trendlines available are the usual elementary functions: polynomial, exponential, logarithmic, linear, etc., and there seems to be no indication on how to add a trendline of a distribution (not sure that is even possible, perhaps there's a package I can upload or something...) How can I go from here to discover a distribution of the data?

Eleven-Eleven
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  • Ultimately, the question of relevance to you concerns comparing two empirical distributions. This is a popular topic here, with many answers available: please [search our site](http://stats.stackexchange.com/search?q=compare+distribution) and read over any threads that might appear relevant. You might also consider viewing your data in a different way: as a [tag:time-series], in which you retain the information about when each tip was received. Time series analysis provides models and methods to track your data and (to an extent) forecast future values. – whuber Jan 12 '14 at 17:19

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First, I am not sure what you mean by "skewed normal" - by definition a normal distribution is not skewed.

Second, using Excel to do statistics isn't the greatest. It's a spreadsheet. If you're going to do things like this, I suggest downloading R (it's free) and playing.

Third, to me "trendline" implies trend over time. Do you want to track tips over time? Or is that just some odd terminology? I will assume the latter.

Fourth, money data is very often skew and, often, a good solution is to take logs of the data and plot those. Your wife's case appears to be one of these, from what you've shown us. At least, the maximum is much farther from the mean than the minimum could be (you didn't tell us the lowest, but the theoretical minimum is $0. I don't use Excel much, but surely you can take logs and plot those. Can you plot a loess or other smooth line in Excel? (But the log data may be close to normal). You should also look for outliers (extreme data points).

Peter Flom
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  • The histogram looks like it could be approximately normal, but it is definitely "skewed" to the left. The reason I said trendline is excel has that trendline option. You are right to assume I'm not using it in the correct sense. I thought that I might be able to find a continuous analog for the histogram and overlay that onto the data. Finally, I took a computational stats class in college a couple of years ago and used R, but it's been a while since I've used it. I suppose I could go back and relearn it... – Eleven-Eleven Jan 12 '14 at 13:52
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    R has a learning curve, so it depends on whether you are going to do more playing with statistics. Histograms are dangerous for assessing shape - changing the bin or starting value can change the appearance of the distribution quite a bit. See [this thread](http://stats.stackexchange.com/questions/51718/assessing-approximate-distribution-of-data-based-on-a-histogram/51753#51753) for more about histograms. A density plot of some sort is probably what you want. – Peter Flom Jan 12 '14 at 14:36
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    That's great! I'm a high school math teacher so I'm always interesting in learning new things; programs, methods, etc. I studied statistics in college to become an actuary, so I have a pretty good knowledge of the basics, but t's been a while so relearning shouldn't be that difficult. I appreciate the help. – Eleven-Eleven Jan 12 '14 at 15:23