Visual Inspection of the Tips data

What you were told

This is data collected by one male waiter, at a suburban shopping mall restaurant, for a two and a half month period. The restaurant serves a varied menu.

What you learned from the histograms of tips

$1 barwidth

The shape of the data is skewed to the right, which says that there are more small tips, and fewer large tips.

It is unimodal with a peak at $1-2 and gradually falling off to the right. This says that there are more groups of diners that pay tips in the range $1-4. Assuming there is a relationship between tip and total bill this suggests that the total bills may be mostly $15-60 roughly. It suggests the restaurant is not an expensive one.

There are very few tips less than $1.

$0.50 barwidth

It is no longer unimodal but bi- or even tri-modal. There is more to the tipping habits than implied by the large barwidth of $1.

Also several very high tips are now apparent in the data. These are outliers, but from a waiting perspective these are the customers that you like!

$0.25 barwidth

It is clearly multimodal in shape now. There are large peaks at $2,3,4,5 which suggests that patrons have a habit of rounding their tips to the nearest dollar amount.

(Personal comment: I wonder if this behavior is different depending on whether the bill paid by credit card or cash.)

$0.10 barwidth

This is a very fine resolution plot. There are now secondary peaks visible at $1.50,2.50,3.50 which suggests rounding not just to the nearest dollar amount but many people round to the nearest 50c.

Also, it is clear that there are no tips recorded which are less than $1.

What you learned from the scatterplots of tip versus total bill

Tip versus Total Bill

There are more patrons that pay lower tips and lower total bills, and fewer and fewer spend at the high end, that is, it is skewed as we observed when looking at tips alone.

There are lines of points visible at the tips level of $2,3,4 and to the keen eye also at the $1.50,2.50,3.50 amounts. This says that same as what we learned from the histograms that patrons tend to round their tips to the nearest dollar or half dollar amounts.

There is also a lower bound of tip at $1.

There is a linear relationship between tip and total bill, as you might expect. If you eyeball the the trend it looks to be about 15%. But there are a lot more points below the diagonal than above, that is, more patrons tip below the recommended level of 15%than above.

Tip vs Total Bill by Sex of the Bill Payer

(Note: The scale on both plots is the same, to allow for direct comparison.)

There appear to be more bills paid by males.

There are more larger bills paid by males, but not too many. The larger tips/larger bills are paid by males.

The eyeballed slope looks higher for the males than for the females.

(Note that we don't have any more information on the remaining member s of the dining parties or even the size at this point, so we cannot tell whether the groups are dining together for business, as friends or for a romantic tete-a-tete. So we cannot infer whether a guy is trying to impress his girlfriend on their first date or a business colleague.)

Tip vs Total Bill by Sex of the Bill Payer and whether there was a Smoker in the Party or Not

Smokers plots show a lot more variability than the non-smokers. There is a little relationships between the total bill and the tip for smoking parties! (What are they smoking?)

Female non-smokers, with the exception of 3 low tippers are very consistent tippers as observed by the lack of variability.


Bryant and Smith, 1995
Bryant, P. G. and Smith, M. A. (1995). Practical Data Analysis: Case Studies in Business Statistics. Richard D. Irwin Publishing, Homewood, IL.
Fri Jan 16 11:07:21 CST 1998