Data Exploration: Menu Prices Cont.

Now, create a five-number summary for the dinner prices.

Let’s analyze the data we just discovered.

The price range at the downtown restaurants is wide, from [latex]$7[/latex]  to [latex]$47[/latex] per plate.

We can easily see in the histogram that most places charge [latex]$8[/latex] – [latex]$15[/latex] on average. But since these average prices, we don’t really have information about the individual ranges at each restaurant. We see that we have one very extreme value of [latex]$47[/latex] per plate. It would be interesting to find out how many and how expensive that restaurant truly is (or is one extremely pricey dinner, say surf and turf at market prices, pulling the mean up there?). We also might wonder about the three restaurants with average dinner plates of [latex]$7[/latex]. Are they factoring in the kids menu or a senior menu at a very casual sandwich shop to bring the average cost down? Or are there a couple of hot dog vendors with permanent corner spots? Not being able to answer those questions without further study, we can at least safely report an array of [latex]19[/latex] affordable places to eat downtown.

Note the skewness of [latex]1.72[/latex] in the list of descriptive statistics. We could have know just by looking at that that we had an outlier present. Any skewness over [latex]1[/latex] is at least fairly significant. But we can also see that the median value is [latex]12.5[/latex] while the mean is [latex]15.5[/latex].

The standard deviation of the data at [latex]9.87[/latex] tells us that the average plate varies from the center by about [latex]$10[/latex]. The spread lets us know that dining options downtown are are highly variable. So, we could say that a diner without a plan could reasonably expect to pay between [latex]$7[/latex] (maybe for a corner hot dog) and [latex]$22.50[/latex] for a restaurant experience. Of course, they could always spring for lobster and a filet.

Great job exploring the menu price data. Hopefully, you now see the benefit of using spreadsheets when analyzing data. While it is good to know how to analyze the data yourself, a spreadsheet can be really helpful with large number sets.