Summarizing Numerical Data

STAT 20: Introduction to Probability and Statistics

Why are measures of spread so important? Consider the following question.

There are two new food delivery services that open in Berkeley: Oski Eats and Cal Cravings. A friend of yours that took Stat 20 collected data on each and noted that Oski Eats has a mean delivery time of 29 minutes and Cal Cravings a mean delivery time of 27 minutes. However, one is more predictable than the other….

So: which would would you rather order from, and why? Debate with your group.

• Most people probably prefer Oski Eats.
  • It’s slightly slower, but more consistent.
  • There’s zero chance of having to wait 40+ minutes for your food.
• You could also prefer Cal Cravings! If either:
  1. You like to gamble
  2. You are in a rush. If you have to leave in 20 minutes, Cal Cravings is the only one who has ever delivered that fast. It still probably won’t get there in time, but if you use Oski Eats it definitely won’t won’t get it in time.

Activity: mean, median, mode – which is best?

It depends on 1) your data, and 2) what you want your “summary” to speak to.

Get out a piece of paper. You’ll be watching a 3 minute video that discusses characteristics of a typical human. Note which numerical summaries are used and what for.

After the video, you can write on the board each of mean, median, mode and have students list measures that were reported. There are many modes because lots of the data that they collect is categorical.

General Advice

1. Means are often a good default for symmetric data.

2. Means are sensitive to very large and small values, so can be deceptive on skewed data. > Use a median

3. Modes are often the only option for categorical data.

Worksheet: Summarizing Numerical Data

25:00

Break

05:00

Lab: Computing on the Data

25:00