Cogito
Probability and Statistics · Chapter 2 · Lesson 1
Mean, Median, and Mode
Three centres, and when each one lies.
12 problems · about 20 minutes · TEKS P.S.1.D, S-ID.A.2
What this lesson teaches
The student computes measures of centre and selects the appropriate one for a given distribution.
- The mean averages, the median takes the middle, and the mode is most frequent.
- The median resists outliers; the mean does not.
- A skewed distribution pulls the mean toward its tail.
Warm Up
Straightforward practice. Get the method working first.
5 problemsData 3, 7, 11. What is the mean?
Answer 7
Why 7.
Which measure of centre resists outliers?
Answer The median.
Why The median.
Data 2, 4, 6. Mean?
Answer 4
Why 12 ÷ 3.
Data 1, 3, 3, 7. Median?
Answer 3
Why Average the middle two.
Data 2, 5, 5, 5, 9. Mode?
Answer 5
Why The most frequent.
Build It Up
The same ideas with more to keep track of.
3 problemsData 10, 20, 30, 40. Mean?
Answer 25
Why 100 ÷ 4.
A distribution is skewed right. Is the mean above or below the median? 1 above, 2 below.
Answer 1
Why The tail drags the mean.
Which measure works for categorical data? 1 mean, 2 median, 3 mode.
Answer 3
Why You cannot order or average colours.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsSort each situation by which centre reports it best.
Answer Use the mean: Symmetric test scores, no outliers, Heights of a class · Use the median: House prices with a few mansions, Incomes in a small town
Why Extremes are what push you toward the median.
Data 5, 5, 5, 5. Mean?
Answer 5
Why They are all the same.
The Average: Data 4, 6, 8, 10, 12. What is the mean?
Answer 8
Why 8.
The Middle: Data 3, 5, 9, 11, 100. What is the median?
Answer 9
Why 9.