Cogito
Integrated Math 1 · Chapter 8 · Lesson 1
Summarising One Variable
Centre, spread, and shape.
12 problems · about 20 minutes · S-ID.A.2, S-ID.A.3
What this lesson teaches
The student summarises a data set with appropriate measures of centre and spread.
- The mean averages; the median takes the middle and resists outliers.
- Range uses the extremes; the IQR uses the middle half.
- Report a centre and a spread that are consistent with each other.
Warm Up
Straightforward practice. Get the method working first.
5 problemsData 6, 10, 14. What is the mean?
Answer 10
Why 10.
Which pairing is consistent?
Answer Median with interquartile range.
Why Median pairs with IQR.
Data 3, 5, 7. Mean?
Answer 5
Why 15 ÷ 3.
Data 2, 4, 6, 8, 20. Median?
Answer 6
Why The middle of five.
Data 5, 9, 14, 20. Range?
Answer 15
Why 20 − 5.
Build It Up
The same ideas with more to keep track of.
3 problemsQ1 = 6, Q3 = 15. IQR?
Answer 9
Why 15 − 6.
Which centre resists outliers? 1 mean, 2 median.
Answer 2
Why The middle value.
Which spread ignores the extremes? 1 range, 2 IQR.
Answer 2
Why It uses the middle half.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsSort each measure by which summary it belongs with.
Answer Goes with the mean: Standard deviation, Symmetric data · Goes with the median: Interquartile range, Skewed data
Why Pair resistant measures with resistant measures.
Data 10, 20, 30, 40, 50. Mean?
Answer 30
Why 150 ÷ 5.
The Mean: Data 4, 8, 12, 16. What is the mean?
Answer 10
Why 10.
The Median: Data 200, 210, 220, 230, 900. What is the median?
Answer 220
Why 220.