Cogito
Algebra 2 · Chapter 8 · Lesson 2
Reading a Box Plot
Five numbers that describe a whole data set.
11 problems · about 22 minutes · S-ID.A.1, S-ID.A.2
What this lesson teaches
The student reads a five-number summary from a box plot and compares distributions.
- A box plot shows five numbers: minimum, Q1, median, Q3, and maximum.
- Each of the four regions holds a quarter of the values, however wide it looks.
- The IQR measures the middle half and ignores the extremes.
Warm Up
Straightforward practice. Get the method working first.
4 problemsQ1 = 4, Q3 = 15. IQR?
Answer 11
Why 11.
Q1 = 10, Q3 = 22. IQR?
Answer 12
Why Subtract.
What percent of values lie below the median?
Answer 50
Why Half.
What percent lie above Q3?
Answer 25
Why One quarter.
Build It Up
The same ideas with more to keep track of.
3 problemsDoes a wider region hold more values? 1 for yes, 0 for no.
Answer 0
Why Every region holds a quarter.
How many numbers make up the five-number summary?
Answer 5
Why It is in the name.
Sort each statistic by whether raising the largest value changes it.
Answer It moves: Maximum, Mean · It stays put: Median, Q1
Why Anything computed from every value will move.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsMin 2, max 30. What is the range?
Answer 28
Why Max − min.
Does the IQR use the extremes? 1 for yes, 0 for no.
Answer 0
Why Only the middle half.
The Spread: Q1 = 5 and Q3 = 13. What is the IQR?
Answer 8
Why 8.
The Share: What percent of values lie between Q1 and Q3?
Answer 50
Why 50%.