Virginia SOL Math / Grade 8 / Probability & Statistics

8.PS.2

Boxplots

What you'll learn

  • Represent data using a boxplot
  • Find the five-number summary of a data set
  • Analyze and compare data using boxplots

Words to know

Boxplot —
a graph showing the five-number summary of data
Median —
the middle value of an ordered data set
Quartile —
a value dividing data into four equal parts
Interquartile range —
the difference between the third and first quartiles
Range —
the difference between the greatest and least values

Why it matters Boxplots summarize how data spread out and clump together, making it easy to compare two groups at a glance.

Worked examples

Model ItI do

Find the five-number summary of 2, 4, 6, 8, 10, 12, 14.

The minimum is 2 and the maximum is 14. The median is the middle value, 8. The lower half is 2, 4, 6 with median Q1 = 4; the upper half is 10, 12, 14 with median Q3 = 12. Summary: 2, 4, 8, 12, 14.

Try It TogetherWe do

Using that summary, find the interquartile range and range.

The interquartile range is Q3 minus Q1 = 12 - 4 = 8. The range is maximum minus minimum = 14 - 2 = 12.

Now YouYou do

Find the median of the data set 5, 7, 9, 11, 13.

Order the data and locate the middle value. Check your answer in the back of this chapter.

Practice

Mastered 0 of 11

Warm-up

Ease in with the basics.

  1. 1.Find the median of 4, 8, 12, 16, 20.

  2. 2.Find the range of 5, 9, 14, 20.

  3. 3.If Q1 = 8 and Q3 = 20, what is the interquartile range?

On Level

The core Quick Check from the book.

  1. 1.Find the median of 3, 6, 9, 12, 15.

  2. 2.Find Q1 for the ordered data 1, 3, 5, 7, 9, 11.

  3. 3.Find the range of 4, 8, 15, 16, 23, 42.

  4. 4.If Q1 = 10 and Q3 = 25, what is the interquartile range?

  5. 5.How many values does a five-number summary contain?

Challenge

Stretch your thinking.

  1. 1.Find the five-number summary of 3, 5, 7, 9, 11, 13, 15, 17.

  2. 2.A boxplot has minimum 10, Q1 = 15, median 22, Q3 = 30, maximum 40. Find the interquartile range and the range.

  3. 3.Two boxplots compare Class A (median 75) and Class B (median 82). Which class had higher typical scores, and what does the median tell you?