1.3 Five Number Summaries and Box Plots

Slide 1- 1

A small class of 9 students took a math test. Using the

information below, find 9 possible test scores that would

work.Lowest Score: 47Range: 46Mean: 75Median: 81Mode: 91

Write your test scores in numerical order. Show your work

and explain how you got your answer.

DISCOVERING ALGEBRA 1.3

Five-number summaries and box plots

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Five number summary

• Minimum: lower extreme (lowest number)

• First Quartile: (Q1) lower quartile, bottom 25%

• Second Quartile: (Q2) Median, 50%

• Third Quartile: (Q3) Upper quartile, top 75%

• Maximum: upper extreme (biggest number)

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Example(Finding the 5 number summary)

• Below are the divorce rates in the following countries

Country Divorce rate (per 1,000 people

Austria 2.0

Denmark 3.0

Finland 2.9

France 1.9

Germany 2.0

Hungary 2.4

Italy 0.4Netherlands 1.9

Norway 2.2

Poland 1.3

Sweden 2.2Switzerland 2.0United Kingdom

2.9

US 4.8

Step 1: Put numbers in order

Ordered List

0.4, 1.3, 1.9, 1.9, 2.0, 2.0, 2.0, 2.2, 2.2, 2.4, 2.9, 2.9, 3.0, 4.8

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Step 2: Find the Min

Step 3: Find the Max

Step 4: Find Q2 (Median)

Step 5: Find Q1 (25 percentile)

The five number summary is:

min = 0.4

Q1 = 1.9

Q2 = 2.1

Q3 = 2.9 Range = 4.4

max = 4.8 IQR = 1Step 6 : Find Q3 (75 percentile)

MIN = 0.4 Q1 = 1.9Q2 = 2.1

Q3 = 2.9 MAX = 4.8

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Constructing box and whisker plots

• A box and whisker plot (sometimes called a boxplot) is a graph that presents information from a five-number summary.

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Box Plot for Divorce Rates

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5

MIN MAX

Q2

Q1 Q3

What is the five-number summary for the following data set?Chicago Bulls Total

points scored

Michael Jordan 2357

Toni Kukoc 984

Scottie Pipen 841

Ron Harper 764

Luc Longley 663

Scott Burrell 416

Chicago Bulls Total points scored

Steve Lerr 376

Dennis Rodman 375

Randy Brown 288

Jud Buechler 198

Bill Wnnington 167

Slide 1- 8

Draw a box plot for the five-number summary for the Bulls.

Slide 1- 9

What do you observe in the data set?

Why is this type of graph sometimes called a box-and-whisker plot?