Post on 12-Jan-2016
description
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
3
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.
7
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?