box-and-whisker plots
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Box-and-Whisker Plots. Making and Interpreting Box-and-Whisker Plots. Becky AfghaniLBUSD Math Office2003. You will:. Construct and Interpret Box and Whisker Plots. What is a Box-and Whisker Plot?. Suppose you have a large set of data and want to know how it is distributed. - PowerPoint PPT PresentationTRANSCRIPT
Box-and-Whisker Plots
Making and Interpreting Box-and-Whisker Plots
Becky Afghani LBUSD Math Office 2003
You will:Construct and
InterpretBox and Whisker Plots
What is a Box-and Whisker Plot?
• Suppose you have a large set of data and want to know how it is distributed.
• Think of a teacher’s class set of test scores.
• A box-and-whisker plot displays the median, the quartiles, and the greatest and least values.
Why use a Box-and Whisker Plot?
• The box-and-whisker plot is a visual way to show the data.
• The median and quartiles can easily be read.
• The shape of the box and the whiskers gives information about how the numbers are spread out.
Who uses Box-and Whisker Plots?
• Scientists who perform experiments display their results using box-and-whisker plots.
• Medical researchers display their findings using box-and-whisker plots.
• Anyone who reads a scientific report needs to understand how a box-and-whisker works.
We will make a Box-and Whisker Plot
Here are all of the test scores from your class on the last math test.
(Not really!)
87 75 83 94 10074 68 98 99 8583 100 72 68 100
You will need a five-number summary in order to construct the box-and-
whisker plot.Minimum
Lower quartile (Q1)Median (Q2)
Upper quartile (Q3)Maximum
?????
Step 1: Write the data in order from least to greatest.
87 75 83 94 10074 68 98 99 85
83 100 72 68 100
68, 68, 72, 74, 75, 83, 83, 85, 87, 94, 98, 99, 100, 100, 100
Step 2: Find the minimum and maximum values of the
data.68, 68, 72, 74, 75, 83, 83, 85, 87, 94, 98, 99, 100, 100,
100
minimum The minimum is 68.maximumThe maximum is 100.
The 5 number SummaryMinimum1st (lower) quartileMedian(2nd Q)3rd (upper) quartileMaximum
Tell your neighbor how to find the minimum and
maximum.To find the
maximum...To find theminimum...
Step 3: Find the median of the data.
68, 68, 72, 74, 75, 83, 83, 85, 87, 94, 98, 99, 100, 100, 100
7 in the upper half
7 in the lower half
1 in the middle
The median is 85.
The 5 number SummaryMinimum 681st (lower) quartileMedian(2nd Q)3rd (upper) quartileMaximum
Tell your neighbor how to find the median.
To find themedian...
Step 4: Find the lower quartile (Q1) of the data.
68, 68, 72, 74, 75, 83, 83, 85, 87, 94, 98, 99, 100, 100, 100
upper halflower half
The middle number is not in the lower or
upper half.
Step 4: Find the lower quartile (Q1) of the data.
68, 68, 72, 74, 75, 83, 83, 85, 87, 94, 98, 99, 100, 100, 100
upper halflower half
The lower quartile is 74.
Choral Response: What is the lower quartile?
The median ofthe lower half
The median ofthe lower half
The median ofthe lower half
The median ofthe lower halfThe median of
the lower half
Step 5: Find the upper quartile (Q3) of the data.
68, 68, 72, 74, 75, 83, 83, 85, 87, 94, 98, 99, 100, 100, 100
upper halflower half
The middle number is not in the upper or
upper half.
Step 5: Find the upper quartile (Q3) of the data.
68, 68, 72, 74, 75, 83, 83, 85, 87, 94, 98, 99, 100, 100, 100
upper halflower half
The upper quartile is 99.
Choral Response: What is the upper quartile?
The median ofthe upper half
The median ofthe upper half
The median ofthe upper half
The median ofthe upper halfThe median of
the upper half
Now that we have our five-number summary, we can
construct the box-and-whisker plot.Minimum
Lower quartile (Q1)Median (Q2)
Upper quartile (Q3)Maximum
68748599
100
Write in Your Notes:What are the five items in
the five number summary?
I can thinkof one...
I bethe knows!
Step 6: Draw a number line that can show the data.
68, 68, 72, 74, 75, 83, 83, 85, 87, 94, 98, 99, 100, 100, 100
50 60 70 80 90 100
Step 7: Mark the minimum, maximum, median and both quartiles on the number line.
50 60 70 80 90 100
MinimumLower quartile (Q1)
Median (Q2)Upper quartile (Q3)
Maximum
68748599100
Step 8: Draw a box between the lower and upper
quartiles.
50 60 70 80 90 100
MinimumLower quartile
(Q1)Median (Q2)Upper quartile (Q3)
Maximum
68748599
100
Step 9: Draw a vertical line through the median.
50 60 70 80 90 100
MinimumLower quartile
(Q1)Median (Q2)Upper quartile (Q3)
Maximum
68748599
100
Step 10: Draw two “whiskers” from the quartiles
to the minimum and maximum.
50 60 70 80 90 100
MinimumLower quartile
(Q1)Median (Q2)Upper quartile (Q3)
Maximum
68748599
100
Interpreting the box-and-whisker plot
50 60 70 80 90 100
Remember these are test scores.
25% of the test scores are in each whisker and each section of the box.
25% 25% 25% 25%
Find the false statement.
50 60 70 80 90 100
68 74 85 99100
A) One fourth of the test scores were between 85 and 99.
B) One half of the test scores were between 74 and 99.
C) One half of the test scores were between 85 and 100.
D) Three fourths of the test scores were between 68 and 85.
Make another box-and-whisker plot from this
data:Age at First Inauguration of
American Presidents from 1900 to 1999
456
2 3 61 1 1 2 4 4 5 5 6 60 1 2 4 942 is 42
years
Minimum and Maximum
42 is the minimum
69 is the maximum
Age at First Inauguration of American Presidents from 1900 to
1999456
2 3 61 1 1 2 4 4 5 5 6 60 1 2 4 942 is 42
years
MedianAge at First Inauguration of
American Presidents from 1900 to 1999
456
2 3 61 1 1 2 4 4 5 5 6 60 1 2 4 942 is 42
years
How manydata itemsare there?
18 items
What ishalf of 18?
9th item
10th item
?
What ishalfwaybetween
54 and 55?
54.5 is the median
Lower QuartileAge at First Inauguration of
American Presidents from 1900 to 1999
456
2 3 61 1 1 2 4 4 5 5 6 60 1 2 4 942 is 42
years
54.5
How manyitems are
in the lowerhalf?
9 itemsWhich item
is in themiddle?
The 5th item
51 is the lower
quartile
Upper QuartileAge at First Inauguration of
American Presidents from 1900 to 1999
456
2 3 61 1 1 2 4 4 5 5 6 60 1 2 4 942 is 42
years
54.5
How manyitems are
in the upperhalf?
9 itemsWhich item
is in themiddle?
The 5th item
60 is the upper
quartile
The Box-and-Whisker Plot
40 50 60 70
Age at First Inauguration of American Presidents from 1900 to 1999
456
2 3 61 1 1 2 4 4 5 5 6 60 1 2 4 9
42 is 42 years
54.5
Find the false statement.
A) The oldest president at his inauguration was 69.
B) One fourth of the presidents were 60 or over when inaugurated.
C) One half of the presidents were inaugurated between ages 50 and 60.D) The youngest president to be inaugurated in the 1900s was 42.
40 50 60 70
Multiple Box-and-Whisker Plots Can Be Used to Compare Data
0 10 20 30 40 50 60 70 80 90 100
Average Monthly High Temperatures in Anchorage, Alaska
0 10 20 30 40 50 60 70 80 90 100
Average Monthly High Temperatures in Long Beach, California
Describe the variability between the data sets and compare the two 5 number summaries
Find the false statement.
A) The range of average monthly high temperatures is broader in Anchorage than in Long Beach.
B) The average monthly high temperatures in Long Beach are warmer than Anchorage.C) Half of the average monthly highs in Long Beach are between 27 and 59 degrees.
0 10 20 30 40 50 60 70 80 90 100
Average Monthly High Temperatures in Anchorage, Alaska
0 10 20 30 40 50 60 70 80 90 100
Average Monthly High Temperatures in Long Beach, California
In your notes...1. List the five items
required for a box-and-whisker plot.
2. Write a short description for each.