Transcript Document

Displaying Numerical Data Using
Box Plots
1
Warm Up
OBJECTIVE: SWBAT display numerical data using box plots.
Language Objective: SWBAT use content specific vocabulary to
describe all parts of a box plot to a partner.
A group of taste testers reviewed a brand of natural peanut butter.
They gave the peanut butter a rating of 0-100 points depending on its
quality. The ratings are below:
34
40
52
57
57
60
60
63
67
69
69
71
71 89
Find the minimum, maximum, median, range, and interquartile
range (IQR) for this set of data.
Min = 34 points
Max = 89 points
Interquartile range (IQR) = 12 points
Median = 61.5 points
Range = 55 points
Challenge: What would the 15th score have to be in order for the peanut
86 points
butter to have a mean rating of 63 points?
2
Warm Up
OBJECTIVE: SWBAT display numerical data using box plots.
Language Objective: SWBAT use content specific vocabulary to
describe all parts of a box plot to a partner.
A group of taste testers reviewed a brand of natural peanut butter.
They gave the peanut butter a rating of 0-100 points depending on its
quality. The ratings are below:
IQR = Q3 – Q1
34
40
52
57
57
60
60
63
67
69
69
71
71 89
Find the minimum, maximum, median, range, and interquartile
range (IQR) for this set of data.
Min = 34 points
Max = 89 points
Interquartile range (IQR) = 12 points
Median = 61.5 points
Range = 55 points
Challenge: What would the 15th score have to be in order for the
peanut butter to have a mean rating of 63 points? 86 points
3
Launch
Whole Class
A box plot is one of the ways this data can be
displayed.
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40
52
57
57
60
60
63
67
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69
71
71
89
Launch
Example of a box plot:
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Whole Class
Launch
Vocabulary
Box Plot:
A graph that uses a rectangle (box) to represent the
middle 50% of a set of data and “whiskers” at both
ends to represent the remainder of the data.
6
Launch
Turn-and-talk
A box plot is constructed from the five-number summary of a set
of data.
Using the graph and what you know about range and interquartile
range, what do you think the five-number summary consists of?
7
Launch
Turn-and-talk
A box plot is constructed from the five-number summary of a set
of data.
Using the graph and what you know about range and interquartile
range, what do you think the five-number summary consists of?
8
Five-Number Summary
Minimum
Lower Quartile (Q1)
Median
Upper Quartile (Q3)
Maximum
34
40
52
57
57
Median = 61.5
60
Minimum
63
67
69
69
71
71
89
Upper Quartile (Q3)
Lower Quartile (Q1)
9
60
Maximum
Launch
Think-Pair-Share
The box plot below shows how the five-number summary corresponds to the
box and whiskers of the box plot.
Based on the figures above, how do you make a box plot using the five-number
summary?
10
Launch
Notes
Once you have found the five-number summary, follow these
steps to make a box plot:
1. Write the data in order from least to greatest
2. Draw a number line that can show the data in equal intervals
3. Mark the median
4. Mark the median of the upper half (the upper quartile, or Q3)
5. Mark the median of the lower half (the lower quartile, or Q1)
6. Mark the maximum (the greatest number)
7. Mark the minimum (the lowest number)
8. Draw a box between the lower quartile and the upper quartile
9. Draw a vertical line through the median inside the box
10. Draw two horizontal lines ("whiskers") from the rectangle to
the extremes (minimum and maximum)
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Copy in your journal
12
Explore – Class Challenge!
1) In your head, estimate the NUMBER OF HOURS you spend
using electronics in ONE WEEK .
-TV
-Computer
-Video Games, etc.
2) On the paper in front of you, in large writing, write your
estimate.
3) Without talking, form a line from least to greatest in the
front of the room. Hold your estimates in front of you for
people to see.
13
Explore
Number of hours per week 6th graders spend using electronics.
Write all the numbers in order on the board.
To Do:
1) Quietly return to your seat
2) Record the information above in your notes
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Explore –
Next Steps:
1) Using the data, independently find the five-number summary
in your notes
2)Compare your five-number summary with your partner.
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Answer in Journal
Questions to discuss:
-Based on the data that we collected, how much time
does the typical student spend using electronics weekly?
-When are box plots useful? For example, why would
someone choose to create a box plot instead of a bar
graph?
Agenda
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Explore
Whole Class
Let’s compare your box plot with a box plot that was
created using an applet!
Online Tool
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Agenda
Practice
The five-number summary divides a data distribution into four
parts.
In this activity you will have to decide what percent of the data
values fall in given intervals.
1
2
3
4
Agenda
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Practice
About what percent of the data values fall in the
following interval?
• after the upper quartile
25%
Agenda
19
Practice
About what percent of the data values fall in the
following interval?
• before the median
50%
Agenda
20
Practice
About what percent of the data values fall in the
following interval?
• after the median
50%
Agenda
21
Practice
About what percent of the data values fall in the
following interval?
50%
•in the box (between the upper and lower quartiles)
Agenda
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Practice
About what percent of the data values fall in the
following interval?
• before the upper quartile
75%
Agenda
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Practice
About what percent of the data values fall in the
following interval?
• before the lower quartile
25%
Agenda
24
Practice
About what percent of the data values fall in the
following interval?
• after the lower quartile
75%
Agenda
25
Practice
About what percent of the data values fall in the
following interval?
25%
• between the median and the upper quartile
Agenda
26
Practice
About what percent of the data values fall in the
following interval?
25%
• between the median and the lower quartile
Agenda
27
Assessment
Ms. Simmons made the box-and-whisker plot below to show some statistics
about the ages of the students in her class at a community college.
Which of the following best represents the median age of the students in her
class?
A.
B.
C.
D.
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Agenda
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Assessment
The box-and-whisker plot below shows the distribution of the daily high
temperatures, in degrees Fahrenheit, in the town of Clifton during the year 2004.
Based on the box-and-whisker plot, in which of the following intervals of
temperatures is it most likely that exactly 50% of the daily high temperatures are
located?
A.
B.
C.
D.
38°F to 54°F
38°F to 81°F
54°F to 72°F
54°F to 81°F
Agenda
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Assessment
Ms. Dumont kept a record of the numbers of students enrolled in foreign
language classes at Central High School during the past 20 years. She
used her data to make the box-and-whisker plot shown below.
Based on Ms. Dumont’s plot, what is the interquartile range of the
numbers of students enrolled in foreign language classes?
A.
B.
5
15
C.
D.
30
50
Agenda
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Assessment
A community center offers classes for students. The range of the number of
students in each class is 13. The median number of students in each class is 9.
Which of the following box-and-whisker plots could represent the numbers of
students in the classes?
Agenda
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Assessment –
True or False?
The class median is less than 80.
True
Agenda
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Assessment –
True or False?
Half the class scored between 60 and 80.
True
Agenda
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Assessment –
True or False?
At least one student earned a score of 100.
True
Agenda
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Assessment –
True or False?
The class mean is probably less than the median.
True
Agenda
35
Assessment –
True or False?
If there are 30 students in the class, at least 10 scored
above 80.
False
Agenda
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