Displaying Numerical Data Using Box Plots

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Displaying Numerical Data Using Box Plots
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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. Challenge What would the
15th score have to be in order for the peanut
butter to have a mean rating of 63 points?
Min 34 points Max 89 points
Median 61.5 points Range 55 points
Interquartile range (IQR) 12 points
86 points
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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. Challenge What would the 15th
score have to be in order for the peanut butter
to have a mean rating of 63 points?
Min 34 points Max 89 points
Median 61.5 points Range 55 points
Interquartile range (IQR) 12 points
86 points
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Launch Whole Class
A box plot is one of the ways this data can be
displayed.
34 40 52 57 57 60 60
63 67 69 69 71 71 89
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Launch Whole Class
Example of a box plot
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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.
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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?
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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?
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Five-Number Summary Minimum Lower Quartile
(Q1) Median Upper Quartile (Q3) Maximum
Median 61.5
34 40 52 57 57 60 60
63 67 69 69 71 71 89
Minimum
Upper Quartile (Q3)
Lower Quartile (Q1)
Maximum
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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?
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Launch Notes
Once you have found the five-number summary,
follow these steps to make a box plot1. Write
the data in order from least to greatest2. Draw
a number line that can show the data in equal
intervals3. Mark the median4. 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 quartile9. Draw a vertical line
through the median inside the box10. Draw two
horizontal lines ("whiskers") from the rectangle
to the extremes (minimum and maximum)
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Copy in your journal
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Explore Class Challenge!

• In your head, estimate the NUMBER OF HOURS you
  spend
• using electronics in ONE WEEK
  . -TV -Computer -Video Games, etc.
• On the paper in front of you, in large writing,
  write your estimate.
• 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.

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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
• Using the data, independently find the
  five-number summary
• in your notes
• 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
Lets compare your box plot with a box plot that
was created using an applet!
Online Tool
Agenda
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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.
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2
3
Agenda
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Practice

• About what percent of the data values fall in the
  following interval?
• after the upper quartile

25
Agenda
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Practice

• About what percent of the data values fall in the
  following interval?
• before the median

50
Agenda
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Practice

• About what percent of the data values fall in the
  following interval?
• after the median

50
Agenda
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Practice

• About what percent of the data values fall in the
  following interval?
• in the box (between the upper and lower
  quartiles)

50
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
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Practice

• About what percent of the data values fall in the
  following interval?
• after the lower quartile

75
Agenda
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Practice

• About what percent of the data values fall in the
  following interval?
• between the median and the upper quartile

25
Agenda
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Practice

• About what percent of the data values fall in the
  following interval?
• between the median and the lower quartile

25
Agenda
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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. 25
B. 27 C. 29 D. 31
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. 38F to 54F
B. 38F to 81F C. 54F to 72F D. 54F to
81F
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. Dumonts plot, what is the
interquartile range of the numbers of students
enrolled in foreign language classes? A. 5 C.
30 B. 15 D. 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
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Assessment
True or False?
If there are 30 students in the class, at least
10 scored above 80.
False
Agenda