Box and Whiskers... Analyzing and Creating

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The students will be able to analyze and display their findings in a box plot

Big Idea

The students will be using discovery techniques to learn about box and whisker plots


10 minutes

The DO NOW is going to be a review of the measures of central tendency.  This will be a whole group discussion based upon the teacher scripted questions. (see questions)

The reason I chose to do this first was to get the students thinking about those measures and how they will relate to the box plots.  Box plots are great for showing median and range, however, they do not represent the mean or m ode.  It is possible to find the mean and mode by just looking at the raw data, but if the information is already in the chart then they won’t be able to find it.

Analyzing and Creating Box Plots

60 minutes

Begin the middle part of the lesson by explaining and displaying a box plot.  Allow students to make observations about what they see in the box plot.  Apply the definitions to the visual. (slide 4)

Next, using the teacher script, walk the students through how to construct the box plot using the table from slide 5. During the construction phase, ask the students how many values are in the lower half of the scores.(MP2)  Also, point out to students that box plots are good for comparing similar data very quickly but do not show individual values.  Before asking questions about the box plot, allow students to compare their charts.  All charts should look similar. Use teacher script to answer questions about their box plots.

Next, have students look at a box plot already made(slide 6).  Allow students time to make observations and talk about those observations with a tablemate.  Use teacher scripted questions to analyze this box plot (Christina’s scores)(MP 2)

After the discussion, you will need to rearrange your groups by ability.  I would do this in advance so that you aren’t scrambling around to move kids.  Tell the kids they are going to work with a new group of students today to create and analyze box plots.  Slide 7 goes through the group norms.  There are 6 team time questions.  Make one for each group.  The following is a breakdown by complexity for each problem

Question 1 (High) Students are asked to create 2 box plots and answer 4 higher level thinking questions

Question 2(High) Students are asked to create 2 box plots and make a comparison between the two

Question 3(Medium) Students are asked to create 2 box plots, but only looking for changes in measures of central tendency

Question4(Medium) Students are asked to create 2 box plots, but only looking for changes in measures of central tendency

Question 5(Low) Students are looking at 2 constructed plots and making any observations they can about the data

Question 6(Low) Students will need to create a box plot and make any observations they can about the data

Once students have had time to create or analyze their data, allow time for groups to present their findings.  Students should:

Read their question to the audience.

Have recorded results on large grid paper.

Talk mathematically about mean, median,mode, range ,quartiles, center, spread and shape.

Plus answer any questions given to them in the problem.

(MP7)  Making observations and applying previously learned information.


10 minutes

 In order to effectively prepare for the closing discussion, keep track of student responses during the team time activity and their presentations.


For example, 

Question 1: The students will be able to say that his number of points increased after the first 8 games.  That Brandon spent more time taking 3-point shots so he was more successful in making them. The median is the only measure of these that is shown on a box plot, so that is the only measure that will be shown between box plots of different data sets.  Box Plots drawn correctly showing the increase from 1.5 in the first 8 games to 6 for all 20 games. The quartiles and maximum values also increase as did the interquartile range.


Question 2:  Students will be able to identify the 5 number summary (7,9,11,13,14), draw two box plots, and answer by saying yes, the box plots show that this year’s seedlings are smaller than last years seedlings.  All 5 number summary values are less.


Question 3: 2 box plots shown.  Work supporting the mean increasing from 20.1 to 43.5 ft; the median increasing from 20 to 45 ft; the mode increasing from 20 to 47 ft.


Question 4: 2 box plots shown.  Work supporting the mean increasing from 4.5 to 5.8; the median increased from 5 to 6; the mode increased from 5 to  8


Question 5:   The students should present information about median, quartiles, interquartile range, variablility (shape, center, and spread)  They should be able to say that Class B scored higher than Class A.  The median score for class A was 43 and the median score for class B was 80.


Question 5:  the box plot drawn should include

Median  80

Lower quartile 62.5

Upper quartile 90

Minimum   45

Maximum  100


I would post the graphs around the room and ask questions about the 5 number summary?  When comparing two graphs, what would be important information to know? When is it a good idea to use a box plot?


This information can be used as whole class discussion or it can be turned in for evidence of student learning.