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# 6-D-1-3

last edited by 2 years, 7 months ago

6.D.1.3  Create and analyze box and whisker plots observing how each segment contains one quarter of the data.

In a Nutshell

This will be student’s first experience with analyzing box and whisker plots.  Box and whisker plots are a visual representation of data sets divided into quartiles. Understanding of median is necessary for accurate construction of the plot. Box and whisker plots are used to represent the shape and spread of a data set and are based upon a five number summary.  To find the needed information, first order the data and find the median.  The median will separate the data into two halves.  In order to further separate the data into quartiles, find the median of the lower half of data (first quartile) and the median of the upper half of data (third quartile).  These three points will create the middle “box”.  Find the data minimum and maximum (whiskers)  and this will complete the five number summary.  Discussion of proportionality and percent supports the idea of equal fourths of data points, not equal fourths between the upper and lower numbers (the range is not divided by four to find the quartiles).

## Teacher Actions

• Develop conceptual understanding through large or small group discussion when interpreting data presented in a box and whisker plot.

• Model data sets by creating many different box and whisker plots.

• Develop conceptual understanding by identifying and interpreting the proportion of the data represented by each quartile.

• Develop mathematical reasoning when analyzing the data to show how percents and proportional thinking can be applied to the box and whisker plot (one fourth or 25%, of the total data points are contained in each).

• Pose purposeful questions that will engage students in discussion about the statistics shown by the box and whisker plot (Ex: How can you tell if the data is skewed?)

• Implement tasks that promote reasoning by using evidence of student thinking through discussion and evaluation of box and whisker plots.

• Develop procedural fluency by providing students opportunity to work with multiple box and whisker plots using a variety of data sets.

## Misconceptions

• Box and whisker plots show the shape and spread of data within a set.

• Box and whisker plots have three components: a box that contains the “middle half” of the data with ends at the upper and lower quartile; a line inside the box representing the median; and a line extending from the box to the lower and upper extremes of the data.

• To construct the box, the data set median must be found, then the median of the upper and lower halves is found to determine the upper and lower quartiles.

• Each quartile represents one fourth of the data points using median.

• Quartile ranges do not have to be equal, but they do contain the same number of data points.

• Forget to order data points before finding the median of the set.

• Believe that a longer portion of the plot has more data in that range.

• Think that the minimum and maximum values are no longer considered in the data set as they are not attached to the box.

OKMath Framework Introduction