Algebra 1Lesson Notes13.8 ______
Objective: Interpret box-and-whisker plots.
box-and-whisker plot: a data display the organizes the data into four groups.
The median of the data splits the data in half.
The lower quartile, the median of the lower half, creates two groups.
The upper quartile, the median of the upper half, creates two groups.
5-number-summary: minimum value, lower quartile, median, upper
quartile,and maximum value.
To create a box-and-whisker plot, plot the 5-number-summary below the number line. Draw boxes around the three middle values and whickers to the end values.
Example 1 (p 887): Make a box-and-whisker plot
The prices (in $) of 27-inch televisions at an electronics store are given below. Make a box-and-whisker plot of the prices.
188 225 192 239 271 286 224 334 924 875 1110
An advantage of a box-and-whisker plot is that you can talk about 25%, 50%, and 75% of the data falling in particular intervals and you see how big the spread is for each interval.
The difference between the lower and upper quartiles is called the interquartile range.
A disadvantage of a box-and whisker plot is that you lose most of the detail data. The only
values you are sure to have are the maximum and minimum (which enable you to calculate
the range).
outlier: a value that is widely separated from the rest of the data.
(exceeds the upper quartile by more than 1.5 times the interquartile range or is less than
the lower quartile range by more than 1.5 times the interquartile range.)
Outliers distort the mean, are visible on stem-and-leaf plots, can be reflected in
histograms, and distort box-and-whisker plots.
Example: Create a box-and-whisker plot with outlier data
The prices (in $) of refrigerators at home supple store are given below. Make a box-and-whisker plot of the prices. Describe the plot.
450 1800 550 500 600 800 2200 1200 1400 2400 2600 7200
Find the mean of the data.
Identify the outlier.
Eliminate the outlier, then find the mean of the data.
How do the values compare?
Example 2 (p 888): Interpret a box-and-whisker plot
Are the following statements true or false about the two sets of data? Explain.
The median of set A is greater than the median of set B.
The range of set A is greater than the range of set B.
The interquartile range of set A is greater than the interquartile range of set B.
More values fall in the upper quartile of set A than fall in the lower quartile of set A.
The same number of values fall in the boxes of set B as fall in the whiskers of set B.
Set A contains more pieces of data than set B.
For set B, 75% of the values are less than or equal to 101.
Both sets of data contain a data value of 120.
60 is not a data value for either set A or set B.
Set A is more likely to contain an outlier.
At least 25% of the data in set A is less than the minimum value forSet B.
HW: A8a pp883-885 #3, 4, 8-12, 16-19
A8b Lesson 13.8 Practice B
Prepare for Quiz 13.6-13.8
fms-Algebra 1 Lesson Notes 13.8 Last printed 1/21/2007 9:15:00 PMPage 1 of 3