1. Analyzing One-Variable Data1
Analyzing One-Variable Data
Lesson 1.8
Summarizing Quantitative Data:
Boxplots and Outliers

2. Boxplots and Outliers Use the 1.5 x IQR rule to identify outliners.
Make and interpret boxplots of quantitative data.
Compare distributions of quantitative data with boxplots.

3. Boxplots and Outliers
Barry Bonds set the major league record by hitting 73 home runs in a single season in The dotplot below shows the number of home runs that Bonds hit in each of his 21 complete seasons:
Bonds’s 73 home run season stands out (in red) from the rest of the distribution. Should this value be classified as an outlier?

4. Boxplots and Outliers
Besides serving as a measure of variability, the interquartile range (IQR) is used as a ruler for identifying outliers.
The 1.5 x IQR Rule
Call an observation an outlier if it falls more than 1.5 × IQR above the third quartile or below the first quartile. That is,
Low Outliers < Q1 –1.5 × IQR
High Outliers > Q × IQR

5. Boxplots and Outliers
It is important to identify outliers in a distribution for several reasons:
They might be inaccurate data values.
They can indicate a remarkable occurrence.
They can heavily influence the values of some summary statistics, like the mean, range, and standard deviation.

6. Boxplots and Outliers
You can use a dotplot, stemplot, or histogram to display the distribution of a quantitative variable. Another graphical option for quantitative data is a boxplot (sometimes called a box-and-whisker plot). A boxplot summarizes a distribution by displaying the location of 5 important values within the distribution, known as its five-number summary.
Five-Number Summary, Boxplot
The five-number summary of a distribution of quantitative data consists of the minimum, the first quartile Q1, the median, the third quartile Q3, and the maximum.
A boxplot is a visual representation of the five-number summary.

7. Boxplots and Outliers
A boxplot is a visual representation of the five-number summary.
How to Make a Boxplot
Find the five-number summary for the distribution.
Draw and label the axis. Draw a horizontal axis and put the name of the quantitative variable underneath.
Scale the axis. Look at the smallest and largest values in the data set. Start the horizontal axis at a number equal to or below the smallest value and place tick marks at equal intervals until you equal or exceed the largest value.
Draw a box that spans from the first quartile (Q1) to the third quartile (Q3).
Mark the median with a vertical line segment that’s the same height as the box.
Identify outliers using the 1.5 × IQR rule.
Draw whiskers—lines that extend from the ends of the box to the smallest and largest data values that are not outliers. Mark any outliers with a special symbol such as an asterisk (*).

8. Boxplots and Outliers
The top dotplot in the figure below shows Barry Bonds’s home run data.
The first quartile, the median, and the third quartile are marked with lines.
The process of testing for outliers with the 1.5 × IQR rule is shown in red.
Because there are no outliers, we draw the whiskers to the maximum and minimum data values, as shown in the finished boxplot at the bottom of the figure.

9. Boxplots and Outliers
Boxplots provide a quick summary of the center and variability of a distribution. Boxplots do not display each individual value in a distribution. And boxplots don’t show gaps, clusters, or peaks.

10. Boxplots and Outliers
Boxplots are especially effective for comparing the distribution of a quantitative variable in two or more groups.

11. Which is best at reducing stress?
LESSON APP 1.8
Which is best at reducing stress?
If you are a dog lover, having your dog with you may reduce your stress level. Does having a friend with you reduce stress? To examine the effect of pets and friends in stressful situations, researchers recruited 45 women who said they were dog lovers. Fifteen women were assigned at random to each of three groups: to do a stressful task (1) alone, (2) with a good friend present, or (3) with their dogs present. The stressful task was to count backward by 13s or 17s. The woman’s average heart rate during the task was one measure of the effect of stress. The following table shows the data.
Identify any outliers in the three groups. Show your work.
Make parallel boxplots to compare the heart rates of the women in the three groups.
Based on the data, does it appear that the presence of a pet or friend reduces heart rate during a stressful task? Justify your answer.

12. Boxplots and Outliers Use the 1.5 x IQR rule to identify outliners.
Make and interpret boxplots of quantitative data.
Compare distributions of quantitative data with boxplots.