Standardized Test Practice
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We should use the five-number summary if the distribution of our data is skewed or has outliers.
See solution.
We are given a list of times Anna received in several 1-kilometer races and are asked to describe the center and spread of the data using either the mean and standard deviation or the five-number summary. Let's recall when we should use each of those measures.
| Measure of Center and Spread | When to Use it |
|---|---|
| Mean and standard deviation | The distribution is relatively symmetric. |
| Five-number summary | The distribution is skewed or has outliers. |
To see which measures we should use, we will use a graphing calculator to plot the times as a box-and-whisker plot. To do so, we first have to enter the values into a list. Push STAT, choose Edit, and then enter the given values in the first column.
Pushing the GRAPH button will tell the calculator to plot the dataset. If you are using a standard viewing window, you will need to change the settings so that the plot is fully visible.
As we can see, our data includes outliers. Therefore, we will use the five-number summary. This includes the minimum value, the first quartile Q_1, the median, the third quartile Q_3, and the maximum value. To calculate these values, push STAT and select CALC. Choose the first option, 1-Var Stats. Then scroll down to reach the needed information.
The times Anna received in the 1-kilometer races range from 6.75 to 8.10 minutes. The median time is 7.30 minutes, and half of the times are between 7.20 and 7.45 minutes.