If the distribution of the data is positively or negatively skewed, use a five-number summary to describe the data.
A
a
See solution.
B
b
See solution.
Practice makes perfect
a
We are given the amounts of time James ran on a treadmill for the first 24 days of his workout. We are asked to use a graphing calculator to make a histogram. First, let's introduce the data. We will push STAT, choose Edit, and then enter the values in the first column.
Having entered the values, we have to instruct the calculator that we want to graph a histogram plot. Push 2nd and Y=, and choose one of the plots in the list. Make sure you turn the plot On, set the Type to histogram, and assign L1 as XList.
To graph the histogram of the data, we will push GRAPH. Note that we may need to change the window size so that it spans the length of the histogram. To do so, we push WINDOW.
We can see that most of the data is on the right. Therefore, this is a negatively skewed distribution.
b
Since the distribution is negatively skewed, we will use the five-number summary to describe the center and the spread of the data. To do this, push STAT and scroll right until you reach CALC. Choose the first option, 1-Var Stats. Select L1 to find the five-number summary of James' workouts.
Let's summarize our results in a table.
Amount of Time Spent on Treadmill
Minimum
7
Lower Quartile
15.5
Median
22.5
Upper Quartile
26
Maximum
30
The workout times range from 7 minutes to a maximum of 30 minutes. The median is 22.5 minutes. In every data sample, half of the data is between the lower and upper quartiles. Therefore, half of James' workouts were between 15.5 and 26 minutes.
