minX =& 70
Q_1 =& 120
Med =& 170
Q_3 =& 250
maxX =& 400
Explanation: See solution.
Practice makes perfect
a
We are given the prices of a random sample of athletic shoes.
Price (dollars)
70
300
400
250
250
150
120
250
100
70
150
160
200
170
300
Let's use a graphing calculator to make a box-and-whisker plot of the data. We will start by organizing the data in a list. Press STAT, choose Edit, and enter all of the data into the first list.
Having entered the data, we can plot a box-and-whisker plot by pushing 2nd and Y= to choose STAT PLOT. Then, we will choose one of the plots in the list, turn the plot ON, and choose the type to be a box-and-whisker plot.
We will have to change the viewing window settings in order to see the plot. This can be done by pressing WINDOW and entering the new window settings.
Finally, we push GRAPH to draw the box-and-whisker plot.
We can see that the data to the right of the median are distributed over a wider range than the data to the left. Therefore, the distribution is positively skewed.
b
We are asked to describe the center and spread of the data. In order to do so, we first will determine how skewed the distribution is.
If the distribution is relatively symmetric, the mean and standard deviation can be used.
If the distribution is skewed or has outliers, the five-number summary can be used.
Since we found in Part A that the data distribution is positively skewed, we will use the five-number summary.
Five Number Summary
The three quartiles, along with the minimum and maximum values, are called a five-number summary of a data set.
We can use the trace feature of our calculator in order to find the quartiles, the minimum, and the maximum. We push TRACE and move the cursor to find each one.
We found the five-number summary of this data set.
minX =& 70 &(Minimum value)
Q_1 =& 120 &(Lower quartile)
Med =& 170 &(Median)
Q_3 =& 250 &(Upper quartile)
maxX =& 400 &(Maximum value)
The five-number summary of the data tells us the following about the prices of the athletic shoes.
