Question

the data set below represents the total number of touchdowns a quarterback threw each season for 10 seasons of play. 29, 5, 26, 20, 23, 18, 17, 21, 28, 20. 1. order the values: 5, 17, 18, 20, 20, 21, 23, 26, 28, 29. 2. determine the median: $\frac{20 + 21}{2}=\frac{41}{2}=20.5$. calculate the measures of variability for the data set. the range is touchdowns. the interquartile range is touchdowns.

Explanation:

Step1: Calculate the range

The range is the difference between the maximum and minimum values. The maximum value is 29 and the minimum is 5.
$29 - 5$

Step2: Calculate the first - quartile ($Q_1$)

The lower half of the data set is 5, 17, 18, 20, 20. The median of the lower half is 18.

Step3: Calculate the third - quartile ($Q_3$)

The upper half of the data set is 21, 23, 26, 28, 29. The median of the upper half is 26.

Step4: Calculate the inter - quartile range (IQR)

The inter - quartile range is $Q_3−Q_1$. So, $26 - 18$

Answer:

The range is 24 touchdowns.
The interquartile range is 8 touchdowns.