Question

The following lists show the free throw percentages of 16 players for the Detroit Pistons and Miami Heat during the 2012-2013 NBA season. Detroit Pistons: 0. 69, 0. 73, 0. 80, 0. 89, 0. 78, 0. 81, 0. 81, 0. 37, 0. 77, 0. 62, 0. 55, 0. 84, 0. 75, 0. 83, 0. 30, 0. 72 Miami Heat: 0. 75, 0. 72, 0. 81, 0. 76, 0. 90, 0. 75, 0. 82, 0. 67, 0. 72, 0. 72, 0. 57, 1. 00, 0. 56, 0. 50, 0. 50, 1. 00 Calculate the median and interquartile range for each set of data. Make sure to label your calculations. Compare the data sets using your calculations from part 1. Write your answer in complete sentences

Answer 1

To calculate the median, we need to first order the data from smallest to largest:

Detroit Pistons: 0.30, 0.37, 0.55, 0.62, 0.69, 0.72, 0.73, 0.75, 0.77, 0.78, 0.80, 0.81, 0.81, 0.83, 0.84, 0.89

Median = (0.78 + 0.80)/2 = 0.79

Miami Heat: 0.50, 0.50, 0.56, 0.57, 0.67, 0.72, 0.72, 0.72, 0.75, 0.75, 0.76, 0.81, 0.82, 0.90, 1.00, 1.00

Median = (0.76 + 0.81)/2 = 0.785

To calculate the interquartile range (IQR), we first need to find the first and third quartiles:

Detroit Pistons: Q1 = 0.69, Q3 = 0.84

IQR = Q3 - Q1 = 0.84 - 0.69 = 0.15

Miami Heat: Q1 = 0.67, Q3 = 0.82

IQR = Q3 - Q1 = 0.82 - 0.67 = 0.15

The median and IQR show that the free throw percentages for the two teams are similar. Both teams have a median around 0.79, and their IQRs are also the same at 0.15. However, we cannot make any conclusions about the spread or variability of the data based on the IQR alone. Further analysis, such as calculating the standard deviation or constructing box plots, would be necessary to fully compare the data sets.

Step-by-step explanation: