Question

the heights of basketball players, in inches, on two different teams is given in the data.
champs: {66, 63, 65, 64, 58, 66, 63, 65, 64, 58, 66, 63, 65, 64, 58}
all stars: {60, 70, 67, 70, 65, 69, 60, 58, 75, 67, 62, 68, 70, 66, 69}
using the correct measure of center, which team typically has the tallest players?
the champs, with a mean of approximately 63.2 inches
the champs, with a median of 64 inches
the all stars, with a mean of approximately 66.4 inches
the all stars, with a median of 67 inches

Explanation:

Step1: Check for outliers (All Stars)

The All Stars data has a value 75, which is an outlier far from other values. For data with outliers, median is the better measure of center.

Step2: Sort Champs data

Sorted Champs: $58, 58, 58, 63, 63, 63, 64, 64, 64, 65, 65, 65, 66, 66, 66$

Step3: Calculate Champs median

There are 15 values. Median = 8th value: $64$

Step4: Sort All Stars data

Sorted All Stars: $58, 60, 60, 62, 65, 67, 67, 68, 69, 69, 70, 70, 70, 66, 75$ (corrected sort: $58, 60, 60, 62, 65, 66, 67, 67, 68, 69, 69, 70, 70, 70, 75$)

Step5: Calculate All Stars median

There are 15 values. Median = 8th value: $67$

Step6: Compare medians

$67 > 64$, so All Stars have higher median.

Answer:

The All Stars, with a median of 67 inches