Question

task 2. comparing measures of central tendency the table shows some statistics about two basketball teams. points scored per game ospreys mean 32.9 median 34 rebels mean 37.1 median 31.5 a. looking at the means, the ______ should win because ____ b. looking at the medians, the ____ should win because ______ c. which team do you think had the highest scores more often? why?

Explanation:

Part a

Step1: Compare mean values

The mean of Ospreys is $32.9$ and the mean of Rebels is $37.1$. Since $37.1>32.9$, the Rebels have a higher mean.

Step2: Determine winning team

A higher mean of points per game suggests that, on average, the Rebels score more points. So looking at the means, the Rebels should win because their mean points per game ($37.1$) is higher than that of the Ospreys ($32.9$).

Part b

Step1: Compare median values

The median of Ospreys is $34$ and the median of Rebels is $31.5$. Since $34 > 31.5$, the Ospreys have a higher median.

Step2: Determine winning team

A higher median indicates that the middle - value of points scored by Ospreys is higher. So looking at the medians, the Ospreys should win because their median points per game ($34$) is higher than that of the Rebels ($31.5$).

Part c

To determine which team had the highest scores more often, we can consider both the mean and the median. The mean of the Rebels ($37.1$) is higher than that of the Ospreys ($32.9$), and the mean is a measure of the average value. A higher average means that, over a number of games, the Rebels are likely to have a higher total number of points and thus score higher more often. Although the Ospreys have a higher median, the mean gives a better sense of the overall average performance. So the Rebels had the highest scores more often because their mean points per game ($37.1$) is higher than that of the Ospreys ($32.9$), indicating a higher average performance.

Answer:

s:
a. Rebels; their mean ($37.1$) > Ospreys' mean ($32.9$)
b. Ospreys; their median ($34$) > Rebels' median ($31.5$)
c. Rebels; higher mean shows better average performance.