Question

question 2 points 3

two basketball teams recorded the number of points scored in 8 games:
team x: 85, 87, 90, 91, 88, 89, 86, 92
team y: 70, 85, 100, 72, 97, 88, 80, 91

which team had a more consistent scoring performance, and why?

team x, because it has a lower standard deviation
team x, because it has a higher mean

Explanation:

Understand consistency in statistics

In statistics, consistency refers to how close the data values are to each other or to the center of the data. A smaller spread indicates higher consistency.

Identify measures of spread

The spread or variability of a dataset is measured by statistics such as range, interquartile range (IQR), variance, and standard deviation. A lower standard deviation means the data points are closer to the mean, indicating a more consistent performance.

Analyze the given datasets

Let's look at the scores for both teams:

• Team X: \(85, 87, 90, 91, 88, 89, 86, 92\)
• Team Y: \(70, 85, 100, 72, 97, 88, 80, 91\)

The scores of Team X are tightly clustered between \(85\) and \(92\) (a range of \(7\)).
The scores of Team Y are widely spread out between \(70\) and \(100\) (a range of \(30\)).

Compare standard deviations

Because Team X's scores have much less variation, Team X has a significantly lower standard deviation than Team Y. Therefore, Team X is the more consistent team because of this lower standard deviation.

Answer:

• Team X, because it has a lower standard deviation (Correct answer)
• Team X, because it has a higher mean