QuestionAugust 26, 2025

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 higher mean Team Y, because it has more varied scores Team X, because it has a lower standard deviation Team Y, because it has a higher standard deviation

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 higher mean Team Y, because it has more varied scores Team X, because it has a lower standard deviation Team Y, because it has a higher standard deviation
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 higher mean
Team Y, because it has more varied scores
Team X, because it has a lower standard deviation
Team Y, because it has a higher standard deviation

Solution
4.4(274 votes)

Answer

Team X, because it has a lower standard deviation Explanation 1. Calculate the Mean for Each Team Team X mean: \frac{85 + 87 + 90 + 91 + 88 + 89 + 86 + 92}{8} = 88.5. Team Y mean: \frac{70 + 85 + 100 + 72 + 97 + 88 + 80 + 91}{8} = 85.375. 2. Calculate the Standard Deviation for Each Team Use formula: **s = \sqrt{\frac{\sum (x_i - \bar{x})^2}{n-1}}**. Team X: s_X = \sqrt{\frac{(85-88.5)^2 + (87-88.5)^2 + \ldots + (92-88.5)^2}{7}} \approx 2.39. Team Y: s_Y = \sqrt{\frac{(70-85.375)^2 + (85-85.375)^2 + \ldots + (91-85.375)^2}{7}} \approx 10.63. 3. Compare Standard Deviations Lower standard deviation indicates more consistency.

Explanation

1. Calculate the Mean for Each Team<br /> Team X mean: $\frac{85 + 87 + 90 + 91 + 88 + 89 + 86 + 92}{8} = 88.5$. Team Y mean: $\frac{70 + 85 + 100 + 72 + 97 + 88 + 80 + 91}{8} = 85.375$.<br /><br />2. Calculate the Standard Deviation for Each Team<br /> Use formula: **$s = \sqrt{\frac{\sum (x_i - \bar{x})^2}{n-1}}$**.<br /> Team X: $s_X = \sqrt{\frac{(85-88.5)^2 + (87-88.5)^2 + \ldots + (92-88.5)^2}{7}} \approx 2.39$.<br /> Team Y: $s_Y = \sqrt{\frac{(70-85.375)^2 + (85-85.375)^2 + \ldots + (91-85.375)^2}{7}} \approx 10.63$.<br /><br />3. Compare Standard Deviations<br /> Lower standard deviation indicates more consistency.
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