Asked by ARIELA FERMIN GARCIA on Jun 19, 2024
Verified
Here are some summary statistics for last year's basketball team scoring output: lowest score =18\text { score } = 18 score =18 points, mean =58\text { mean } = 58 mean =58 points, median =52\text { median } = 52 median =52 points, range =97\text { range } = 97 range =97 points, IQR=46\mathrm { IQR } = 46IQR=46 Q1=23, \mathrm { Q } 1 = 23 \text {, }Q1=23, standard deviation =9\text { deviation } = 9 deviation =9 points.Suppose the opponents' scoring output was 10% lower.Find the opponents' mean and standard deviation.
A) Mean: 52.2 points,SD: 8.1 points
B) Mean: 52.2 points,SD: 9 points
C) Mean: 63.8 points,SD: 9.9 points
D) Mean: 63.8 points,SD: 9 points
E) Mean: 5.8 points,SD: 0.9 points
Standard Deviation
An indicator that assesses the degree to which data values are spread out or clustered around the mean.
Basketball Team
A group of players who come together to compete in the sport of basketball.
Scoring Output
The generated results or scores from an assessment, evaluation, or algorithm, typically used in testing or machine learning contexts.
- Identify the consequences of alterations in data, including rising or falling means or standard deviations, on summary statistics.
- Acquire an understanding to determine the revised mean and standard deviation after changes in the dataset.
Verified Answer
GÇ
Göksun ÇatalkayaJun 24, 2024
Final Answer :
A
Explanation :
The opponents' mean score is 10% lower than the team's mean score, so 58−0.10×58=52.258 - 0.10 \times 58 = 52.258−0.10×58=52.2 points. The standard deviation, being a measure of dispersion that does not depend on the mean, remains unchanged when all values are scaled by the same factor, so it remains 999 points. However, because we're applying a percentage decrease to the mean, not the standard deviation, the standard deviation for the opponents' scores actually decreases by the same percentage, making it 9−0.10×9=8.19 - 0.10 \times 9 = 8.19−0.10×9=8.1 points.
Learning Objectives
- Identify the consequences of alterations in data, including rising or falling means or standard deviations, on summary statistics.
- Acquire an understanding to determine the revised mean and standard deviation after changes in the dataset.