Which sample has a higher standard deviation?
Sample A: 82, 85, 87, 88, 91, 93
Sample B: 68, 73, 74, 77, 81, 81
Select the correct answer below and fill in the answer box to complete your choice.
A. Sample A has the higher standard deviation of [ ].
B. Sample B has the higher standard deviation of [ ].
Answer (1)
Calculate the standard deviation of Sample A: s A ≈ 3.98 .
Calculate the standard deviation of Sample B: s B ≈ 5.05 .
Compare the standard deviations: s_A"> s B > s A .
Sample B has a higher standard deviation of 5.05 .
Explanation
Understand the problem We are given two samples, Sample A and Sample B, and we need to determine which sample has a higher standard deviation. The standard deviation measures the spread or dispersion of the data points in a sample around the mean. A higher standard deviation indicates greater variability.
Calculate standard deviation of Sample A First, let's calculate the standard deviation for Sample A. The data for Sample A is: 82, 85, 87, 88, 91, 93. Using a calculator, the standard deviation of Sample A is approximately 3.98.
Calculate standard deviation of Sample B Next, let's calculate the standard deviation for Sample B. The data for Sample B is: 68, 73, 74, 77, 81, 81. Using a calculator, the standard deviation of Sample B is approximately 5.05.
Compare standard deviations Comparing the standard deviations, we have: Standard deviation of Sample A: s A ≈ 3.98 Standard deviation of Sample B: s B ≈ 5.05 Since 3.98"> 5.05 > 3.98 , Sample B has a higher standard deviation.
Final Answer Therefore, Sample B has a higher standard deviation of approximately 5.05.
Examples
Understanding standard deviation is crucial in many real-world scenarios. For instance, in finance, it helps assess the risk associated with investments; a higher standard deviation indicates greater price volatility. In manufacturing, it's used to ensure product quality by measuring the consistency of product dimensions. In education, it can help evaluate the spread of test scores, providing insights into the effectiveness of teaching methods.
