Question

the table shows the test scores of students who studied for a test as a group (group a) and students who studied individually (group b). student test scores (out of 100) group a 84 80 77 96 92 88 group b 92 86 85 87 83 85 which would be the best measures of center and variation to compare the data? the scores of both groups are skewed, so the median and standard deviation are the best measures for comparison. both distributions are nearly symmetric, so the mean and the standard deviation are the best measures for comparison. both distributions are nearly symmetric, so the median and the interquartile range are the

Explanation:

To determine the best measures of center and variation, we analyze the data distributions:

Step 1: Analyze Symmetry/Skewness

For Group A (scores: 84, 80, 77, 96, 92, 88, ...) and Group B (scores: 92, 86, 85, 87, 83, 85, ...), we check if the data is symmetric or skewed. Skewed data is unevenly distributed, while symmetric data has values balanced around a central point.

Step 2: Recall Measures of Center/Variation

• For symmetric data: Mean (center) and standard deviation (variation) are ideal, as they use all data points.
• For skewed data: Median (center) and interquartile range (IQR, variation) are better, as they are resistant to outliers/skew.

Step 3: Evaluate the Groups

Looking at the scores, both groups have values that are relatively balanced (no extreme skew). For example, Group A has scores like 77, 80, 84, 88, 92, 96 (no extreme outliers dominating), and Group B has 83, 85, 85, 86, 87, 92 (also balanced). Thus, the distributions are nearly symmetric.

Step 4: Select Appropriate Measures

Since the data is nearly symmetric, the mean (center) and standard deviation (variation) are the best measures for comparison.

Answer:

The correct option is: "Both distributions are nearly symmetric, so the mean and the standard deviation are the best measures for comparison."