To determine the best measures of center and variation to compare the data of Group A and Group B, we need to analyze their symmetry, which will guide our choice between measures.
1. Step 1: Examine Group A:
- Group A scores: [84, 80, 77, 96, 92, 88, 88, 84, 92, 100]
- By examining the distribution of scores, we notice that they range from 77 to 100, appearing to be fairly evenly distributed around the center.
2. Step 2: Examine Group B:
- Group B scores: [92, 86, 85, 87, 83, 85, 83, 76, 80, 88]
- By examining the distribution of scores, we notice that they range from 76 to 92, which also appears to be evenly distributed around the center.
3. Step 3: Determine Symmetry:
- To determine if the distributions are symmetric, we look at the mean and median of each group. These values help us assess whether the data is skewed or symmetric.
- For symmetric distributions, the mean and median are approximately equal.
- If both distributions are nearly symmetric, the mean and standard deviation are the most appropriate measures of center and variation.
4. Conclusion:
- Given that both Group A and Group B exhibition nearly symmetric distributions, the mean and the standard deviation are the most appropriate measures of center and variation. These measures best capture the central tendency and spread of the data.
Thus, the best measures of center and variation to use to compare the data are:
"Both distributions are nearly symmetric, so the mean and the standard deviation are the best measures for comparison."
