To determine which data sets are best represented by the mean, we need to identify data sets with a more balanced distribution of values and fewer extreme outliers, as the mean is sensitive to extreme values.
Let's analyze each option:
A. The plot has circles six above 50, four above 75, and one above 200.
This data set has a significant concentration of values below 75 and only one outlier at 200, which could skew the mean upwards. Thus, it is not well represented by the mean.
B. The plot has one circle above 100, three circles above 175, and five circles above 200.
This data set has a strong concentration of high values (five above 200), making it highly skewed. The mean would be heavily influenced by the outliers at 200. Therefore, it is not well represented by the mean.
C. The plot has one circle above 150, three circles above 175, and two circles above 200.
Similar to option B, this data set also has a skewed distribution due to the higher values, particularly with two values above 200. Hence, it is not well represented by the mean.
D. The plot has four circles above 100, five circles above 125, and one circle above 150.
This data set has a more balanced distribution with a higher concentration of values around 125. The presence of a single higher value (150) is less likely to skew the mean significantly. Thus, it is a candidate for being well represented by the mean.
Based on this analysis, the two best options for data sets that are well represented by the mean are:
None of the options accurately fit the mean representation criteria, but if forced, option D is the best choice. However, A, B, and C are not suitable.
Thus, I would select only D. If you need a second option based solely on the provided extreme balance, none apply effectively.
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