Question at position 57 ECADB

Question

BlackTom AI · Accepted Answer

Question context: The figure shows parallel dotplots of total family income for randomly chosen individuals from Indiana and New Jersey, and the prompt asks which of the statements is true.

Option A: 'Both distributions have obvious high outliers.' Here you should inspect whether both plots show extreme high values. If one state’s plot has noticeably more points near the far right tail than the other, this statement would be suspect. If one state appears to have fewer or less pronounced high outliers, the claim would be inaccurate.

Option B: 'The median income for Indiana is greater than the median income for New Jersey.' This compares central tendency. To evaluate, you would look at where the bulk of points center for each state lies. If Indiana’s cluster sits to the right of New Jersey’s cluster, this could be true; otherwise, it’s false. Consider that a higher median would correspond to a center of the Indiana distribution appearing to the right of New Jersey’s center.

Option C: 'The distribution for the randomly selected individuals incomes in New Jersey has less variability than those from Indiana.' This is a statement about spread. Compare the overall spread of the two dotplots: if New Jersey’s incomes cluster more tightly (points concentrated in a narrower range) while Indiana’s incomes span a wider range, then New Jersey has less variability and the statement is true. If, however, New Jersey shows a similar or wider spread, this would be false.

Option D: 'The distribution of total family income for Indiana is roughly symmetric, while the distribution of total family income for New Jersey is slightly skewed right.' This asserts a specific shape for each distribution. You would assess symmetry by looking for mirror-imaged tails around the center. If Indiana’s dots appear balanced around a central value, while New Jersey shows a longer tail to the right, this statement could be partially true; otherwise, it would be incorrect.

Option E: 'New Jersey’s distribution has both the lowest family income and the highest family income.' This makes a claim about the extreme values present. Check whether New Jersey’s plot contains both the minimum value observed in the data and the maximum value observed in the data. If either minimum or maximum in New Jersey is not as extreme as in Indiana (or if Indiana shows a lower minimum or higher maximum), this statement would be false.

Reasoning toward the correct option: Among the five statements, the assessment of variability (spread) is the key distinguishing feature between Indiana and New Jersey in many datasets. If the New Jersey dotplot is visibly more tightly clustered than Indiana’s, option C is the true statement. The other options hinge on nuances of outliers, medians, symmetry, and extrema; unless the plots clearly support those specific claims, they are less likely to be true. In typical comparative dotplots like these, the statement about relative variability (C) tends to be the one that aligns with a visibly narrower spread for one state relative to the other, making it the most plausible true option.

Question at position 57 ECADB

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