Problem

Analyze the dot plot with counts \({1:1,2:3,3:2,8:1}\) using the median-of-halves quartile convention and the \(1.5\times~IQR\) rule. Determine \(n\), median, mode, range, quartiles, \(IQR\), fences, outliers, and a distribution summary.

Source statistical display: Which complete analysis correctly describes the dot plot with counts {1:1,2:3,3:2,8:1}, using the median-of-halves quartile convention and 1.5×IQR rule? No requested counts, analysis, or box-plot conclusion is annotated.

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What this problem is really about

Expand the dot stacks into one ordered list before calculating center and spread. Apply the named quartile convention consistently, use the resulting IQR fences for formal outlier status, and only then describe clusters and unusual values; visual isolation alone is not the same as an outlier test.

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n=7; median=2; mode=2; range=7; Q1=2, Q3=3, IQR=1, fences=[0.5,4.5]; outliers=8; summary=values cluster at 2–3 with one high outlier at 8

n=7; median=2; mode=2; range=7; Q1=2, Q3=3, IQR=1, fences=[0.5,4.5]; outliers=none; summary=uniform across 1–8

n=7; median=2; mode=2; range=7; Q1=2, Q3=3, IQR=1, fences=[0.5,4.5]; outliers=none; summary=symmetric because 1 and 8 are treated as balancing

n=7; median=2; mode=2; range=7; Q1=2, Q3=3, IQR=1, fences=[0.5,4.5]; outliers=1; summary=values cluster at 1–3 with one low outlier at 1

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Analyze the dot plot with counts \({1:1,2:3,3:2,8:1}\) using the median-of-halves quartile convention and the \(1.5\times~IQR\) rule. Determine \(n\), median, mode, range, quartiles, \(IQR\), fences, outliers, and a distribution summary.

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