Question

select the correct answer.

which distribution has the greatest spread?

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$$\begin{tabular}{|l|l|l|} \\hline & mean & standard deviation \\\\ \\hline distribution 1 & 13.7 & 3.1 \\\\ \\hline distribution 2 & 23.6 & 1.3 \\\\ \\hline distribution 3 & 38.4 & 7.2 \\\\ \\hline distribution 4 & 31.4 & 5.5 \\\\ \\hline \\end{tabular}$$

distribution 1
distribution 2
distribution 3
distribution 4

Explanation:

Identify the measure of spread

The spread of a distribution is measured by its standard deviation. A larger standard deviation indicates a greater spread of data around the mean.

Compare the standard deviations

The standard deviations for the four distributions are:

• Distribution 1: \(3.1\)
• Distribution 2: \(1.3\)
• Distribution 3: \(7.2\)
• Distribution 4: \(5.5\)

Determine the greatest value

$$ 7.2 > 5.5 > 3.1 > 1.3 $$

Distribution 3 has the largest standard deviation of \(7.2\), which means it has the greatest spread.

Answer:

• Distribution 1
• Distribution 2
• Distribution 3 (Correct answer)
• Distribution 4