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The table gives the mean and standard deviation of four data distributions.

\begin{tabular}{|l|r|r|}
\hline
& Mean & Standard Deviation \\
\hline
Distribution 1 & 22 & 0.2 \\
\hline
Distribution 2 & 21 & 0.8 \\
\hline
Distribution 3 & 19 & 1.2 \\
\hline
Distribution 4 & 20 & 3.2 \\
\hline
\end{tabular}

Which distribution has the greatest spread?

Sagot :

GinnyAnsweridn
To determine which distribution has the greatest spread, we need to compare the standard deviations of the four distributions. The standard deviation is a measure of how spread out the values in a distribution are. The greater the standard deviation, the greater the spread of the distribution.

Here is the given data in the table format:

[tex]\[ \begin{array}{|l|r|r|} \hline & \text{Mean} & \text{Standard Deviation} \\ \hline \text{Distribution 1} & 22 & 0.2 \\ \hline \text{Distribution 2} & 21 & 0.8 \\ \hline \text{Distribution 3} & 19 & 1.2 \\ \hline \text{Distribution 4} & 20 & 3.2 \\ \hline \end{array} \][/tex]

To find which distribution has the greatest spread, we look at the standard deviations:

- Distribution 1: Standard Deviation = 0.2
- Distribution 2: Standard Deviation = 0.8
- Distribution 3: Standard Deviation = 1.2
- Distribution 4: Standard Deviation = 3.2

Comparing these values, we can see that the standard deviation of Distribution 4 is the highest, which is [tex]\(3.2\)[/tex].

Thus, Distribution 4 has the greatest spread.

[tex]\[ \boxed{\text{Distribution 4}} \][/tex]
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