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Analyzing Standard Deviation and Mean

The mean test scores with standard deviations of four English classes are given in the table below.

\begin{tabular}{|c|c|c|}
\hline
Class & Mean & \begin{tabular}{c}
Standard \\
Deviation
\end{tabular} \\
\hline
Mrs. Jones & 89 & 1.9 \\
\hline
Mrs. Rijo & 82 & 1.4 \\
\hline
Mr. Phan & 73 & 3.4 \\
\hline
Mrs. Scott & 90 & 6.1 \\
\hline
\end{tabular}

Which statement is most likely to be true?

A. The scores from Mrs. Jones's class are the closest to the class mean.

B. The scores from Mrs. Rijo's class are the closest to the class mean.

C. The scores from Mr. Phan's class are the closest to the class mean.

D. The scores from Mrs. Scott's class are the closest to the class mean.



Answer :

GinnyAnswer
To determine which class has scores that are the closest to the mean, we need to look at the standard deviation of each class. The standard deviation is a measure of how spread out the scores are around the mean; a smaller standard deviation means the scores are clustered more closely around the mean.

We have the following information:
- Mrs. Jones's class: Mean = 89, Standard Deviation = 1.9
- Mrs. Rijo's class: Mean = 82, Standard Deviation = 1.4
- Mr. Phan's class: Mean = 73, Standard Deviation = 3.4
- Mrs. Scott's class: Mean = 90, Standard Deviation = 6.1

We compare the standard deviations:
- Mrs. Jones: 1.9
- Mrs. Rijo: 1.4
- Mr. Phan: 3.4
- Mrs. Scott: 6.1

The smallest standard deviation is 1.4, which belongs to Mrs. Rijo's class. This means that the scores in Mrs. Rijo's class are the closest to the class mean, as there is less variation in the scores.

Thus, the correct statement is:
"The scores from Mrs. Rijo's class are the closest to the class mean."

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