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Polina's math scores are shown in the table.

\begin{tabular}{|l|l|l|l|l|l|}
\hline \multicolumn{6}{|c|}{ Polina's Math Scores } \\
\hline Math Scores & 72 & 65 & 75 & 88 & 90 \\
\hline
\end{tabular}

What is the mean absolute deviation of her math scores?

A. 5.4
B. 6.4
C. 7.8
D. 8.8

Sagot :

GinnyAnsweridn
To find the mean absolute deviation (MAD) of Polina's math scores, we follow these steps:

1. List the Math Scores: Polina's math scores are 72, 65, 75, 88, and 90.

2. Calculate the Mean (Average) Score:
[tex]\[ \text{Mean Score} = \frac{\sum \text{Math Scores}}{\text{Number of Scores}} \][/tex]
[tex]\[ \text{Mean Score} = \frac{72 + 65 + 75 + 88 + 90}{5} = \frac{390}{5} = 78 \][/tex]

3. Calculate the Absolute Deviations from the Mean:
The absolute deviation for each score is the absolute difference between the score and the mean score.
[tex]\[ |72 - 78| = 6 \][/tex]
[tex]\[ |65 - 78| = 13 \][/tex]
[tex]\[ |75 - 78| = 3 \][/tex]
[tex]\[ |88 - 78| = 10 \][/tex]
[tex]\[ |90 - 78| = 12 \][/tex]

So, the absolute deviations are 6, 13, 3, 10, and 12.

4. Calculate the Mean of the Absolute Deviations:
[tex]\[ \text{Mean Absolute Deviation (MAD)} = \frac{\sum \text{Absolute Deviations}}{\text{Number of Deviations}} \][/tex]
[tex]\[ \text{Mean Absolute Deviation (MAD)} = \frac{6 + 13 + 3 + 10 + 12}{5} = \frac{44}{5} = 8.8 \][/tex]

Based on these calculations, the mean absolute deviation of Polina's math scores is [tex]\(\boxed{8.8}\)[/tex].
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