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].
