To determine the mean absolute deviation of Polina's math scores, we need to follow these steps:
### Step 1: Calculate the Mean of the Scores
To find the mean, we sum all the scores and then divide by the number of scores.
Polina's scores are: 72, 65, 75, 88, 90.
Sum of the scores:
[tex]\[ 72 + 65 + 75 + 88 + 90 = 390 \][/tex]
Number of scores:
[tex]\[ 5 \][/tex]
Mean (average) score:
[tex]\[ \frac{390}{5} = 78 \][/tex]
### Step 2: Calculate the Absolute Deviations from the Mean
The absolute deviation for each score is the absolute difference between the score and the mean.
Absolute deviations from 78:
- For 72: [tex]\(|72 - 78| = 6\)[/tex]
- For 65: [tex]\(|65 - 78| = 13\)[/tex]
- For 75: [tex]\(|75 - 78| = 3\)[/tex]
- For 88: [tex]\(|88 - 78| = 10\)[/tex]
- For 90: [tex]\(|90 - 78| = 12\)[/tex]
So, the absolute deviations are:
[tex]\[ 6, 13, 3, 10, 12 \][/tex]
### Step 3: Calculate the Mean of the Absolute Deviations
To find the mean absolute deviation, we sum all the absolute deviations and then divide by the number of deviations.
Sum of absolute deviations:
[tex]\[ 6 + 13 + 3 + 10 + 12 = 44 \][/tex]
Number of deviations:
[tex]\[ 5 \][/tex]
Mean absolute deviation:
[tex]\[ \frac{44}{5} = 8.8 \][/tex]
### Conclusion
The mean absolute deviation of Polina's math scores is [tex]\( 8.8 \)[/tex].
Thus, the correct answer is:
[tex]\[ \boxed{8.8} \][/tex]
