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Here are the science test scores from Ms. O’Donnell’s class:

55, 60, 70, 70, 75, 75, 75, 80, 80, 85, 85, 85, 85, 90, 90, 95, 100

Find the mean absolute deviation (MAD).

(1 point)
The MAD is
.

1 answer

To calculate the mean absolute deviation (MAD), follow these steps:

  1. Find the mean (average) of the scores.
  2. Calculate the absolute deviations from the mean for each score.
  3. Find the average of those absolute deviations.

Step 1: Calculate the Mean

The scores are:

55, 60, 70, 70, 75, 75, 75, 80, 80, 85, 85, 85, 85, 90, 90, 95, 100

To find the mean:

\[ \text{Mean} = \frac{\text{Sum of all scores}}{\text{Number of scores}} \]

Sum of all scores:

\[ 55 + 60 + 70 + 70 + 75 + 75 + 75 + 80 + 80 + 85 + 85 + 85 + 85 + 90 + 90 + 95 + 100 = 1305 \]

Number of scores: 17

\[ \text{Mean} = \frac{1305}{17} \approx 76.76 \]

Step 2: Calculate Absolute Deviations

Now, we find the absolute deviation for each score from the mean:

  • |55 - 76.76| = 21.76
  • |60 - 76.76| = 16.76
  • |70 - 76.76| = 6.76
  • |70 - 76.76| = 6.76
  • |75 - 76.76| = 1.76
  • |75 - 76.76| = 1.76
  • |75 - 76.76| = 1.76
  • |80 - 76.76| = 3.24
  • |80 - 76.76| = 3.24
  • |85 - 76.76| = 8.24
  • |85 - 76.76| = 8.24
  • |85 - 76.76| = 8.24
  • |85 - 76.76| = 8.24
  • |90 - 76.76| = 13.24
  • |90 - 76.76| = 13.24
  • |95 - 76.76| = 18.24
  • |100 - 76.76| = 23.24

Step 3: Calculate the Mean of Absolute Deviations

Sum of absolute deviations:

\[ 21.76 + 16.76 + 6.76 + 6.76 + 1.76 + 1.76 + 1.76 + 3.24 + 3.24 + 8.24 + 8.24 + 8.24 + 8.24 + 13.24 + 13.24 + 18.24 + 23.24 = 172.00 \]

Now, divide by the number of scores (17):

\[ \text{MAD} = \frac{172.00}{17} \approx 10.12 \]

So, the mean absolute deviation (MAD) is approximately 10.12.