Question

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 MAD.

Answer 1

[AI-generated answer — Bot GPT 3.5]

First, we need to find the mean of the data set:

Mean = (55 + 60 + 70 + 70 + 75 + 75 + 75 + 80 + 80 + 85 + 85 + 85 + 85 + 90 + 90 + 95 + 100) / 17
Mean = 1315 / 17
Mean = 77.35 (rounded to two decimal places)

Next, we calculate the absolute deviations from the mean for each data point:

|55 - 77.35| = 22.35
|60 - 77.35| = 17.35
|70 - 77.35| = 7.35
|70 - 77.35| = 7.35
|75 - 77.35| = 2.35
|75 - 77.35| = 2.35
|75 - 77.35| = 2.35
|80 - 77.35| = 2.65
|80 - 77.35| = 2.65
|85 - 77.35| = 7.65
|85 - 77.35| = 7.65
|85 - 77.35| = 7.65
|85 - 77.35| = 7.65
|90 - 77.35| = 12.65
|90 - 77.35| = 12.65
|95 - 77.35| = 17.65
|100 - 77.35| = 22.65

Next, we find the sum of the absolute deviations:

Σ|X -Mean| = 22.35 + 17.35 + 7.35 + 7.35 + 2.35 + 2.35 + 2.35 + 2.65 + 2.65 + 7.65 + 7.65 + 7.65 + 7.65 + 12.65 + 12.65 + 17.65 + 22.65
Σ|X -Mean| = 162.15

Now, we find the MAD by dividing the sum of the absolute deviations by the number of data points:

MAD = Σ|X -Mean| / n
MAD = 162.15 / 17
MAD = 9.54

Therefore, the Mean Absolute Deviation (MAD) of the science test scores in Ms. O’Donnell’s class is 9.54.