Mean Absolute Deviation

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Mean Absolute Deviation

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Mean Absolute Deviation MAD a measure of data dispersion Tells us how far away the numbers in a data set are from the mean Works well for data that has outliers

Mean Absolute Deviation

Outlier A data point which is far removed in value from the others in the data set It is an unusually large or an unusually small value compared to the others.

The score of 20 would be an outlier. Outlier Example Test scores for 6 students were : 84, 92, 88, 79, 91 and 20. The score of 20 would be an outlier.

Mean Absolute Deviation 1. Find the mean of the data. Subtract the mean from each value – the result is called the deviation from the mean. Take the absolute value of each deviation from the mean. 4. Find the sum of the absolute values. 5. Divide the total by the number of items.

Find the mean absolute deviation Test scores for 6 students were : 85, 92, 88, 80, 91 and 20. Find the mean: (85+92+88+80+91+20)/6=76 2. Find the deviation from the mean: 85-76=9 92-76=16 88-76=12 80-76=4 91-76=15 20-76=-56

Find the mean absolute deviation Test scores for 6 students were : 85, 92, 88, 80, 91 and 20. 3. Find the absolute value of each deviation from the mean:

Find the mean absolute deviation Test scores for 6 students were : 85, 92, 88, 80, 91 and 20. 4. Find the sum of the absolute values: 9 + 16 + 12 + 4 + 15 + 56 = 112 5. Divide the sum by the number of data items: 112/6 = 18.7 The mean absolute deviation is 18.7.

Find the mean absolute deviation Test scores for 6 students were : 85, 92, 88, 80, 91 and 74. Find the mean: (85+92+88+80+91+74)/6=85 2. Find the deviation from the mean: 85-85=0 92-85=7 88-85=3 80-85=-5 91-85=6 74-85=-11

Find the mean absolute deviation Test scores for 6 students were : 85, 92, 88, 80, 91 and 74. 3. Find the absolute value of each deviation from the mean:

Find the mean absolute deviation Test scores for 6 students were : 85, 92, 88, 80, 91 and 74. 4. Find the sum of the absolute values: 0 + 7 + 3 + 5 + 6 + 11 = 32 5. Divide the sum by the number of data items: 32/6 = 5.3 The mean absolute deviation is 5.3.

Which girl had the greater mean deviation for her scores? Emma and Sara play 5 games on a handheld video game and record their scores in this table. Game Emma Sara 1 30 15 2 20 25 3 10 4 5 Which girl had the greater mean deviation for her scores?

First, let’s look at Emma’s scores Game Emma 1 30 2 20 3 10 4 5 Find the mean Find the deviation form the mean Take the absolute value of each deviation Find the sum of the absolute values Divide the sum but the number or items

Now, Let’s look at Sara’s Scores Find the mean Find the deviation form the mean Take the absolute value of each deviation Find the sum of the absolute values Divide the sum but the number or items Game Sara 1 15 2 25 3 20 4 5

Now let’s compare the deviations What was the MAD of Emma’s scores?

What is Greg’s mean tip money? Hourly Tips What is Greg’s mean tip money? What is Trent’s mean tip money? What is the mean of the combined tip money? Greg Trent $15 $20 $24 $22 $26 $18 $17

What is MAD of the combined tip money? Hourly Tips What is MAD of the combined tip money? What is Trent’s MAD? What is Greg’s MAD? Greg Trent $15 $20 $24 $22 $26 $18 $17

Whose MAD is closer to the MAD of the combined tip money? Hourly Tips Greg Trent $15 $20 $24 $22 $26 $18 $17 Whose MAD is closer to the MAD of the combined tip money?