MAD Mean Absolute Deviation

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Presentation transcript:

MAD Mean Absolute Deviation Objective Find and interpret the mean absolute deviation for a set of data.

Mean Absolute Deviation The average distance between each data value and the mean.

Measures of Center Mean and Median Measures of Variability Range and MAD

Mean Absolute Deviation The bigger (>) the MAD the more variation. The smaller (<) the MAD the less variation.

Steps 1. Find the mean. 2. Find the distance between data and the mean. 3. Find the average of the differences [Subtract the mean from each value - the result is called the deviation from the mean]

Find the Mean Number of cell phone contacts stored in 8 friends phones : 52, 48, 60, 55, 59, 54, 58, 62 Find the mean: 52+48+60+55+59+54+58+62=56 8

Find the Mean Absolute Deviation Find the deviation from the mean

Find the mean absolute deviation Number of cell phone contacts stored in 8 friends phones : 52, 48, 60, 55, 59, 54, 58, 62 Find the sum of the absolute values: 8 + 4 + 2 + 1 + 2 + 3 + 4 + 6 = 30 Divide the sum by the number of data items: 30 = 3.75 8

Find the mean absolute deviation Number of cell phone contacts stored in 8 friends phones : 52, 48, 60, 55, 59, 54, 58, 62 This means the average distance between each data value and the mean is 3.75 contacts.

Find the Mean Roller coaster speeds for 8 roller coasters were: 58, 88, 40, 60, 72, 66, 80 & 48 Find the mean: 58+88+40+60+72+66+80+48=64 8

Find the Mean Absolute Deviation Find the deviation from the mean

Find the mean absolute deviation Roller coaster speeds were: 58, 88, 40, 60, 72, 66, 80, 48 Find the sum of the absolute values: 6 + 24 + 24 + 4 + 8 + 2 + 16 + 16 = 100 Divide the sum by the number of data items: 100 = 12.5 8

Find the mean absolute deviation Roller coaster speeds were: 58, 88, 40, 60, 72, 66, 80, 48 This means the average distance each data value is from the mean is 12.5 miles per hour.

TRY THESE

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.