Statistics Mean Absolute Deviation

Vocabulary Mean Absolute Deviation (MAD) the average distance of data values from the mean

What is the Mean Absolute Deviation of the data set: 3, 7, 10, 13, 17 Step 1: Find the mean of the data: (3+7+10+13+17) / 5 = 10 Mean of these numbers = 10

Step 2: Find the deviations (distance) of each value to the mean of the data: Value Mean Deviation 3 7 10 13 17 10 7 10 3 10 10 3 10 7

Step 3: Find the mean (average) of the deviations: Value Mean Deviation 3 7 10 13 17 10 7 10 3 10 10 3 10 7 7 + 3 + 0 + 3 + 7 = 20 ÷ 5 = 4

All the values, are, on average, 4 away from the mean Step 4: Analysis Mean Absolute Deviation = 4 All the values, are, on average, 4 away from the mean

What is the Mean Absolute Deviation of the data set: 0, 1, 5, 7, 11, 12, 20 Step 1: Find the mean of the data: (0+1+5+7+11+12+20) ÷ 7 = 8 Mean of these numbers = 8

Step 2: Find the deviations (distance) of each value to the mean of the data: Value Mean Deviation 1 5 7 11 12 20 8 8 8 7 8 3 8 1 8 3 8 4 8 12

Step 3: Find the mean (average) of the deviations: Value Mean Deviation 1 5 7 11 12 20 8 8 8 7 8 3 8 1 8 3 8 4 8 12 8 + 7 + 3 + 1 + 3 + 4 + 12 = 38 ÷ 7 = 5.4

All the values, are, on average, 5.4 away from the mean Step 4: Analysis Mean Absolute Deviation = 5.4 All the values, are, on average, 5.4 away from the mean

The owner of a basketball team wants to trade for a player that is consistent. The average points per game scored by 2 players over the last season are listed below. Which player should the owner choose? Oct Nov Dec Jan Mar Apr Player A 25 22 24 28 30 27 Player B 20 32 29 11

Step 1 – Find the mean of both data sets Oct Nov Dec Jan Mar Apr Player A 25 22 24 28 30 27 Player B 20 32 29 Player A: 25 + 22 + 24 + 28 + 30 + 27 = 156 ÷6 = 26 Player B: 22 + 20 + 25 + 28 + 32 + 29 = 156 ÷6 = 26 12

Step 2 – Subtract each time from the Mean. Player A Player B Avg Pts Mean Deviation 25 26 22 24 28 30 27 Avg Pts Mean Deviation 22 26 20 25 28 32 29 1 4 4 6 2 1 2 2 4 6 1 3 13

Step 3: Find the mean of the Deviations Player A Player B Deviation Deviation 4 1 6 4 2 1 2 2 6 4 1 3 14 ÷ 6 = 2.3 22 ÷ 6 = 3.7 14

Player A MAD = 2.3 MAD = 3.7 Step 4 – Analysis Player B Player A Which player Should he choose? Player A MAD = 2.3 MAD = 3.7 15

Which city should she pick? Maria has a condition where large swings in temperature are detrimental to her health. She is trying to decide what would be the perfect city for her to move to. Below are the average temperatures for September through May for 2 different cities: Sept Oct Nov Dec Jan Feb Mar Apr May City A 65 61 50 35 23 29 39 52 City B 72 70 60 54 58 59 63 67 Which city should she pick?

Step 1 – Find the mean of both data sets City A 65 61 50 35 23 29 39 52 City B 72 70 60 54 58 59 63 67 City A: 65+61+50+35+23+29+39+52+65 = 419 ÷9 = 46.6 City B: 72+70+60+54+58+59+63+67+70 = 573 ÷9 = 63.7 17

Step 2 – Subtract each time from the Mean. City A City B Temp Mean Deviation 65 46.6 61 50 35 23 29 39 52 Temp Mean Deviation 72 63.7 70 60 54 58 59 63 67 18.4 8.3 14.4 6.3 3.4 3.7 11.6 9.7 23.6 5.7 17.6 4.7 7.6 0.7 5.4 3.3 18.4 6.3 18

Step 3: Find the mean of the Deviations City A City B Deviation Deviation 8.3 18.4 6.3 14.4 3.4 3.7 11.6 9.7 23.6 5.7 17.6 4.7 7.6 0.7 5.4 3.3 18.4 6.3 120.4 ÷ 9 = 13.4 48.7 ÷ 9 = 5.4 19

City B MAD = 13.4 MAD = 5.4 Step 4 – Analysis City A City B Which city should Maria choose? City A City B City B MAD = 13.4 MAD = 5.4 20