Mean absolute deviation

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Presentation transcript:

Mean absolute deviation Greg Morrison

Find mean absolute deviation You have used range and the interquartile range to describe the spread of a set of data. You can also use the mean absolute deviation. The mean absolute deviation of a set of data is the average distance between each data value and the mean.

Maximum speeds of roller coaster (MPH) Example The Table shows the maximum speeds of eight roller coasters. Find the mean absolute deviation of the set of data. Describe what the mean absolute deviation represents. Maximum speeds of roller coaster (MPH) 58 88 40 60 72 66 80 48

Find the mean 𝟓𝟖+𝟖𝟖+𝟒𝟎+𝟔𝟎+𝟕𝟐+𝟔𝟔+𝟖𝟎+𝟒𝟖 𝟖 = 𝟓𝟏𝟐 𝟖 = 64 Step 1 Find the mean 𝟓𝟖+𝟖𝟖+𝟒𝟎+𝟔𝟎+𝟕𝟐+𝟔𝟔+𝟖𝟎+𝟒𝟖 𝟖 = 𝟓𝟏𝟐 𝟖 = 64

Mind the absolute value Step 2: Find the distance of each data value from the mean (Hint: Subtract the lesser value from the greater value) This gives us the absolute value (how far each number is from the mean) Mind the absolute value 64 – 58 = 88 – 64 = 64 – 40 = 64 – 60 = 72 – 64 = 66 – 64 = 80 – 64 = 64 – 48 = Absolute Value 6 24 4 8 2 16

Step 3: Find the mean of the distances 𝟔+𝟐𝟒+𝟐𝟒+𝟒+𝟖+𝟐+𝟏𝟔+𝟏𝟔 𝟖 = 𝟏𝟎𝟎 𝟖 = 12.5 The mean absolute deviation is 12.5.

Step 4 (describe or interpret data) This means that the average distance each data value is from the mean is 12.5 miles per hour.

Speeds of Top Ten Fastest Birds (mph) Your Turn The table shows speeds of ten birds. Find the mean absolute deviation of the data. Round to the nearest whole number. Describe what the mean absolute deviation represents. What is the first Step? Speeds of Top Ten Fastest Birds (mph) 88 77 65 70 72 95 80 106 68

Step 1 Find the Mean 𝟖𝟖+𝟕𝟕+𝟔𝟓+𝟕𝟎+𝟔𝟓+𝟕𝟐+𝟗𝟓+𝟖𝟎+𝟏𝟎𝟔+𝟔𝟖 𝟏𝟎 = 𝟕𝟖𝟔 𝟏𝟎 = 𝟖𝟖+𝟕𝟕+𝟔𝟓+𝟕𝟎+𝟔𝟓+𝟕𝟐+𝟗𝟓+𝟖𝟎+𝟏𝟎𝟔+𝟔𝟖 𝟏𝟎 = 𝟕𝟖𝟔 𝟏𝟎 = The mean is 78.6 or 79 What is the next step?

Step 2: Find the distance of each data value from the mean (Hint: Subtract the lesser value from the greater value) What is the next step? Absolute Value 88 – 79 = 9 79 – 77 = 2 79 – 65 = 14 79 – 70 = 9 79 – 72 = 7 95 – 79 = 16 79 – 80 = 19 106 – 79 = 27 79 – 68 =11

Step 3 Find the mean of the distances 𝟗+𝟐+𝟏𝟒+𝟗+𝟏𝟒+𝟕+𝟏𝟔+𝟏𝟗+𝟐𝟕+𝟏𝟏 𝟏𝟎 = 𝟏𝟐𝟐 𝟏𝟎 = 12.2 or The mean absolute deviation is 12