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Find a Seat

Learn how to calculate the mean, median, mode, range, and mean absolute deviation for different data sets. Compare the spread of the data using range and mean absolute deviation. Use the box method for finding mean absolute deviation.

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Find a Seat

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  1. Find a Seat • Get out your pencil (pen if you must) & Paper • Get a Calculator If you need one • Find the Mean, Median and Mode of each of the following data Sets • 1,1,2,5,6,9,10 • 1,2,10,9,5,6,1 • 1,2,3,4,10,10,10 • 7,4,5,6,9

  2. Use Measures of Central Tendency and Dispersion Goal: Compare mean, median, mode, range and mean absolute deviation. MM1D3a MM1D4

  3. Vocabulary • mean: the average of a numerical set. x • median: The middle number in a numerical set when the values are written in numerical order. • mode: the value(#) that occurs most frequently • measure of dispersion: describes the distribution or spread of the data. (range) • range: the difference between the greatest value and the smallest value.

  4. Deviation from the mean: the difference of a data value and the mean of a set of data. x – x MAD • Mean absolute deviation: the average deviation from the mean (the average of how far each data is from the mean)

  5. Your Notes MAD-calculate the mean absolute deviation for the set of numbers 5, 5, 6, 7, 12, 13 Step 1: Calculate the mean of the data set. x - x Step 2: Find the absolute values of the differences of each data point and the mean.

  6. Step 3: Find the sum of the absolute values. Step 4: Divide the sum by the total number of values in the data set. This means that all the data is on average about ____ units from the mean of ___.

  7. Example 2 The top 4 finishing times (in seconds) for two different teams in the 50 meter dash are given. Compare the spread of the data for the two sets using (a) the range and (b) the mean absolute deviation. Team A: 5.8, 6.0, 6.2, 6.4 Team B: 5.7, 5.9, 6.5, 6.7 Solution: a) Team A: Team B: The range for Team ____ is greater than the range for Team ___, so the data for Team ____ covers a wider interval than the date for Team ____.

  8. Step 1: Calculate the mean of the data set. b) The mean for Team A is _____, so the mean absolute deviation is: Step 2: Find the absolute values of the differences of each data point and the mean. Step 3: Find the sum of the absolute values. Step 4: Divide the sum by the total number of values in the data set.

  9. Step 1: Calculate the mean of the data set. b) The mean for Team B is _____, so the mean absolute deviation is: Step 2: Find the absolute values of the differences of each data point and the mean. Step 3: Find the sum of the absolute values. Step 4: Divide the sum by the total number of values in the data set.

  10. Mean MAD Team A 6.1 0.2 Team B 6.2 0.4 The mean absolute deviation for Team ____ is greater, so the average variation from the mean is greater for the data for Team ____ than for the data for Team _____.

  11. Checkpoint 2. In Example 2, suppose the slowest time for Team B was 6.6 seconds. Recalculate the range and mean absolute deviation. Team B: 5.7, 5.9, 6.5, 6.6 Range:_______ Mean:_______ Step 1 Step 2 Step 3 Step 4

  12. Box Method for MAD Step 2 Step 3 Step 4 Step 1

  13. Step 1: Calculate the mean of the data set. Step 2: Find the absolute values of the differences of each data point and the mean. Step 3: Find the sum of the absolute values. Step 4: Divide the sum by the total number of values in the data set.

  14. Find the Range and the mean absolute deviation of the following data sets:Be sure to copy the data set to your paper • 10, 7, 13, 10, 8 • 110, 114, 104, 108, 106 • 87, 75, 85, 77, 74, 82 • 15, 17, 15, 17, 21, 17, 15, 23 • 40, 46, 41, 46,49, 49, 46, 44, 44 • 50.8, 51.6, 51.9, 52, 52.5, 52.8, 53.1

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