16 2.notebook. May 17, Module 16 Lesson 2: Mean Absolute Deviation M.A.D. Measure of Variability
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1 Module 16 Lesson 2: Mean Absolute Deviation M.A.D Objective: summarize numerical data set in relation to their context Measure of Variability is a single number used to describe the spread of a data set. Must have mastered the mean Find the mean of the following numbers. Round your answer to the nearest whole number. 60, 58, 54, 56, 63, 65, 62, 59, 56, 58 (MAD) mean of the distance between the data values and the mean of the data set Apr 26 11:05 AM To find the MAD 1. Find the mean of the given data 2. Find the difference each set of data is from the mean 3. find the mean of the differences Find the mean of the following numbers. Round your answer to the nearest whole number ~ data difference from the mean Now find the mean of the values in the second column round to the nearest whole number Apr 26 11:14 AM Apr 26 11:07 AM 1
2 ~ ~ 3 Find the MAD round to the nearest whole number Apr 26 11:19 AM Apr 26 11:21 AM ~ ~ 50 Lets do #2 on page 457 together MAD for A's 9 Apr 26 11:23 AM Apr 26 2:04 PM MAD for B's Which waiter's smoothies showed less variability? Apr 26 2:06 PM Apr 26 2:07 PM 2
3 Additional Example 1 A carpenter wants to hire an assistant. He is interviewing Robert and Tanya to see who is more precise at cutting lumber. Each person was told to cut 10 pieces of wood, and the lengths of their cuts in feet are given below. Whose cuts had less variability in length? Robert: 2.3, 2.4, 2.3, 2.5, 2.5, 2.8, 2.4, 2.5, 2.3, 2.5 Tanya: 2.0, 2.2, 2.1, 2.4, 2.3, 2.4, 2.6, 2.5, 2.4, 2.3 A fudge factory is testing two machines. Each machine is programmed to add 1.5 ounces of frosting to each piece of fudge. The actual amounts of frosting in ounces on 10 pieces of fudge frosted by each machine are given below. Determine which machine has less variability. Explain. Machine A: 1.489, 1.479, 1.505, 1.491, 1.499, 1.511, 1.477, 1.502, 1.491, Machine B: 1.506, 1.506, 1.508, 1.494, 1.510, 1.502, 1.506, 1.492, 1.486, /6 Apr 26 2:08 PM 1. Calculate the mean absolute deviation for Catapult A. 3. Which catapult has less variability? Explain. 2. Calculate the mean absolute deviation for Catapult B. 3/6 4/6 4. Calculate the mean absolute deviation for tomatoes from Culver Farm. 6. Which tomatoes have less variability? Explain. 5. Calculate the mean absolute deviation for tomatoes from Jonesville Farm. 5/6 6/6 3
4 Additional Example 1 A carpenter wants to hire an assistant. He is interviewing Robert and Tanya to see who is more precise at cutting lumber. Each person was told to cut 10 pieces of wood, and the lengths of their cuts in feet are given below. Whose cuts had less variability in length? Robert: 2.3, 2.4, 2.3, 2.5, 2.5, 2.8, 2.4, 2.5, 2.3, 2.5 Tanya: 2.0, 2.2, 2.1, 2.4, 2.3, 2.4, 2.6, 2.5, 2.4, 2.3 The MAD for Robert is 0.11 ft, and the MAD for Tanya is 0.14 ft, so Robert's cuts had less variability in length. Additional Example 2 A fudge factory is testing two machines. Each machine is programmed to add 1.5 ounces of frosting to each piece of fudge. The actual amounts of frosting in ounces on 10 pieces of fudge frosted by each machine are given below. Use a spreadsheet to determine which machine has less variability. Explain. Machine A: 1.489, 1.479, 1.505, 1.491, 1.499, 1.511, 1.477, 1.502, 1.491, Machine B: 1.506, 1.506, 1.508, 1.494, 1.510, 1.502, 1.506, 1.492, 1.486, The MAD for Machine A is , and the MAD for Machine B is , so Machine B has less variability. 1/6 2/6 1. Calculate the mean absolute deviation for Catapult A. 2.6 feet 3. Which catapult has less variability? Explain. Catapult B has the smaller MAD, so Catapult B has less variability. 2. Calculate the mean absolute deviation for Catapult B. 2.0 feet 3/6 4/6 4. Calculate the mean absolute deviation for tomatoes from Culver Farm ounce 6. Which tomatoes have less variability? Explain. The tomatoes from Jonesville Farm have a lower MAD, so they have less variability. 5. Calculate the mean absolute deviation for tomatoes from Jonesville Farm ounce 5/6 6/6 4
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