12 Mean Absolute Deviation - Glencoe

Lesson12Main IdeaFind and interpretthe mean absolutedeviation for a setof data.Mean Absolute DeviationCELL PHONES The table shows the number ofcontacts eight friends have stored in each oftheir cell phones.Number ofContacts Stored1. Find the mean of the data.52486055595458622. What is the difference between the data value 52 and the mean?3. Which value is farthest from the mean?New Vocabularymean absolutedeviationMath Onlineglencoe.com6.SP.5c4. Overall, are the data values close to the mean or far away from themean? Explain.You have used the interquartile range which describes the variabilityof a set of data. Another way to describe the variability of a set of datais to use its mean absolute deviation. The mean absolute deviationof a set of data is the average distance between each data value andthe mean.Mean Absolute DeviationThe mean absolute deviation of a set of data is the average distancebetween each data value and the mean.1. Find the mean.2. Find the distance between each data value and the mean. That is,find the absolute value of the difference between each data valueand the mean.3. Find the average of those differences.The mean number of contacts stored and the distance each data value isfrom the mean is shown below. Each data value is represented by an .mean 48528 56421 60234662 is 6 unitsaway fromthe mean.The average of the distances is , or 3.75.8 4 2 1 2 3 4 68So, the mean absolute deviation is 3.75. The average distance betweeneach data value and the mean is 3.75 contacts.Lesson 12 Mean Absolute Deviation51

Find Mean AbsoluteDeviationROLLER COASTERS The table shows themaximum speeds of eight roller coastersat an amusement park. Find the meanabsolute deviation of the set of data.Describe what the mean absolutedeviation represents.Step 1Maximum Speedsof Roller Coasters (mph)5888406072668048Find the mean.58 88 40 60 72 66 80 48 648The mean is 64 miles per hour.Step 2Find the absolute value of the differences between eachvalue in the data set and the mean.mean 40 5024Step 36016 704 2681680 9024Find the average of the absolute values of the differencesbetween each value in the data set and the mean.24 16 6 4 2 8 16 24 12.58The mean absolute deviation is 12.5. This means that the averagedistance each data value is from the mean is 12.5 miles per hour.a. BIRDS The table shows the maximumflying speeds of the ten fastest birdsworldwide. Find the mean absolutedeviation of the set of data. Round tothe nearest hundredth. Describe whatthe mean absolute deviation represents.Speeds of Top TenFastest Birds (mph)887765706572958010668You can compare the mean absolute deviations for two data sets.A data set with a smaller mean absolute deviation has data valuesthat are closer to the mean than a data set with a greater meanabsolute deviation.

Compare VariationBASEBALL The top five salaries and the bottom five salariesfor the 2010 New York Yankees are shown in the table below.Salaries are in millions of dollars and are rounded to the nearesthundredth.2010 New York Yankees Salaries (millions of )Top Five SalariesBottom Five Salaries33.00 24.29 22.60 20.63 16.500.45 0.44 0.43 0.41 0.41a. Find the mean absolute deviation for each set of data. Roundto the nearest hundredth.Top Five SalariesFind the mean.33.00 24.29 22.60 20.63 16.50 23.405The mean is about 23.40 million.Find the mean absolute deviation by finding the absolutevalues of the differences between each data value and themean. Then average the differences.Mean Absolute DeviationThe absolute values of thedifferences between eachdata value and the meanfor the top five salariesare calculated below. 33.00 - 23.40 9.60 24.29 - 23.40 0.89 22.60 - 23.40 0.80 20.63 - 23.40 2.77 16.50 - 23.40 6.909.60 0.89 0.80 2.77 6.90 4.195The mean absolute deviation is about 4.19 million.Bottom Five SalariesFind the mean.0.45 0.44 0.43 0.41 0.41 0.435The mean is about 0.43 million.Find the mean absolute deviation by finding the absolutevalues of the differences between each data value and themean. Then average the differences.0.02 0.01 0 0.02 0.02 0.015The mean absolute deviation is about 0.01 million.b. Write a few sentences comparing their variation.The mean absolute deviation for the bottom five salaries ismuch less than that for the top five salaries. The data for thebottom five salaries are closer together than the data for thetop five salaries.

b. MOVIES The table shows the running time in minutes for twokinds of movies. Find the mean absolute deviation for each setof data. Round to the nearest hundredth. Then write a fewsentences comparing their variation.Running Time for Movies (min)Comedy90Example 18810098115120150135144Find the mean absolute deviation for each set of data. Round to the nearesthundredth if necessary. Then describe what the mean absolute deviationrepresents.1.2.Number of Daily Visitorsto a Web Site112Example 295Drama145108160Zoo Admission Prices ( )1229.509.008.259.258.008.503. WATER PARKS The table shows the height of waterslides at two differentwater parks. Find the mean absolute deviation for each set of data.Round to the nearest hundredth. Then write a few sentences comparingtheir variation.Height of Waterslides (ft)Splash Lagoon75Example 19580110Wild Water Bay8812010894135126Find the mean absolute deviation for each set of data. Round to thenearest hundredth if necessary. Then describe what the mean absolutedeviation represents.4.6.Known Moons of Planets5.Hard Drive ital Camera Prices ( )7.Grand SlamSingles Titles Won140 125 190 148 156212 178 188 196 2241487651011886

Example 28. FUNDRAISING The table shows the amount of money raised by thehomerooms for two grade levels at a middle school. Find the meanabsolute deviation for each set of data. Round to the nearest hundredth.Then write a few sentences comparing their variation.Money Raised ( )Sixth GradeSeventh Grade88 116 94 108 112 124 144 91 97 122 128 132Real-World LinkRNew York City isthe largest city inthe U.S., witha population ofabout 8.4 millionwithin the citylimits. If thesurroundingmetropolitanareas areincluded, itis closer to20 million.9. BRIDGES The table shows the lengths of the longest bridges in the UnitedStates and in Europe. Find the mean absolute deviation for each set ofdata. Round to the nearest hundredth if necessary. Then write a fewsentences comparing their variation.Longest Bridges (kilometers)United StatesEurope38.4 36.7 29.3 24.1 17.712.9 11.3 10.98.98.917.2 11.7 7.8 6.8 6.66.15.1 5.0 4.3 3.910. BASKETBALL The table shows the number of points scored each game fortwo different basketball teams. Find the mean absolute deviation for eachset of data. Round to the nearest hundredth if necessary. Then write afew sentences comparing their variation.Number of Points ScoredBLakeside PanthersJefferson Eagles44 38 54 48 26 3658 42 64 62 70 40POPULATION For Exercises 11–14, refer to the tablethat shows the recent population, in millions, of theten largest U.S. cities.11. Find the mean absolute deviation. Round to thenearest hundredth.Population of LargestU.S. Cities (millions)1.53.81.31.62.91.40.92.38.41.312. How many data values are closer than one mean absolute deviationaway from the mean?13. Which population is farthest from the mean? How far away from themean is that population? Round to the nearest hundredth.14. Are there any populations that are more than twice the mean absolutedeviation from the mean? Explain.VOCABULARY For Exercises 15 and 16, look up the word deviate in adictionary or online.15. What does the word deviate mean? How can it help you remember whatthe mean absolute deviation refers to?16. How does the word absolute help you to remember how to calculate themean absolute deviation?Lesson 12 Mean Absolute Deviation55

NUTRITION For Exercises 17 and 18, refer to the table that shows the numberof Calories in several sandwiches at two restaurants.Number of Calories per SandwichSusan’s Sub ShopThe Picnic Basket490 380 270 430 510 410550 320 470 430 610 29017. Find the mean absolute deviation for each set of data. Round to thenearest hundredth.18. For either data set, are there any data values that are more than twice themean absolute deviation from the mean? Explain.C19. OPEN ENDED Create two sets of data, each with five values, that satisfythe following conditions.The mean absolute deviation of Set A is less than the mean absolutedeviation of Set B.The mean of Set A is greater than the mean of Set B.CHALLENGE For Exercises 20 and 21, refer to thetable that shows the recorded speeds of severalcars on a busy street.Recorded Speeds (mph)35 38 41 35 36 5520. Calculate the mean absolute deviation both with and without the datavalue of 55. Round to the nearest hundredth if necessary.21. Explain how including the value of 55 affects the mean absolute deviation.22. REASONING Explain why the mean absolute deviation is calculated usingabsolute value.23. WRITE MATH Write a letter to a classmate explaining how to find the meanabsolute deviation and what it tells you about a set of data.TTest Practice24. The table shows the prices for parking atvarious beaches along the samecoastline.Beach Parking ( )2.50 3.75 1.25 2.25 3.00Which of the following is the meanabsolute deviation for the set of data?F. It describes the variation of the datavalues around the median.G. It describes the absolute value of themean.B. 0.66H. It describes the average distancebetween each data value and themean.C. 2.50I.A. 0.25D. 2.555625. Which of the following is trueconcerning the mean absolute deviationof a set of data?Domain: Statistics and ProbabilityIt describes the variation of the datavalues around the mode.

The mean absolute deviation of a set of data is the average distance between each data value and the mean. 1. Find the mean. 2. Find the distance between each data value and the mean. . Sixth Grade Seventh Grade 88 116 94 108 112 124 144 91 97 122 128 132 9.The table shows the lengths of the longest bridges in the United BRIDGES States and in .File Size: 2MBPage Count: 6Explore furtherMean Absolute Deviation Worksheet 1.pdfdocs.google.comMean Absolute Deviation Worksheetswww.mathworksheets4kids.comMean Absolute Deviation Calculatorwww.alcula.comGrade 6 McGraw Hill Glencoe - Answer Keys Answer keys .www.mathpractice101.comMean Absolute Deviation Worksheet - Houston ISDwww.houstonisd.orgRecommended to you b