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Mean, Median, and ModeThe following data represent shoe sizes for elevensoccer players playing in a match:43, 42, 39, 41, 41, 40, 38, 40, 40, 39, and 40What size appears the most frequently? Arrangethe sizes in order from smallest to biggest. Whatsize is in the middle of the ordered data? Find thesum of the shoe sizes and divide the sum by 11.What is the result? Does the result show a shoesize? If it does not, explain.The mean, median, and mode are central tendency measures. Suppose wehave the following data: 2, 3, 5, 7, 8, 8, and 9.2, 3, 5, 7, 8, 8, 9The mode is the dataitem that appears themost frequently2, 3, 5, 7, 8, 8, 9The median is the valueof the middle memberof a set of numberswhen they are arrangedin order2+ 3+ 5+ 7+ 8+8+9=426742=dataofNumbervaluesdataofSum=MeanWhat are you goingto learn?to define theconcepts of mean,median, and modeto calculate mean,median, and modeKey Terms:• mean• median• mode33..22Figure 2.45566 // SSttuuddeenntt’’ss BBooookk -- SSttaattiissttiiccss
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Rate of Death in Surabayain 1999Month NumberJanuaryFebruaryMarchAprilMayJuneJulyAugustSeptemberOctoberNovemberDecember82163131141115149103130144154163216Source: Office of CivilAffairs SurabayaFigure 2.5Find the mean, the median andthe mode of the data on the rightabout the death rate in Surabaya in 1999.Solutiona. To find the mean, find the sum of the data and then divide the sumby 12 as follows:1221616315414413010314911514113116382 +++++++++++= 1691/12 = 140.9167b. To find the median, arrange the data in order from smallest tobiggest: 82, 103, 115, 130, 131, 141, 144, 149, 154, 163, 163, 2165,1422144141 =+ Because the number of the data is even, themedian is determined by summing the twodata in the middle and then dividing the sumby 2. Therefore, the median of the data is142.5.c. To find the mode, study the data in the table and find the data itemthat appears the most frequently (the value that has the highestfrequency). Because number 163 appears twice, while the othernumbers appear only once, therefore, the mode of the data is 163.MMaatthheemmaattiiccss ffoorr JJuunniioorr HHiigghh SScchhooooll GGrraaddee 99 // 5577
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• Mode is the data item with the highest frequency.• Median is the value of the middle member of a set ofnumbers when they are arranged in order from smallest tobiggest• Mean =dataofNumbervaluesdataofSumFind the mean, median, and mode of each of the following data sets:a. Scores on a mathematics test: 100, 72, 86, 86, 84, 92, 86, 90.b. Numbers of sleepinghours: 10, 8, 9, 10, 9, 9, 10, 9, 7.Solutiona. The mathematics score of the 8students: 100, 72, 86, 86, 84, 92,86, 90.Mean = 87890869284868672100=+++++++The mode is 86, because the score appears most frequently (3 times) inthe data set.To find out the median, all the score must be put in order from thesmallest to the biggest as follows: 72, 84, 86, 86, 86, 90, 92, 100. As thenumber of the score is even, the median is the sum of the two scores inthe middle position divided by 2, that is 8628686=+.b. The numbers of sleeping hours: 10, 8, 9, 10, 9, 9, 10, 9, 7.Mean =91010999109810 +++++++++= 95588 // SSttuuddeenntt’’ss BBooookk -- SSttaattiissttiiccss
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The mode is 9 because the score appears most frequently (4 times) in thedata set.To find out the median, all the score must be put in order from smallestto biggest as follows: 7, 8, 9, 9, 9, 9, 10,10, 10. Because the number of thescore is odd, the median is the score in the middle position, that is 9.1. Find the mean, median and mode of each of the following data sets:a. Scores on a physics test: 6, 7, 7, 8, 8, 8, 10, 10.b. The number of the male students in each class: 31, 26, 30, 35, 25, 24, 35,30, 30, 24.2. The following is the data that shows the ownership of domestic animalsamong the students in a junior high school class: 1, 0, 1, 3, 0, 2, 3, 1, 0, 6, 1,7, 2, 1, 1, 2, 3, 0, 1, 2, 6, 2, 0, 3.a. Copy and complete the following table with the data.Number ofstudents1 2 3 4 5 6 7 ……Number ofanimals1 0 ........ ........ ........ ......... .......... .......b. Find out :1). The total number of the students in the class.2). The total number of the domestic animals.3). The mode of the domestic animal ownership. What does it mean?4). The mean of the domestic animal ownership. What does it mean?Country AmountAustraliaCanadaFranceGermanyItalyJapanMexicoNetherlandsNew ZealandEnglandOthers227933017031778197323815921422218115961038Source: World Almanac3. The average amount of money spent by visitors in the United States (indollar per person) is as follows:a). Find out the median of the data. What doesit mean?b). Which country spent the most, and howmuch?c). Which countries spent more than theNetherlands?MMaatthheemmaattiiccss ffoorr JJuunniioorr HHiigghh SScchhooooll GGrraaddee 99 // 5599
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