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Understanding Data Distribution with Mean Absolute Deviation (MAD)

Learn how to describe dataset variation using MAD, comparing data points to the mean, through examples and explanations.

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Understanding Data Distribution with Mean Absolute Deviation (MAD)

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  1. Howcanyoudescribehowfarapartthe responsesarefromthecenterinadataset? Inthislessonyouwilllearnhowto describethedistributionofdataby usingthemeanabsolutedeviation. MAD

  2. First Let’sReview Readingadotplot Howmanybooksdid8thgradersatLilburnMiddleSchoolreadthissummer? 0 4 6 16 22 10 14 18 20 12 8 2 NumberofBooks

  3. Let’sReview Themeanofasetofdataistheaverage. Howmanysiblingsdoyouhave? 5 4 1 0 2 3 0+0+0+1+1+1+2+2+3+4+5+5=24 24÷12=2

  4. Let’sReview Absolutevalueisthedistanceanynumberis from0. |-5|=5 |3|=3

  5. Variability: Describeshowthespreadoutorclosely clusteredthedatasetis. Thereare3waystodeterminethespread: 1.Range 2.InterquartileRange 3.MeanAbsoluteDeviation

  6. ACommonMistake Themeanandmeanabsolutedeviationareoften confusedbecausetheybothincludetheword, “mean.” Meanabsolute deviation Mean

  7. MeanAbsoluteDeviation(MAD): MAD-istheaveragedistancebetweeneach datavalueandthemean.

  8. Findthemeanabsolutedeviation. Howmanysiblingsdoyouhave? 012345 Step1:Findthe 0 0 0 1 1 1 2 2 3 4 mean 5 +5 24÷12=2

  9. Findthemeanabsolutedeviation. Howmanysiblingsdoyouhave? 2 2 2 1 1 1 0 0 0 1 2 3 4 5 1 2 3 3 3 12 2 2 2 1 1 1 0 0 3 Step2:Findthedistancebetween themeanandthevalues||

  10. Remember: Staypositive! 6 5 32 lllllllllllllll 3 6 91215 6+3+2+5 4 MAD= =4

  11. Findthemeanabsolutedeviation. Howmanysiblingsdoyouhave? 012345 2 2 2 1 1 1 0 0 1 2 3 3 3 2 2 2 1012 10 1 +3 1818÷12=1.5 of Step3:Findtheaverage thedistance.

  12. You can alsoinformallycompare twopopulations byusingthemeanabsolute deviation(MAD).

  13. NFCMAD: 6+33+45+24+21+15+12 7 =22.2 AFCMAD: 4+17+30+8+10+6+2 7 =11 Comparison The mean absolute deviation for the NFC is greater than the mean absolute deviation for the AFC. That means the data for penalties for the AFC are closer together. The NFC has a farther spread.

  14. GuidedPractice – Try these two problems Findtherangeandmeanabsolutedeviation ofthisdata.

  15. Findthemeanabsolutedeviation. Howmanypetsdoyouhave? 0,1,5,0,3,1,0,2,2,6

  16. Race it!!!! Findtherangeandmeanabsolutedeviation ofthisdata. 6 4 10 12 8 2 NumberofCDsowned

  17. Whatisthemeanabsolutedeviationofthe dataset? Howmanybooksdidyoureadthissummer? 3,5,2,3,3,1,4,4,3,2

  18. Whatisthemeanabsolutedeviationofthe datasetandwhatdoesitmean? Howmanypairsofshoesdoyouown? 3,7,2,8,3,19,5,9

  19. Findtherangeandmeanabsolutedeviation ofthis data. Howmanypairsofshoesdo8thgradersat LilburnMiddleSchoolown?

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