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Effects of Uniform Data Changes on Range, Interquartile Range, Variance and Standard Deviation

Effects of Uniform Data Changes on Range, Interquartile Range, Variance and Standard Deviation. 14, 16, 20, 18, 22. Find range, interquartile range, variance and standard deviation for the set of data above. 14, 16, 20, 18, 22. Range = 22 – 14 = 8. 14, 16, 18, 20, 22. First Quartile = 15,

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Effects of Uniform Data Changes on Range, Interquartile Range, Variance and Standard Deviation

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  1. Effects of Uniform Data Changes on Range, Interquartile Range, Variance and Standard Deviation

  2. 14, 16, 20, 18, 22 Find range, interquartile range, variance and standard deviation for the set of data above.

  3. 14, 16, 20, 18, 22 Range = 22 – 14 = 8 14, 16, 18, 20, 22 First Quartile = 15, Third Quartile = 21 Interquartile range = 21 – 15 = 6

  4. 14, 16, 20, 18, 22 Mean = (14+16+20+18+22)5 = 90  5 = 18 Sum of squared deviation from the mean =(14 – 18)2 + (16 – 18)2 + (20 – 18)2 + (18 – 18)2 + (22 – 18)2 = (-4)2 + (-2)2 + (2)2 + (0)2 + (4)2 = 40 Variance = 40  5 = 8 Standard Deviation = sqrt(8) = 2.828

  5. 14, 16, 20, 18, 22 If each data in the set is added a constant value of 5, find: a) range, b) interquartile range, c) variance and d) standard deviation for the new set of data above.

  6. 14+5, 16+5, 20+5, 18+5, 22+5 New set of data: 19, 21, 23, 25, 27 New Range = 27 – 19 = 8 New First quartile = 20 New Third quartle = 26 New Interquartile range = 26 – 20 = 6

  7. 14+5, 16+5, 20+5, 18+5, 22+5 New set of data: 19, 21, 23, 25, 27 New Mean = 18 + 5 = 23 Sum of squared of deviation from the mean = (19 – 23)2 + (21 – 23)2 + (23 – 23)2 +(25 – 23)2 + (27 – 23)2 = (-4)2 +(-2)2 + 02 + (2)2 + (4)2 = 40 Variance = 40  5 =8 Standard deviation = sqrt(8) = 2.828

  8. Effect 14, 16, 20, 18, 22, Range = 8 Interquartile range = 6 Variance = 8 Std. Dev = 2.828 19, 21, 25, 23, 27, Range = 8 Interquartile range = 6 Variance = 8 Std. Dev = 2.828

  9. Conclusion:Effects on Range, Interquartile Range, Variance and Standard Deviation when the data is added/substractedby a constant k isNO CHANGE

  10. 14, 16, 20, 18, 22 If each data in the set is MULTIPLIED BY a constant value of 5, find: a) range, b) interquartile range, c) variance and d) standard deviation for the new set of data above.

  11. 145, 165, 20  5, 18  5, 22  5 New set of data: 70, 80,100, 90,110 New Range = 110 – 70 = 40 New First quartile = 75 New Third quartle = 105 New Interquartile range = 75 – 105 = 30

  12. New set of data: 70, 80,100, 90,110 New Mean = 18  5 = 90 Sum of squared of deviation from the mean = (70 – 90)2 + (80 – 90)2 + (100 – 90)2 +(90 – 90)2 + (110 – 90)2 = (-20)2 +(-10)2 + (10)2 + (0)2 + (20)2 = 1000 Variance = 1000  5 =200 Standard deviation = sqrt(200)= 14.14

  13. Effect 14, 16, 20, 18, 22, Range = 8 Interquartile range = 6 Variance = 8 Std. Dev = 2.828 70, 80,100, 90,110 Range = 40 Interquartile range = 30 Variance = 200 Std. Dev = 14.14

  14. Conclusion:Effects on Range, Interquartile range, Variance and Std Dev when the data is MULTIPLIED by a constant k isnew range = koriginal rangenew interquartile = koriginal Interquatilenew variance = k2original variancenew std. dev = k original std.dev

  15. Effect of changes on M.D.

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