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

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 (1416201822)?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
145, 165, 205, 185, 225

• 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
145, 165, 205, 185, 225

• 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

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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
ConclusionEffects 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.

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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

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• 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

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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
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ConclusionEffects 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
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Effect of changes on M.D.
M. of dispersion Change New M.of D
Range Interquartile range variance std. deviation k No change.
Range Interquartile range Std. deviation k k original value.
Variance k k2 original value.
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