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What is the standard deviation of {-3, -6, -5, -10} approximately equal to, if the standard deviation of {3, 6, 5, 10} is approximately equal to 2.5?
  • a)
    -5.0
  • b)
    -2.5
  • c)
    0
  • d)
    2.5
  • e)
    5.0
Correct answer is option 'D'. Can you explain this answer?
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What is the standard deviation of {-3, -6, -5, -10} approximately equa...
Finding standard deviation of {-3, -6, -5, -10}
Step 1
Mean of {-3,-6,-5,-10} = {( -3) + (-6) + (-5) + (-10)}/4 = -6
Step 2
Distances of each point from the mean:
  • -3 – (-6) = 3
  • -6 – (-6) = 0
  • -5 – (-6) = 1
  • -10-(-6) = -4
Step 3
Squared Distance from Mean
  • = (3)2 + (0)2 + (1)2 + (-4)2
  • = 9 + 0 + 1 + 16 = 26
Step 4
  • Average = 26/4 = 6.5
Step 5
  • Standard Deviation = √6.5 ≌ 2.5
    • Note that this Standard Deviation is the same as Standard deviation of {3, 6, 5, 10}.
 Remember -The standard deviation of a set remains the same even if all the elements are multiplied by (-1)
Answer: Option (D)
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What is the standard deviation of {-3, -6, -5, -10} approximately equal to, if the standard deviation of {3, 6, 5, 10} is approximately equal to 2.5?a)-5.0b)-2.5c)0d)2.5e)5.0Correct answer is option 'D'. Can you explain this answer?
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