Mathematics
Grade10
Easy

Question

Answer the following with the help of the data given below:
There are two brands of light bulbs which are brand M and Brand J. Here are the life spans of both brands (in hrs):
Brand M : 100 , 200 , 150 ,120  , 140 , 100
Brand J : 120 , 180 , 190 , 140 , 130 , 110
Which of the brands have a high standard deviation?

  1. Brand J             
  2. Brand M             
  3. Both a and b          
  4. None of the above

The correct answer is: Brand M


    The mean for Brand M=135
    The standard deviation for Brand M=
    space space space space space square root of fraction numerator left parenthesis negative 35 right parenthesis squared plus left parenthesis 65 right parenthesis squared plus left parenthesis 15 right parenthesis squared plus left parenthesis negative 15 right parenthesis squared plus left parenthesis 5 right parenthesis squared plus left parenthesis negative 35 right parenthesis squared over denominator 6 end fraction end root
equals square root of fraction numerator 1225 plus 4225 plus 225 plus 225 plus 25 plus 1225 over denominator 6 end fraction end root
equals square root of 7150 over 6 end root
almost equal to 34.52
    The mean for Brand J=145
    The standard deviation for Brand J=
    space space space space space square root of fraction numerator left parenthesis negative 25 right parenthesis squared plus left parenthesis 35 right parenthesis squared plus left parenthesis 45 right parenthesis squared plus left parenthesis negative 5 right parenthesis squared plus left parenthesis negative 15 right parenthesis squared plus left parenthesis negative 35 right parenthesis squared over denominator 6 end fraction end root
equals square root of fraction numerator 625 plus 1225 plus 2025 plus 25 plus 225 plus 1225 over denominator 6 end fraction end root
equals square root of 5350 over 6 end root
almost equal to 29.86
    Brand M have high standard deviation.

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