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standard deviation

by mysseo » Mon Jan 02, 2012 9:31 pm
70, 75, 80, 85, 90, 105, 105, 130, 130, 130

The list shown consists of the times, in seconds, that it took each of 10 schoolchildren to run a distance of 400 meters. If the standard deviation of the 10 running times is 22.4 in seconds, rounded to the nearest tenth of a second, how many of the 10 running times are more than 1 standard deviation below the mean of the 10 running times?

A. One
B. TWo
C. Three
D. Four
E. Five
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by Anurag@Gurome » Mon Jan 02, 2012 9:51 pm
mysseo wrote:70, 75, 80, 85, 90, 105, 105, 130, 130, 130

The list shown consists of the times, in seconds, that it took each of 10 schoolchildren to run a distance of 400 meters. If the standard deviation of the 10 running times is 22.4 in seconds, rounded to the nearest tenth of a second, how many of the 10 running times are more than 1 standard deviation below the mean of the 10 running times?

A. One
B. TWo
C. Three
D. Four
E. Five
How many of the 10 running times are more than 1 standard deviation below the mean of the 10 running times means how many data points from given 10 are less than Mean - S.D.

S.D = 22.4
Mean = (70 + 75 + 80 + 85 + 90 + 105 + 105 + 130 + 130 + 130)/10 = 1000/10 = 100
100 - 22.4 = 77.6 and there are only 2 data points below 77.6: 70 and 75

The correct answer is B.
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by mysseo » Mon Jan 02, 2012 10:37 pm
Thank you Anurag, the wording of the question" more than 1 S.D below the mean" made me confused. Now it's clear.
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by Anurag@Gurome » Mon Jan 02, 2012 10:51 pm
mysseo wrote:Thank you Anurag, the wording of the question" more than 1 S.D below the mean" made me confused. Now it's clear.
You are welcome.
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by ArunangsuSahu » Tue Jan 03, 2012 6:28 pm
S.D=22.4(Given)

Mean=(70+75+80+85+90+105*2+130*3)/10=100

1 unit of S.D below the mean is =100-1*22.4=77.6

There are 2 such points 70,75
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