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Mean and Median

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by rumy » Wed Aug 11, 2010 3:03 am
if a certain sample set has mean of 20 and Standard deviation of 3. which of the following values is more than 2.5 standard deviations from the mean.

a) 12
b) 13.5
c) 17.0
d) 23.5
e) 26.5
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by clock60 » Wed Aug 11, 2010 3:13 am
seems like 12
20+3*2.5=27.5
20-3*2,5=12,5
the only number that out of range 12,5<x<27,5. is 12
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by albatross86 » Wed Aug 11, 2010 3:15 am
1 standard deviation = 3
2 standard deviations = 3*2 = 6
2.5 standard deviations = 3*2.5 = 7.5

Standard deviation represents the average deviation of all members of the set from the mean of that set. This means that we are looking for a number that is more than 7.5 units away from 20.

=> 12 (which is 8 units away) Pick A.
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by sheelanadh » Wed Aug 11, 2010 4:19 am
albatross86 wrote:1 standard deviation = 3
2 standard deviations = 3*2 = 6
2.5 standard deviations = 3*2.5 = 7.5

Standard deviation represents the average deviation of all members of the set from the mean of that set. This means that we are looking for a number that is more than 7.5 units away from 20.

=> 12 (which is 8 units away) Pick A.

thank u .... please explain me in little bit clarity....
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by beatthegmatinsept » Wed Aug 11, 2010 7:59 am
sheelanadh wrote:
albatross86 wrote:1 standard deviation = 3
2 standard deviations = 3*2 = 6
2.5 standard deviations = 3*2.5 = 7.5

Standard deviation represents the average deviation of all members of the set from the mean of that set. This means that we are looking for a number that is more than 7.5 units away from 20.

=> 12 (which is 8 units away) Pick A.

thank u .... please explain me in little bit clarity....
Given,
Mean = 20
SD = 3
For something to be 1 SD away from the mean, the number will be either greater than (20+3= 23) OR less than (20-3=17).
Using the same logic, for something to be 2 SD's away, the number will be either greater than (20+6+26) OR less than (20-6=14).
The question asks 2.5 SD. So, 2.5 SD = 2.5(3) = 7.5. SO your answer should be either greater than 27.5 OR less than 12.5. The only answer choice that meets that criteria is A.
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