BTGmoderatorDC wrote:Justin took a test of French at school and scored 72 marks out of 100. If there were 20 students who appeared for the test, within how many standard deviations from the mean did Justin's score lie?
(1) Darren and Matthew scored 70 and 75 respectively and their scores were within one standard deviation from the mean.
(2) The mean score of 20 students was 65 and Andrew who scored 59 was within one standard deviation of the mean.
OA A
Source: e-GMAT
This question involves the concept of standard deviation. Note that the computation of SD is not within the scope of the GMAT; however, its application is within the scope.
Let's take each statement one by one.
(1) Darren and Matthew scored 70 and 75 respectively and their scores were within one standard deviation from the mean.
We see that Justin's score 72, is greater than 70 as well as smaller than 75. Given that both scores 72 and 75 are within one standard deviation from the mean, 72 must also be within one standard deviation from the mean. Sufficient.
(2) The mean score of 20 students was 65 and Andrew who scored 59 was within one standard deviation of the mean.
So, we have mean = 65 and a score 59 (< 65) is within one standard deviation of the mean; thus, Mean - 1SD ≤ 59 => 65 - 1SD ≤ 59 => SD ≤ 6.
Thus, on the upper limit ≥ Mean + 1SD = 65 + 1*6 = 71.
Since 72 is greater than 71, we cannot determine how many standard deviations from the mean Justin's score lie. Insufficient.
The correct answer:
A
Hope this helps!
-Jay
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