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The list above shows the scores of 10 schoolchildren on a certain test
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Updated on: 13 Feb 2015, 04:32
Updated on: 13 Feb 2015, 04:32
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A
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Difficulty:
45%
(medium)
Question Stats:
63% (01:42) correct
37%
(01:55)
wrong
based on 272
sessions
40, 45, 50, 55, 60, 75, 75, 100, 100, 100.
The list above shows the scores of 10 schoolchildren on a certain test. If the standard deviation of the 10 scores is 22.4, rounded to the nearest tenth, how many of the scores are more than 1 standard deviation below the mean of the 10 scores?
A. One
B. Two
C. Three
D. Four
E. Five
The list above shows the scores of 10 schoolchildren on a certain test. If the standard deviation of the 10 scores is 22.4, rounded to the nearest tenth, how many of the scores are more than 1 standard deviation below the mean of the 10 scores?
A. One
B. Two
C. Three
D. Four
E. Five
I arrived to the solution but i would like to find a quickest way..I computed the average for the scores from 40 to 60 which is the number in the middle because they are evenly spaced. Then I multiply 50*5added 2*75 and 3*100 and divided everything by 10 obtaining the average which is 70.
Then I subtracted 22.4 from 70 and I found : 47.6. Then I counted the scores that are less than 47.6 that are 2 (40,45) and i arrived at the answer..
Thank you in advance!
Then I subtracted 22.4 from 70 and I found : 47.6. Then I counted the scores that are less than 47.6 that are 2 (40,45) and i arrived at the answer..
Thank you in advance!
Originally posted by gmatmania17 on 13 Feb 2015, 02:33.
Last edited by Bunuel on 13 Feb 2015, 04:32, edited 2 times in total.
Last edited by Bunuel on 13 Feb 2015, 04:32, edited 2 times in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
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Re: The list above shows the scores of 10 schoolchildren on a certain test
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13 Feb 2015, 03:49
13 Feb 2015, 03:49
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You can use normal distribution curve to solve it. Simply drawn, its a bell shaped curve; on either side of the middle you draw two lines. So you have divided the curve from left to right in 6 parts and the % of the area under them is roughly (from left to right) 2%, 14%, 34%, 34%, 14%, 2% respectively. On either side of the center, mean increases and decreases by 10 units whereas standard deviation increases and decreases by 1 unit. By that logic, 60 comes on the graph at a point that covers 2% and 14% of the graph which is a total of 16%.
Now 16% of ten students is 1.6 students which is roughly 2 students.
Now 16% of ten students is 1.6 students which is roughly 2 students.
Re: The list above shows the scores of 10 schoolchildren on a certain test
[#permalink]
13 Feb 2015, 04:37
13 Feb 2015, 04:37
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Expert Reply
gmatmania17 wrote:
40, 45, 50, 55, 60, 75, 75, 100, 100, 100.
The list above shows the scores of 10 schoolchildren on a certain test. If the standard deviation of the 10 scores is 22.4, rounded to the nearest tenth, how many of the scores are more than 1 standard deviation below the mean of the 10 scores?
A. One
B. Two
C. Three
D. Four
E. Five
The list above shows the scores of 10 schoolchildren on a certain test. If the standard deviation of the 10 scores is 22.4, rounded to the nearest tenth, how many of the scores are more than 1 standard deviation below the mean of the 10 scores?
A. One
B. Two
C. Three
D. Four
E. Five
I arrived to the solution but i would like to find a quickest way..I computed the average for the scores from 40 to 60 which is the number in the middle because they are evenly spaced. Then I multiply 50*5added 2*75 and 3*100 and divided everything by 10 obtaining the average which is 70.
Then I subtracted 22.4 from 70 and I found : 47.6. Then I counted the scores that are less than 47.6 that are 2 (40,45) and i arrived at the answer..
Thank you in advance!
Then I subtracted 22.4 from 70 and I found : 47.6. Then I counted the scores that are less than 47.6 that are 2 (40,45) and i arrived at the answer..
Thank you in advance!
The average of {40, 45, 50, 55, 60, 75, 75, 100, 100, 100} is 70.
1 standard deviation below the mean is 70 - 22.4 = 47.6. Hence there are two scores (40 and 45) more than 1 standard deviation below the mean.
Answer B.
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