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The list above shows the scores of 10 schoolchildren on a certain test

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gmatmania17
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The list above shows the scores of 10 schoolchildren on a certain test [#permalink] New post   Updated on: 13 Feb 2015, 04:32
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Difficulty:

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Question Stats:

63% (01:41) correct 37% (01:54) wrong based on 253 sessions
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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

Show Spoiler
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!
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B

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.
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 [#permalink] New post   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.
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Re: The list above shows the scores of 10 schoolchildren on a certain test [#permalink] New post   13 Feb 2015, 04:37
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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

Show Spoiler
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!


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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Re: The list above shows the scores of 10 schoolchildren on a certain test [#permalink] New post   13 Feb 2015, 05:00
Hi Bunuel,

Is there a quickest way to solve it?

Thank you

Regards
Sabri Amer
Bunuel wrote:
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

Show Spoiler
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!


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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Re: The list above shows the scores of 10 schoolchildren on a certain test [#permalink] New post   13 Feb 2015, 05:09
Expert Reply
gmatmania17 wrote:
Hi Bunuel,

Is there a quickest way to solve it?

Thank you

Regards
Sabri Amer
Bunuel wrote:
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

Show Spoiler
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!


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.

Similar questions to practice:
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the-standard-deviation-of-a-normal-distribution-of-data-is-99221.html
a-vending-machine-is-designed-to-dispense-8-ounces-of-coffee-93351.html
arithmetic-mean-and-standard-deviation-of-a-certain-normal-104117.html
the-lifetime-of-all-the-batteries-produced-by-a-certain-comp-101472.html
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I think this is the fastest method. Should take no more than a minute.
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Re: The list above shows the scores of 10 schoolchildren on a certain test [#permalink] New post   13 Feb 2015, 05:16
Bunuel wrote:
I think this is the fastest method. Should take no more than a minute.


Do you mean a minute in total? It took me around 1:40 in total to arrive to the answer, maybe 30-40s to finish reading the question :roll:
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The list above shows the scores of 10 schoolchildren on a certain test [#permalink] New post   13 Feb 2015, 05:17
I think the slowest part is computing the average.. Do you have a technique to do that?


Is there a quickest way to solve it?

Thank you

Regards

Bunuel wrote:
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

Show Spoiler
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!


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.

Similar questions to practice:
the-mean-and-the-standard-deviation-of-the-8-numbers-shown-98248.html
the-standard-deviation-of-a-normal-distribution-of-data-is-99221.html
a-vending-machine-is-designed-to-dispense-8-ounces-of-coffee-93351.html
arithmetic-mean-and-standard-deviation-of-a-certain-normal-104117.html
the-lifetime-of-all-the-batteries-produced-by-a-certain-comp-101472.html
70-75-80-85-90-105-105-130-130-130-the-list-shown-consist-of-100361.html
for-a-certain-exam-a-score-of-58-was-2-standard-deviations-b-128661.html
a-certain-characteristic-in-a-large-population-has-a-143982.html
the-residents-of-town-x-participated-in-a-survey-83362.html
the-standard-deviation-of-a-normal-distribution-of-data-is-99221.html
the-mean-and-the-standard-deviation-of-the-8-numbers-shown-98248.html
if-a-certain-sample-of-data-has-a-mean-of-20-0-and-a-127810.html
given-that-the-mean-of-set-a-is-10-what-is-the-range-of-two-141964.html
if-a-certain-sample-of-data-has-a-mean-of-24-0-and-the-value-171843.html
for-a-certain-exam-a-score-of-58-was-2-standard-deviations-b-128661.html
[/quote]

I think this is the fastest method. Should take no more than a minute.[/quote]
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Re: The list above shows the scores of 10 schoolchildren on a certain test [#permalink] New post   02 Feb 2019, 20:47
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 mean of above numbers will be 70, Mean = Sum of all terms/ Number of terms

Now M-SD = 70 - 22.4 = 57.6

How many values are between 1SD and Mean
2

B
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Re: The list above shows the scores of 10 schoolchildren on a certain test [#permalink] New post   11 Jan 2024, 00:11
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Re: The list above shows the scores of 10 schoolchildren on a certain test [#permalink]
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