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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, 03:32
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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 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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Originally posted by gmatmania17 on 13 Feb 2015, 01:33.
Last edited by Bunuel on 13 Feb 2015, 03:32, 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, 02:49
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
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13 Feb 2015, 03:37
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 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: themeanandthestandarddeviationofthe8numbersshown98248.htmlthestandarddeviationofanormaldistributionofdatais99221.htmlavendingmachineisdesignedtodispense8ouncesofcoffee93351.htmlarithmeticmeanandstandarddeviationofacertainnormal104117.htmlthelifetimeofallthebatteriesproducedbyacertaincomp101472.html7075808590105105130130130thelistshownconsistof100361.htmlforacertainexamascoreof58was2standarddeviationsb128661.htmlacertaincharacteristicinalargepopulationhasa143982.htmltheresidentsoftownxparticipatedinasurvey83362.htmlthestandarddeviationofanormaldistributionofdatais99221.htmlthemeanandthestandarddeviationofthe8numbersshown98248.htmlifacertainsampleofdatahasameanof200anda127810.htmlgiventhatthemeanofsetais10whatistherangeoftwo141964.htmlifacertainsampleofdatahasameanof240andthevalue171843.htmlforacertainexamascoreof58was2standarddeviationsb128661.html
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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, 04:00
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 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: themeanandthestandarddeviationofthe8numbersshown98248.htmlthestandarddeviationofanormaldistributionofdatais99221.htmlavendingmachineisdesignedtodispense8ouncesofcoffee93351.htmlarithmeticmeanandstandarddeviationofacertainnormal104117.htmlthelifetimeofallthebatteriesproducedbyacertaincomp101472.html7075808590105105130130130thelistshownconsistof100361.htmlforacertainexamascoreof58was2standarddeviationsb128661.htmlacertaincharacteristicinalargepopulationhasa143982.htmltheresidentsoftownxparticipatedinasurvey83362.htmlthestandarddeviationofanormaldistributionofdatais99221.htmlthemeanandthestandarddeviationofthe8numbersshown98248.htmlifacertainsampleofdatahasameanof200anda127810.htmlgiventhatthemeanofsetais10whatistherangeoftwo141964.htmlifacertainsampleofdatahasameanof240andthevalue171843.htmlforacertainexamascoreof58was2standarddeviationsb128661.html



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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, 04:09
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 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: themeanandthestandarddeviationofthe8numbersshown98248.htmlthestandarddeviationofanormaldistributionofdatais99221.htmlavendingmachineisdesignedtodispense8ouncesofcoffee93351.htmlarithmeticmeanandstandarddeviationofacertainnormal104117.htmlthelifetimeofallthebatteriesproducedbyacertaincomp101472.html7075808590105105130130130thelistshownconsistof100361.htmlforacertainexamascoreof58was2standarddeviationsb128661.htmlacertaincharacteristicinalargepopulationhasa143982.htmltheresidentsoftownxparticipatedinasurvey83362.htmlthestandarddeviationofanormaldistributionofdatais99221.htmlthemeanandthestandarddeviationofthe8numbersshown98248.htmlifacertainsampleofdatahasameanof200anda127810.htmlgiventhatthemeanofsetais10whatistherangeoftwo141964.htmlifacertainsampleofdatahasameanof240andthevalue171843.htmlforacertainexamascoreof58was2standarddeviationsb128661.htmlI 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
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13 Feb 2015, 04:16
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 3040s to finish reading the question



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The list above shows the scores of 10 schoolchildren on a certain test
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13 Feb 2015, 04:17
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 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: themeanandthestandarddeviationofthe8numbersshown98248.htmlthestandarddeviationofanormaldistributionofdatais99221.htmlavendingmachineisdesignedtodispense8ouncesofcoffee93351.htmlarithmeticmeanandstandarddeviationofacertainnormal104117.htmlthelifetimeofallthebatteriesproducedbyacertaincomp101472.html7075808590105105130130130thelistshownconsistof100361.htmlforacertainexamascoreof58was2standarddeviationsb128661.htmlacertaincharacteristicinalargepopulationhasa143982.htmltheresidentsoftownxparticipatedinasurvey83362.htmlthestandarddeviationofanormaldistributionofdatais99221.htmlthemeanandthestandarddeviationofthe8numbersshown98248.htmlifacertainsampleofdatahasameanof200anda127810.htmlgiventhatthemeanofsetais10whatistherangeoftwo141964.htmlifacertainsampleofdatahasameanof240andthevalue171843.htmlforacertainexamascoreof58was2standarddeviationsb128661.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
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02 Feb 2019, 19:47
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 MSD = 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
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