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The list shown consist of the times, in seconds, that it

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The list shown consist of the times, in seconds, that it  [#permalink]

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New post Updated on: 14 Oct 2014, 06:00
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Question Stats:

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70, 75, 80, 85, 90, 105, 105, 130, 130, 130
The list shown consists of the times, in seconds, that it took each of 10 schoolchildren to run a distance of 400 on of meters. If the standard devastation of the 10 running times is 22.4 seconds, rounded to the nearest tenth of a second, how many of the 10 running times are more than 1 standard deviation below the mean of the 10 running times?

A. one
B. two
C. three
D. four
E. five

Originally posted by raghavs on 28 Mar 2010, 09:42.
Last edited by Bunuel on 14 Oct 2014, 06:00, edited 3 times in total.
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Re: The list shown consist of the times, in seconds, that it  [#permalink]

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New post 23 Jan 2012, 03:01
2
5
karthiksms wrote:
Could someone please explain this? thanks


70 75 80 85 90 105 105 130 130 130

The list shown consist of the times, in seconds, that it took each of 10 school children to run a distance of 400 meter. If the SD of ten running times is 22.4 seconds, rounded to nearest tenth of second, how many of the 10 running times are more than one SD below the mean of the 10 running times?

A. one
B. two
C. three
D. four
E. five

"How many of the 10 running times are more than one SD below the mean" means how many data points from given 10 are less than mean-1SD.

We are given that SD=22.4, so we should find mean --> mean=100 --> there are only 2 data points below 100-22.4=77.6, namely 70 and 75.

Answer: B.

Also discussed here: 70-75-80-85-90-105-105-130-130-130-the-list-shown-consist-of-100361.html

Similar problems:
math-questions-mean-score-88502.html?hilit=below%20mean%20deviation
statistics-question-99221.html?hilit=below%20mean%20deviation#p764887

Hope it helps.
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Re: The list shown consist of the times, in seconds, that it  [#permalink]

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New post 28 Mar 2010, 11:13
1
raghavs wrote:
standard deviation..first question stumped me


OA--TWO


the mean of the 10 running times is 100 sec. we need to find how many of the recorded times are less than 1 SD below the mean i.e how many took less than 100 sec - 1SD = 100 sec - 22.4 sec = 77.6sec. The times are 70 and 75. hence 2
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Re: The list shown consist of the times, in seconds, that it  [#permalink]

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New post 28 Mar 2010, 21:35
raghavs wrote:
standard deviation..first question stumped me


OA--TWO


mean is 99
SD is 22.4
One SD block away = 99-22.4 = 76.6
so there are two numbers less than mean which are One SD block away 70 & 75 hence TWO.
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Re: The list shown consist of the times, in seconds, that it  [#permalink]

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New post 23 Jan 2012, 06:57
first add the values and devide by 10 to get the mean of 100.
then butract 22.4 from the 100.....> 100-22.4=76.6

check how many numbers in the list are less than 76.6! there are two numbers

hope this helps
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Re: The list shown consist of the times, in seconds, that it  [#permalink]

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New post 03 Jun 2013, 02:09
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Re: The list shown consist of the times, in seconds, that it  [#permalink]

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New post 03 Jun 2013, 04:15
1
The first step here is to calculate the mean :

(70+75+80+85+90+105+105+130+130+130)/10 = 100

SD = 22.4,

one SD below the mean = (100 – 22.4) = 77.6

Only 2 values 70 and 75 are less than 77.6, hence B is the answer
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Re: The list shown consist of the times, in seconds, that it  [#permalink]

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New post 03 Jun 2013, 15:23
To find the mean, take a wild stab and pick a number within the range provided by the given numbers. Now, find the delta between that number and each number in the set. So now you get the overall delta from your "assumed mean". Split that up equally among each number. So adding that to your "assumed mean" will give you the actual mean.

I took 100 and found the difference between it and each of the numbers in the set. Turns out that the overall delta neatly becomes 0. So 100 is the actual mean.
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Re: The list shown consist of the times, in seconds, that it  [#permalink]

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New post 04 Jun 2013, 03:39
2
70 75 80 85 90 105 105 130 130 130

The list shown consist of the times, in seconds, that it took each of 10 school children to run a distance of 400 meter. If the SD of ten running times is 22.4 seconds, rounded to nearest tenth of second, how many of the 10 running times are more than one SD below the mean of the 10 running times?
A. one
B. two
C. three
D. four
E. five

The most time consuming part in this question is to define the mean. Under exam pressure and time pressure it is very easy to make mistake.
it is easier to group numbers: 130*3=390; 105*2=210; 75+85=160; 70+80=150; 90;
Next stage combine results, again using more convenient ways to calculate: 390+210=600; 160+150=310; 90. 600+310+90=1000. Since there are 10 numbers the mean is 100. Questions asks to find the quantity of numbers one SD BELOW the mean, which is 100-22,4=77,6. There are only two numbers below 77,6. The answer is B
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Re: The list shown consist of the times, in seconds, that it  [#permalink]

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New post 03 Sep 2013, 23:55
ziko wrote:
70 75 80 85 90 105 105 130 130 130

The list shown consist of the times, in seconds, that it took each of 10 school children to run a distance of 400 meter. If the SD of ten running times is 22.4 seconds, rounded to nearest tenth of second, how many of the 10 running times are more than one SD below the mean of the 10 running times?
A. one
B. two
C. three
D. four
E. five

The most time consuming part in this question is to define the mean. Under exam pressure and time pressure it is very easy to make mistake.
it is easier to group numbers: 130*3=390; 105*2=210; 75+85=160; 70+80=150; 90;
Next stage combine results, again using more convenient ways to calculate: 390+210=600; 160+150=310; 90. 600+310+90=1000. Since there are 10 numbers the mean is 100. Questions asks to find the quantity of numbers one SD BELOW the mean, which is 100-22,4=77,6. There are only two numbers below 77,6. The answer is B



Pardon me for my understanding, but "are <more than> <one SD below the mean> of the 10 running times?
So isn't it asking values greater than 77.6 ?
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Re: The list shown consist of the times, in seconds, that it  [#permalink]

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New post 04 Sep 2013, 01:49
ygdrasil24 wrote:
ziko wrote:
70 75 80 85 90 105 105 130 130 130

The list shown consist of the times, in seconds, that it took each of 10 school children to run a distance of 400 meter. If the SD of ten running times is 22.4 seconds, rounded to nearest tenth of second, how many of the 10 running times are more than one SD below the mean of the 10 running times?
A. one
B. two
C. three
D. four
E. five

The most time consuming part in this question is to define the mean. Under exam pressure and time pressure it is very easy to make mistake.
it is easier to group numbers: 130*3=390; 105*2=210; 75+85=160; 70+80=150; 90;
Next stage combine results, again using more convenient ways to calculate: 390+210=600; 160+150=310; 90. 600+310+90=1000. Since there are 10 numbers the mean is 100. Questions asks to find the quantity of numbers one SD BELOW the mean, which is 100-22,4=77,6. There are only two numbers below 77,6. The answer is B



Pardon me for my understanding, but "are <more than> <one SD below the mean> of the 10 running times?
So isn't it asking values greater than 77.6 ?


WRONG reading:
How many of the 10 running times are more than one SD below the mean. So more than Mean-SD.

CORRECT reading:
How many of the 10 running times are more than one SD below the mean. So less than Mean-SD.
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Resources:
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: The list shown consist of the times, in seconds, that it  [#permalink]

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New post 04 Sep 2013, 02:13
Bunuel wrote:
ygdrasil24 wrote:
ziko wrote:
70 75 80 85 90 105 105 130 130 130

The list shown consist of the times, in seconds, that it took each of 10 school children to run a distance of 400 meter. If the SD of ten running times is 22.4 seconds, rounded to nearest tenth of second, how many of the 10 running times are more than one SD below the mean of the 10 running times?
A. one
B. two
C. three
D. four
E. five

The most time consuming part in this question is to define the mean. Under exam pressure and time pressure it is very easy to make mistake.
it is easier to group numbers: 130*3=390; 105*2=210; 75+85=160; 70+80=150; 90;
Next stage combine results, again using more convenient ways to calculate: 390+210=600; 160+150=310; 90. 600+310+90=1000. Since there are 10 numbers the mean is 100. Questions asks to find the quantity of numbers one SD BELOW the mean, which is 100-22,4=77,6. There are only two numbers below 77,6. The answer is B



Pardon me for my understanding, but "are <more than> <one SD below the mean> of the 10 running times?
So isn't it asking values greater than 77.6 ?


WRONG reading:
How many of the 10 running times are more than one SD below the mean. So more than Mean-SD.

CORRECT reading:
How many of the 10 running times are more than one SD below the mean. So less than Mean-SD.


Why couldnt they have written it as
How many of the 10 running times are less than one SD below the mean. This is frustrating for me :(
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Re: The list shown consist of the times, in seconds, that it  [#permalink]

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New post 13 Jul 2016, 17:24
Instead of wasting valuable time adding up all 10 numbers, you can spot some easy clues the GMAT leaves behind. The first 5 numbers are perfectly symmetric around 80, so you know mean of the first 5 is 80. The second half of numbers can be quickly added together- 3*130 = 390 and 105*2 = 210 for a sum of 600. Divide by 5 to get 120. Since the first half has a mean of 80 and second half has a mean of 120, and both halves have equal weight (they both represent 5 integers), the average of both halves will be right in the middle at 100. From there figuring out the answer is business as usual.

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Re: The list shown consist of the times, in seconds, that it  [#permalink]

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New post 19 Oct 2018, 14:23
raghavs wrote:
70, 75, 80, 85, 90, 105, 105, 130, 130, 130
The list shown consists of the times, in seconds, that it took each of 10 schoolchildren to run a distance of 400 on of meters. If the standard devastation of the 10 running times is 22.4 seconds, rounded to the nearest tenth of a second, how many of the 10 running times are more than 1 standard deviation below the mean of the 10 running times?

A. one
B. two
C. three
D. four
E. five


The average (mean) is:

(70 + 75 + 80 + 85 + 90 + 105 + 105 + 130 +130 +130)/10 = 1000/10 = 100

Thus, 1 standard deviation below the mean is 100 - 22.4 = 77.6, so there are 2 running times that are more than 1 standard deviation below the mean.

Answer: B
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Re: The list shown consist of the times, in seconds, that it &nbs [#permalink] 19 Oct 2018, 14:23
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