std dev

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sameerballani: Legendary Member; Posts: 544; Joined: Mon Dec 27, 2010 8:10 amFollowed by: 2 members; Thanked: 45 times

by sameerballani » Wed Jun 22, 2011 5:24 am

70,75,80,85,90,105,105,130,130,130

the list shows the time taken by each of ten school children to run a race of 400m.
If std dev=22.4(rounded to nearest tenth)
How many of 10running time are more than 1 std dev below the mean of the 10 running times.?
a-1
B-2
C-3
D-4
E-5

plEASE explain
OA: later

Thanks

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Source: Beat The GMAT — Problem Solving | Wed Jun 22, 2011 5:24 am

Frankenstein: Legendary Member; Posts: 1448; Joined: Tue May 17, 2011 9:55 amFollowed by: 53 members; Location: India; Thanked: 375 times

by Frankenstein » Wed Jun 22, 2011 5:40 am

Hi,
Mean of the series is sum of(70,75,80,85,90,105,105,130,130,130)/10 = 1000/10 = 100
S.D = 22.4
running times more than 1SD below mean means the values which are farther than 1SD from mean(and less than mean) = values which are less than (mean - SD) = 100-22.4 = 78.6
Only 70,75 are less than this

Hence, B

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sameerballani: Legendary Member; Posts: 544; Joined: Mon Dec 27, 2010 8:10 amFollowed by: 2 members; Thanked: 45 times

by sameerballani » Wed Jun 22, 2011 5:50 am

Frankenstein wrote:Hi,
Mean of the series is sum of(70,75,80,85,90,105,105,130,130,130)/10 = 1000/10 = 100
S.D = 22.4
running times more than 1SD below mean means the values which are farther than 1SD from mean(and less than mean) = values which are less than (mean - SD) = 100-22.4 = 78.6
Only 70,75 are less than this

Hence, B

just to confirm in case it had been 2sd, we will find m-2sd and the number of individual values below it.

I hope i make sense
thanks

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Frankenstein: Legendary Member; Posts: 1448; Joined: Tue May 17, 2011 9:55 amFollowed by: 53 members; Location: India; Thanked: 375 times

by Frankenstein » Wed Jun 22, 2011 5:56 am

sameerballani wrote: just to confirm in case it had been 2sd, we will find m-2sd and the number of individual values below it.

I hope i make sense
thanks

Hi,
Generally if the question says, what are the elements less than n*SD from mean, then we have to find the numbers between (mean - n*SD) and (mean+n*SD)
if the question says, what are the elements greater than n*SD from mean, then we have to find the numbers less than (mean - n*SD) and more than (mean+n*SD)
In this question, we are asked to find the numbers more than n*SD below mean, so we need to find only the ones less than (mean - n*SD)
If the question had been to find the numbers more than n*SD above mean, so we need to find only the ones more than (mean + n*SD)

Cheers!

Things are not what they appear to be... nor are they otherwise

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sameerballani: Legendary Member; Posts: 544; Joined: Mon Dec 27, 2010 8:10 amFollowed by: 2 members; Thanked: 45 times

by sameerballani » Wed Jun 22, 2011 7:07 am

thanks a lot !!

Frankenstein wrote:
sameerballani wrote: just to confirm in case it had been 2sd, we will find m-2sd and the number of individual values below it.

I hope i make sense
thanks
Hi,
Generally if the question says, what are the elements less than n*SD from mean, then we have to find the numbers between (mean - n*SD) and (mean+n*SD)
if the question says, what are the elements greater than n*SD from mean, then we have to find the numbers less than (mean - n*SD) and more than (mean+n*SD)
In this question, we are asked to find the numbers more than n*SD below mean, so we need to find only the ones less than (mean - n*SD)
If the question had been to find the numbers more than n*SD above mean, so we need to find only the ones more than (mean + n*SD)

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edvhou812: Master | Next Rank: 500 Posts; Posts: 143; Joined: Sat Nov 06, 2010 9:06 pmFollowed by: 1 member; Thanked: 10 times

by edvhou812 » Wed Jun 22, 2011 8:19 pm

mistake

Last edited by edvhou812 on Wed Jun 22, 2011 8:27 pm, edited 1 time in total.

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Frankenstein: Legendary Member; Posts: 1448; Joined: Tue May 17, 2011 9:55 amFollowed by: 53 members; Location: India; Thanked: 375 times

by Frankenstein » Wed Jun 22, 2011 8:25 pm

edvhou812 wrote:Middle pair is 99 and 105, so median is (99+105)/2 = 97.5. The respective differences of 70 and 75 from 97.5 is greater than 22.4.

Hi,
Your logic is not correct. Why do you need median for this? We need to calculate deviation from mean.

How many of 10running time are more than 1 std dev below the mean of the 10 running times?

Cheers!

Things are not what they appear to be... nor are they otherwise

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edvhou812: Master | Next Rank: 500 Posts; Posts: 143; Joined: Sat Nov 06, 2010 9:06 pmFollowed by: 1 member; Thanked: 10 times

by edvhou812 » Wed Jun 22, 2011 8:29 pm

Frankenstein wrote:
edvhou812 wrote:Middle pair is 99 and 105, so median is (99+105)/2 = 97.5. The respective differences of 70 and 75 from 97.5 is greater than 22.4.
Hi,
Your logic is not correct. Why do you need median for this? We need to calculate deviation from mean.

How many of 10running time are more than 1 std dev below the mean of the 10 running times?

Fair enough. Looks like I messed up pretty big, but got lucky. I went ahead and "deleted" my post so that I don't misguide someone else.

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MBA.Aspirant: Master | Next Rank: 500 Posts; Posts: 401; Joined: Tue May 24, 2011 1:14 amFollowed by: 5 members; Thanked: 37 times

by MBA.Aspirant » Wed Jun 22, 2011 8:56 pm

mean = 1000/10 = 100

100 - 22.4 = 77.6

only 70, 75 < 77.6

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winniethepooh: Master | Next Rank: 500 Posts; Posts: 370; Joined: Sat Jun 11, 2011 8:50 pmFollowed by: 2 members; Location: Arlington, MA.; Thanked: 27 times

by winniethepooh » Wed Jun 22, 2011 9:51 pm

Hey Frankenstein, can u please explain me what the last line of the question means?
I didn't understand the meaning of it?
What is 1 standard deviation?

How many of 10running time are more than 1 std dev below the mean of the 10 running times.?

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MBA.Aspirant: Master | Next Rank: 500 Posts; Posts: 401; Joined: Tue May 24, 2011 1:14 amFollowed by: 5 members; Thanked: 37 times

by MBA.Aspirant » Wed Jun 22, 2011 10:19 pm

Standard deviation measures the dispersal of values +/- around the mean. So if the mean = 100 and std =20, this means the value below the mean is 100-20 =80 and the value above the mean is 100+20= 120.

Here he wants the value 1 std below the mean so it's 100 - 1 std (22.4) = 77.6

If he wanted the value 2 std below the mean then it's 100 - 2 std (2*22.4) = 55.2

same scenario with above the mean except that it's +

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Frankenstein: Legendary Member; Posts: 1448; Joined: Tue May 17, 2011 9:55 amFollowed by: 53 members; Location: India; Thanked: 375 times

by Frankenstein » Wed Jun 22, 2011 10:25 pm

winniethepooh wrote:Hey Frankenstein, can u please explain me what the last line of the question means?
I didn't understand the meaning of it?
What is 1 standard deviation?

How many of 10running time are more than 1 std dev below the mean of the 10 running times.?

Hi,
We know that mean is 100 and various elements(each of the 10) are distributed at various distances from mean. Consider 75. It is at a distance 25(100-75) from mean. So, it is more than 1SD(22.4) from mean right?
Consider 130. It is at a distance 30(130-100) from mean. So, it is also more than 1SD(22.4) from mean right?
But, he asked to find the ones below the mean . So, we have to count only the ones which are less than mean and at a distance greater than 1SD.
That is why 70,75 are the desired numbers.

Cheers!

Things are not what they appear to be... nor are they otherwise

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amit2k9: Master | Next Rank: 500 Posts; Posts: 461; Joined: Tue May 10, 2011 9:09 amFollowed by: 3 members; Location: pune; Thanked: 36 times

by amit2k9 » Thu Jun 23, 2011 4:06 am

good concept here.Good learning indeed.

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