Standard deviation question

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MICHAEL S: Newbie | Next Rank: 10 Posts; Posts: 2; Joined: Sat Apr 11, 2009 9:53 am; Location: PENNSYLVANIA; GMAT Score:540

by MICHAEL S » Sat Apr 11, 2009 9:58 am

Hi all,

Here is something that I've encountered recently. As a side note, I think the GMAT Prep software; when it comes to the practices tests aren't all that effective. Maybe it's just me but when it shows you the correct answer, it doesn't provide an explaination as to why. So how does one really learn from their mistakes?

Anyway,

Here's the question:

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

The list shown consists of the times, in seconds, that it took each of the 10 schoolchildren to run a distance of 400 meters. If the standard deviation 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?

One
Two
Three
Four
Five

How did they arrive at 2?

MICHAEL S

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Source: Beat The GMAT — Problem Solving | Sat Apr 11, 2009 9:58 am

dtweah: Master | Next Rank: 500 Posts; Posts: 487; Joined: Fri Mar 27, 2009 5:49 am; Thanked: 36 times

Re: Standard deviation question

by dtweah » Sat Apr 11, 2009 11:03 am

MICHAEL S wrote:Hi all,

Here is something that I've encountered recently. As a side note, I think the GMAT Prep software; when it comes to the practices tests aren't all that effective. Maybe it's just me but when it shows you the correct answer, it doesn't provide an explaination as to why. So how does one really learn from their mistakes?

Anyway,

Here's the question:

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

The list shown consists of the times, in seconds, that it took each of the 10 schoolchildren to run a distance of 400 meters. If the standard deviation 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?

One
Two
Three
Four
Five

How did they arrive at 2?

First Find the average . Don't add and divide, time consuming.

70,75,80,85,90,105,105,130,130,130 (Add 30 to 70, split 30 up btw 80 and 90)
100 75 100 85 100 105 105 100 100 130 (split 30 btw 75 and 85)
100 90 100 100 100 105 105 100 100 100 (increase 90 by 10)
100 100 100 100 100 100 100 100 100 100

Ave is 100.

One standard dev below the means:
100 - 22.4 = 77.6

Any score less than 77.6 is more than one SD below the main.
Only 70 and 75 below 77.6

Hope this helps.

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Mon Apr 13, 2009 3:00 am

If exactly 5 of the ten positive integers are more than 100, then their average has to be equal to or more than 100; but here, if we try approximation, we could miss it. So we have to find the accurate mean first, but if it seems to be time consuming, then try it differently to save time, one of which is displayed by dtweah here. We know the data is 10 in number, let's add groups that do our favor

(70 + 80 + 90 + 3*130) + (75 + 85 + 2*105)
= 240 + 390 + 160 + 210
= (240 + 160) + (390 + 210) [add groups that do our favor]
= 400 + 600
= 1000

so average 100; it really didn't take more than 45 seconds to get that practically. Now, 1 SD below the mean is 100 - 22.4 = 77.6; and below this are only two entries there (70 and 75).

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

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M09: Master | Next Rank: 500 Posts; Posts: 110; Joined: Tue Dec 23, 2008 4:52 am; Thanked: 3 times

by M09 » Fri May 08, 2009 6:08 am

Guys,

I still dont get it.

Here's what I understood from the problem statement.

how many of the 10 running times are more than 1 standard deviation below the mean of the 10 running times?

For the second bold part, answer is 100 - 22.4 = 77.6
I completely get it but

after this I'm puzzled...the way I look at it is how many of the 10 running times are more 77.6.

can aynone please help ??

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scoobydooby: Legendary Member; Posts: 1035; Joined: Wed Aug 27, 2008 10:56 pmFollowed by: 1 member; Thanked: 104 times

by scoobydooby » Fri May 08, 2009 12:41 pm

1SD below the mean (100)
=>100-1SD=77.6

more than 1 SD below the mean=>100-2SD, 100-3SD, 100-4SD and so on. we would be subtracting bigger numbers from 100=>the result would get smaller and smaller. the result would be definitely smaller than what we would get with 100-1SD ( 77.6) so we take the numbers less than 77.6

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