Hard statistics average problem.

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Manish878: Newbie | Next Rank: 10 Posts; Posts: 6; Joined: Fri Oct 23, 2015 8:42 am

by Manish878 » Mon Mar 21, 2016 6:14 am

Hi,

I am having a hard time with normal distribution. I would be extremely be grateful if you could help me clear my doubt regarding a certain aspect of normal distribution graph below.

I have attached the screenshot of a QC problem below. The solution to the problem is option D (Cannot be determined) , however I am getting the average score as 550. Hence option C. Could you please clarify why the final result is option D and not C?

Best,
Manish A.

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Source: Beat The GMAT — Problem Solving | Mon Mar 21, 2016 6:14 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Mon Mar 21, 2016 6:49 am

This is a GRE question.
Normal distributions are NOT tested on the GMAT.

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Manish878: Newbie | Next Rank: 10 Posts; Posts: 6; Joined: Fri Oct 23, 2015 8:42 am

by Manish878 » Mon Mar 21, 2016 7:51 am

Hi Brent,

I am aware that the concept isn't tested on the GMAT and I am prepping for my GRE. Brent, Could you please answer the question anyway since it will immensely help my GRE preparation? .

Thanx!

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regor60: Master | Next Rank: 500 Posts; Posts: 416; Joined: Thu Oct 15, 2009 11:52 am; Thanked: 27 times

by regor60 » Mon Mar 21, 2016 8:08 am

Look into whether skewness of zero can rightfully be assumed, otherwise don't know

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Mon Mar 21, 2016 9:23 am

Manish878 wrote:Hi Brent,

I am aware that the concept isn't tested on the GMAT and I am prepping for my GRE. Brent, Could you please answer the question anyway since it will immensely help my GRE preparation? .

Thanx!

You are assuming that the graph is symmetrical about the mean of 550.
However, we cannot assume that 500 and 600 are the same distance from mean (even though it certainly APPEARS to be the case)

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Manish878: Newbie | Next Rank: 10 Posts; Posts: 6; Joined: Fri Oct 23, 2015 8:42 am

by Manish878 » Mon Mar 21, 2016 9:29 am

However, we cannot assume that 500 and 600 are the same distance from mean (even though it certainly APPEARS to be the case)

Could you please elucidate more on this? I am not getting the idea. The distance is 50 from both 500 and 600 from mean

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Mon Mar 21, 2016 9:36 am

Manish878 wrote:
However, we cannot assume that 500 and 600 are the same distance from mean (even though it certainly APPEARS to be the case)
Could you please elucidate more on this? I am not getting the idea. The distance is 50 from both 500 and 600 from mean

500 and 600 are both 50 points from 550. That is true.

However, please explain how you know that the mean is 550.
Imagine the same normal curve, where 500 and 600 are shifted to the left one cm. Given this, would you still conclude that the mean is 550?

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Manish878: Newbie | Next Rank: 10 Posts; Posts: 6; Joined: Fri Oct 23, 2015 8:42 am

by Manish878 » Mon Mar 21, 2016 9:49 am

Imagine the same normal curve, where 500 and 600 are shifted to the left one cm. Given this, would you still conclude that the mean is 550?

I guess you got me here. In non normal distribution problem I always calculated mean as average of 2 numbers. It definitely seems that the mean changes when the 2 lower and upper limit are pushed to extreme left or right side of the curve.

Brent, could you please point me an article (if you are generous you could explain here) about how mean changes ase the numbers(lower & upper) are pushed along the curve? i am new to statistics.

Sorry for the trouble.

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regor60: Master | Next Rank: 500 Posts; Posts: 416; Joined: Thu Oct 15, 2009 11:52 am; Thanked: 27 times

by regor60 » Mon Mar 21, 2016 11:18 am

Manish878 wrote:
Imagine the same normal curve, where 500 and 600 are shifted to the left one cm. Given this, would you still conclude that the mean is 550?
I guess you got me here. In non normal distribution problem I always calculated mean as average of 2 numbers. It definitely seems that the mean changes when the 2 lower and upper limit are pushed to extreme left or right side of the curve.

Brent, could you please point me an article (if you are generous you could explain here) about how mean changes ase the numbers(lower & upper) are pushed along the curve? i am new to statistics.

Sorry for the trouble.

That's the skewness issue I already mentioned. Look it up.

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