Standard Deviation Percentile Formula in Book

[navigalactus]

Here's the situation. In the GRE Word Problems 3rd Edition Strategy Guide Page No. 91- 3rd bullet point, the formula given for finding Percentiles appears to be wrong as it is contradictory with the other formulas with which some of the problems are solved in the Book. It States> To find the Percentile below the mean, 50%-50%-(1/2X2/3), the same mistake appears to be with the Percentile Calculation above the mean and I guess it is something else because answer is no way 17 percent or anything near to that. I would request Experts to clarify this, thanks
Also please elaborate the formula for calculating Percentile of a given value and given the mean. Suppose z-score comes out to be 1.3 standard deviations above the mean, Then how will the Percentile be calculated

[navigalactus]

Comeon someone clarify this. Tommy, man where are you?

I've found the formula to get percentiles from non integer z-scores but that is a long one.

Atleast clear the formula incorrectly printed in the book so I can make correction. Incorrectly because doing it doesnot bring the intended values and it is printed different in more than two places as I remember, only one out of which can be correct.

[tommywallach]

Hey Guys,

I believe there's an error on that page that has been addressed in our errata, and will be corrected in future editions.

The truth is you don't need to worry about any kind of complex formula for solving percentiles. I promise. The statistics/SD stuff tested on the GRE is usually quite basic (even if the book goes a little bit more on the advanced side). If you can find an official question that belies my point, I'm certainly open to looking at it, but knowing the basic percentile ranges for SD and interquartile range should be plenty.

-t

[navigalactus]

No my friend, the Errata section (2nd or 3rd) does not have an entry for this problem yet. And I get stuck at many of the questions which uses this formula printed Page No. 91- 3rd bullet point, and that doesn't feel great. The formula in question is> 50%-50%-(1/2X2/3). Moreover, the solution given for those problems uses that formula using different constants everytime, and that's what is throwing me off. I request you to kindly explain that formula please

[tommywallach]

Hey Navi,

Sorry that it isn't in the errata. It ought to just say: 50% - 1/2 * 1/3, and the other should say 50% + 1/2 * 1/3. However, believe me when I say you do not need to know these equations. They aren't really equations at all, actually; they're just showing you the math behind stuff you ought to know.

50th percentile = middle line
1 SD to the left = 17% (because it's 1/3 of the data away from 50)
2 SD to the left = 4% (because the first one is about 33, and the second is about 13)
etc.

Just memorize those benchmarks and you'll be fine. Those other things aren't actually equations at all (there are no variables); they're just illustrations of the percentage benchmarks.

If you can point me to a real question that you got wrong because of a failure to understand this "equation", I'll certainly look at it, but I've never seen one, and I don't see how there could be one, as it isn't an equation you can actually manipulate, so it has no value in terms of solving anything.

Hope that helps!

-t

[navigalactus]

50th percentile = middle line
1 SD to the left = 17% (because it's 1/3 of the data away from 50)
2 SD to the left = 4% (because the first one is about 33, and the second is about 13)
etc.

Hello Tommy,
Hmmmm thanks for clarifying some of my doubt, 34-14-2 rule right? I'm still not able to get how to get percentiles out of z-score

1 SD to the left=16.66%
1 SD to the right= 83%
2 SD to the left= 2%
2 SD to the right= 98%
3 SD to the right= 99.99%

[tommywallach]

Hey Navi,

Not quite clear on how you wrote it there. Left and right aren't any different. Do you want to explain that better. 1 SD to the right is 34%, not 16.66%. 83%, for example, would be EVERYTHING else.

-t

[navigalactus]

Hey Tommy,
I've prepared and attached a chart for you, how I got the above values, that indicate percentile values for that section, please have a look :) 34-14-2 are the values for probability that a particular range of values relative to the mean fall in what section. Percentile values correspond to the position of a particular value within the entire set, there's a very long method to precisely find that out but I was hoping to find a short and quick method

[tommywallach]

Hey Navi,

No need for that (very over complicated) diagram. Again, you simply need the 34-14-2. Anything else is just stuff you'll always be able to derive from 34-14-2.

-t