Question: Units of Standard Deviation

Comment on Units of Standard Deviation

Hi. I have solved this and got 12. Because I counted the numbers more than 6.9 which are 7,7,7,8,8,8,9,11,13,14,14,18.
Why you took the numbers which are less than 6.9? Shouldn't we take more than?
Please anyone explain.
gmat-admin's picture

The questions asks us to find the values that are more than 0.5 units of standard deviation BELOW the mean.

Why not the range of numbers between 6.9-9?
gmat-admin's picture

Here's an analogous question: "Which of the following temperatures are more than 10 degrees below -3 degrees?"
{-24, -20, -17, -14, -8, -3, 0, 5, 11, 19}

Well, 10 degrees below -3 degrees is -13. We want temperatures that are MORE THAN 10 degrees below -3. So, these are: -24, -20, -17, and -14

Does that help?

Hi,

What would be the ans. if the Q says "How many nos. LESS than 0.5 units from Sd/- below the mean"? Would it cover only values from 4.8 to 9 (mean) or 4.8 to 18?

Thanks
gmat-admin's picture

Sorry, I'm not sure what you mean by "... Sd/- below the mean"
Can you please elaborate?

Thanks for the Reply!

I just meant what would be the answer if the same question above would ask "..., how many numbers in set A are LESS than 0.5 units of standard deviation below the mean?"
gmat-admin's picture

In that case, we would want all of the values that are BETWEEN 0 units of SD and 0.5 units of SD BELOW the mean.

0 units of SD BELOW the mean = 9 - 0(4.2)
= 9 - 0
= 9

O.5 units of SD BELOW the mean = 9 - 0.5(4.2)
= 9 - 2.1
= 6.9

So, the values that meet your condition are BETWEEN 6.9 and 9

So, the 7's and 8's meet this condition.

Cheers,
Brent

Ok Thanks,
Now if you refer to the 2019, GMAT Official Q. No. 166, there they have taken all the values below
"m(mean) + d(SD)" instead of only values between "m" and "m+d".

Where is my understanding lacking?


gmat-admin's picture

I have a feeling you may be misreading "LESS THAN 1 SD" as "BELOW THE MEAN"
You might want to review this video: https://www.gmatprepnow.com/module/gmat-statistics/video/809

Here's question #166 from the OG2019: https://gmatclub.com/forum/a-certain-characteristic-in-a-large-populatio...

The question asks "What percent of the distribution is LESS THAN m+d?"

m+d represents one unit of standard deviation above the mean.
So, for example, if the mean (m) = 10 and the SD (d) = 3, then they want all values less than 13

CONVERSELY, if the question asked "What percent of the distribution is LESS THAN 1 unit of standard deviation from the mean?", then we'd need to include all values BETWEEN m-d and m+d.

Does that help?

Cheers,
Brent

Absolutely crystal clear, Thank you so much!!!

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