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?


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?

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.


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:

Here's question #166 from the OG2019:

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?


Absolutely crystal clear, Thank you so much!!!

Add a comment

Office Hours

Have questions about your preparation or an upcoming test? Need help modifying the Study Plan to meet your unique needs? No problem. Just book a Skype meeting with Brent to discuss these and any other questions you may have. 

Change Playback Speed

You have the option of watching the videos at various speeds (25% faster, 50% faster, etc). To change the playback speed, click the settings icon on the right side of the video status bar.

Have a question about this video?

Post your question in the Comment section below, and I’ll answer it as fast as humanly possible.

Free “Question of the Day” emails!