# Question: Units of Standard Deviation

## Comment on Units of Standard Deviation

### Hi. I have solved this and

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? ### The questions asks us to find

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

Why not the range of numbers between 6.9-9? ### Here's an analogous question:

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,

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 ### Sorry, I'm not sure what you

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

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?" ### In that case, we would want

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,

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? ### I have a feeling you may be

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,

Absolutely crystal clear, Thank you so much!!!