# 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!!!

### Hi Brent,

Hi Brent,

for the comment above, is it the same as asking 'how many values are within 0.5 units of SD below the mean?' ### Not quite.

Not quite.
We ARE looking for values below (less than) the mean.
However, we want values that are MORE THAN 0.5 units from the mean (not WITHIN 0.5 units of SD from the mean)

Does that help?

### Hi Brent,

Hi Brent,

I was referring to this comment:

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. ### No, that's isn't what we're

No, that's isn't what we're looking for.

We want values that are MORE THAN 0.5 units from the mean (and also BELOW the mean).

A score of is 8.58 is 0.1 units of SD BELOW the mean.
This score doesn't work because we want values that are MORE THAN 0.5 units from the mean

A score of is 8.16 is 0.2 units of SD BELOW the mean.
This score doesn't work because we want values that are MORE THAN 0.5 units from the mean

A score of is 7.32 is 0.4 units of SD BELOW the mean.
This score doesn't work because we want values that are MORE THAN 0.5 units from the mean

A score of 6.9 is EXACTLY O.5 units of SD BELOW the mean.
This score doesn't work because we want values that are MORE THAN 0.5 units from the mean

A score of 6.48 is O.6 units of SD BELOW the mean.
This score WORKS because we want values that are MORE THAN 0.5 units from the mean

A score of 5.64 is O.8 units of SD BELOW the mean.
This score WORKS because we want values that are MORE THAN 0.5 units from the mean

A score of 4.8 is 1 unit of SD BELOW the mean.
This score WORKS because we want values that are MORE THAN 0.5 units from the mean

A score of 2.7 is 1.5 units of SD BELOW the mean.
This score WORKS because we want values that are MORE THAN 0.5 units from the mean

etc

So, any value that's LESS THAN 6.9 will be MORE THAN 0.5 units of SD BELOW the mean.

Does that help?

### Hi Brent,

Hi Brent,

I got it and thank you for the clear explanation!

If the question was 'How many values are LESS THAN 0.5 units of SD below the mean?' the answer for this should be values that are between 9 and 6.9 ? and this same question could also be phrased as 'How many values are within 0.5 units of SD below the mean?' ### Yes, all of that is correct.

Yes, all of that is correct.

Cheers,
Brent