Standard Deviation from Inspection

[Yendall]

Data:

Question 3
Using the 68–95–99.7% rule, the standard deviation for temperature is closest to
A. 1 °C
B. 2 °C
C. 3 °C
D. 4 °C
E. 6 °C

I came across a pretty cool equation to find the standard deviation:

From inspection I estimated the range to be:

Using the formula:

So i thought the standard deviation was 3 degrees. The answer is 2.

What is the proper way to find the Standard Deviation from inspection?

[Daenerys Targaryen]

i think you might need to divide by 6 instead of 4; 68–95–99.7% is split into 3 SD either way of the mean, thus 6 all together.
If you divide by six you get 2.25, which is the closest to two. Not sure if this is the proper way, but i have come across questions and interperted it like this and got it correct.

[Stick]

Data:
(Image removed from quote.)
Question 3
Using the 68–95–99.7% rule, the standard deviation for temperature is closest to
A. 1 °C
B. 2 °C
C. 3 °C
D. 4 °C
E. 6 °C

I came across a pretty cool equation to find the standard deviation:

From inspection I estimated the range to be:

Using the formula:

So i thought the standard deviation was 3 degrees. The answer is 2.

What is the proper way to find the Standard Deviation from inspection?

You've got the formula wrong. It's actually (99.7% of the data lies within three standard deviations from the mean, which is six standard deviations in total).

Using that:







Which gives you your correct answer.

I only discovered this formula a few days ago myself. It should be stated more explicitly in the study design in my opinion. :S

[Daenerys Targaryen]

Yeah, I learnt it through one of the exams.

[Stick]

As did I, when I got a question wrong in a Heffernan paper and looked at the solutions.

[Yendall]

I'm just assuming

accounts for 67% of data

accounts for 95% of data

accounts for 99.7% of data

I'll remember that for the exam, cheers guys.

[Stick]

I'm just assuming

accounts for 67% of data

accounts for 95% of data

accounts for 99.7% of data

I'll remember that for the exam, cheers guys.

No, that's not true either. I think you've just got your logic a bit mixed up about it all. If you want to find any percentage of the data, you're going to need to find out what one standard deviation is first and then multiply it (not just change the denominator like you've done).

[Daenerys Targaryen]

Yeah, what stick said. Coz SD is the same for each block or whatever they're called.

[StumbleBum]

I came across a pretty cool equation to find the standard deviation:

I believe that equation relates solely to small sets of data, that's what the essentials book states anyway...

[panda31]

Hey Stick, what do you mean by finding the standard deviation then multiplying it? what do you multiply it with - and do you find the standard deviation of the whole of the data first?
Could you explain it?
Thanks

[StumbleBum]

Hey Stick, what do you mean by finding the standard deviation then multiplying it? what do you multiply it with - and do you find the standard deviation of the whole of the data first?
Could you explain it?
Thanks

I believe he's referring to the 68-95-99.7 rule. Where you find what the standard deviation of a data set is, along with the mean. Then you multiply the standard deviation by 1 and add and subtract from either side of the mean to get approximately 68% of the data. For 95% of the data you add and subtract two multiplied by the standard deviation from the mean; and by 3 for 97.7% of the data.

Although that's just what I assumed from what he said, could be talking about something else..?

[Daenerys Targaryen]

Yeah, thats what he means.
Find the SD, then use that and the mean how you usually would.

[Yendall]

No, that's not true either. I think you've just got your logic a bit mixed up about it all. If you want to find any percentage of the data, you're going to need to find out what one standard deviation is first and then multiply it (not just change the denominator like you've done).

What I mean is that you can't use the first two formulas because we will always have to deal with 99.7% of data. We don't get smaller data sets from VCAA. We won't get a distribution with only 68% of the data shown (most likely), and it wouldn't make sense to get that and not 99.7%. But say you did get a range of data that was only 68% of a bigger set of data, the range and standard deviation of that particular 68% will work with the first formula, right?

I would always use the last formula because you have to account for -3SD and +3SD in all cases

[StumbleBum]

But say you did get a range of data that was only 67% of a bigger set of data, the range and standard deviation of that particular 67% will work with the first formula, right?

Why do you keep saying 67% and not 68%?
But yes that is correct, 68% of the data would be distributed about 2 SD's (assuming this is about the mean also) so the range of that 68% divided by two would give you the value for the SD.

[Yendall]

Sorry I meant 68%, I'm fairly delirious.