sig fig or decimal places for variance?

Smythe

A set of numbers: 34.1, 35.6, 35.8, 34.3, 32.9, 33.7

I have calculated the variance to be = 0.208

Would it be better to quote to three sig fig as i have done. This being the number of sig fig of the numbers in the set.

Or should I quote it as 0.2, this being the same number of decimal places of the numbers in the set.

Thanks

citrus burst

You should keep it as 0.208.

Zero's at the start of things don't count towards significant figures.

eg 0.00042 has two significant figures; 4 and 2

Victor

I agree with citrus burst.

Writing "0.2" suggests it could be anywhere from 0.1500 to 0.2499, which is a large range. If your salary varied from €1,500 to €2,499 each month, financial planning might be quite difficult. However, if it only varied between €2,075 and €2,084, you would be much better informed.

Separately, there is the materialness of the variance. For some purposes, a change in the order of 0.2 is utterly meaningless in the scale of things, whereas for others it is immensely important. For example, if your set of numbers: 34.1, 35.6, 35.8, 34.3, 32.9, 33.7 are estimated sales prices and your input costs are 1.0, you probably wouldn't mind the differences in the sales prices. However, if your input costs are 33.0, that 0.2 becomes very important.

For academic purposes, stick with 0.208 unless told otherwise. If writing in an statistics exam and the examiner can see where you went wrong, you are likely to only lose one mark. The risk is that if you round too much, you might come to the final wrong conclusion, you might lose further marks.

In real world examples, you will have a better idea of whether it needs to be 0.2, 0.21 or 0.208. Calculating it to 0.208354328650143 is probably meaningless as it is only an estimate.

FISMA

Smythe wrote: »

A set of numbers: 34.1, 35.6, 35.8, 34.3, 32.9, 33.7
I have calculated the variance to be = 0.208
Would it be better to quote to three sig fig as i have done. This being the number of sig fig of the numbers in the set.
Or should I quote it as 0.2, this being the same number of decimal places of the numbers in the set.
Thanks

Smythe,
I really have no idea if there's a rule of thumb for this one.

The precision in your numbers appears to be 3, hence, I would report the variance at .208.

Can you not follow the rules of sig figs/decimals when doing the calculation? If you do, how many sig figs and decimals do you end up with ?

Smythe

Thanks guys.

I think I'll go with 0.208, after speaking with someone else about this as well, I think that's definitely the correct way.

Thanks again.

ray giraffe

Looks like you calculated it wrong, the variance of those numbers is over 1...

Smythe

ray giraffe wrote: »

Looks like you calculated it wrong, the variance of those numbers is over 1...

Really? I'll check that again then. Thanks

Smythe

ray giraffe wrote: »

Looks like you calculated it wrong, the variance of those numbers is over 1...

I recalculated the variance using Excel this time and got, as you suggested, over 1.

I got 1.248

Thanks ray giraffe