Calculating variance on calculator gone wrong

I tried to calculate the variance for the following question on a casio calculator fx-85gt:
number absent: 0 1 2 3 4 5
number of days: 54 24 11 4 2 1
and i got 1.06 even though the answer is 1.13
I was wondering if anyone else is getting this value on their calculator as well and if you know where I might be going wrong?

Thank you!

Reply 1

DFranklin

What do you have for

\sum x

and

\sum x^2

Reply 2

Stanspam

Original post by DFranklin

What do you have for

\sum x

and

\sum x^2

15 and 55 respectively

Reply 3

DFranklin

Original post by Stanspam

15 and 55 respectively

OK, to be honest I don't think I know how Casio's do this well enough (my knowledge is quite a few years out of date).

I was expecting

\sum x

to be

0 * 54 + 1 * 24 + 2 * 11 + 3 * 4 + 4 * 2 + 5 * 1 = 71.

and

\sum x^2

to be

0 * 54 + 1 * 24 + 4 * 11 + 9 * 4 + 16 * 2 + 25 * 1 = 473.

You can then find E[x] and E[x^2] and the the variance.

Edit: I remember there being a particular way you were supposed to indicate you had multiple values (so you could enter 54 sets of 0 without entering "0" 54 times, but not the details. I'm guessing that's where you've gone wrong, but it's only a guess.

(edited 7 years ago)

Reply 4

Pangol

Original post by Stanspam

Your calculator has given you the standard deviation. You need to square it to get the variance.

Original post by DFranklin

I was expecting

\sum x

to be

0 * 54 + 1 * 24 + 2 * 11 + 3 * 4 + 4 * 2 + 5 * 1 = 71.

and

\sum x^2

to be

0 * 54 + 1 * 24 + 4 * 11 + 9 * 4 + 16 * 2 + 25 * 1 = 473.

I agree with your

\sum x

, but I think that your

\sum x^2

should be 161, not 473. (That's the trouble with stats, numerical slips are so easy to make.

Reply 5

DFranklin

Original post by Pangol

Your calculator has given you the standard deviation. You need to square it to get the variance.

I agree with your

\sum x

, but I think that your

\sum x^2

should be 161, not 473. (That's the trouble with stats, numerical slips are so easy to make.

Meh, that's an error in the spreadsheet I used (and fixed, and then put the old wrong value in here, anyhow).

Thanks, anyway! (Also, good spot on his answer being the s.d.)

Reply 6

Stanspam

Original post by Pangol

Your calculator has given you the standard deviation. You need to square it to get the variance.

I agree with your

\sum x

, but I think that your

\sum x^2

should be 161, not 473. (That's the trouble with stats, numerical slips are so easy to make.

But both the variance and standard deviation are being given as 1.06 by the calculator

And square rooting answer gives 1.03 instead of 1.13

(edited 7 years ago)

Reply 7

Pangol

Original post by Stanspam

But both the variance and standard deviation are being given as 1.06 by the calculator

I expect that you are looking at the population and sample versions of the standard deviation. They are both standard deviations. You need to square them to get the variance.

Reply 8

Stanspam

Original post by Pangol

I expect that you are looking at the population and sample versions of the standard deviation. They are both standard deviations. You need to square them to get the variance.

but squaring these values still produces the wrong answer?
Is there perhaps a different way you achieved the answer using the stats mode on the calculator?

Reply 9

Pangol

Original post by Stanspam

but squaring these values still produces the wrong answer?
Is there perhaps a different way you achieved the answer using the stats mode on the calculator?

When I square either of the standard deviations that the calculator gives us (and I agree with your value), I get the variance you say that you need.

Reply 10

Stanspam

Original post by Pangol

When I square either of the standard deviations that the calculator gives us (and I agree with your value), I get the variance you say that you need.

Thank you so much, I got the answer!

Do you know why I have to square separately for grouped data though, since this step isn't necessary for data that isn't grouped?

Reply 11

DFranklin

Original post by Stanspam

Thank you so much, I got the answer!

Do you know why I have to square separately for grouped data though, since this step isn't necessary for data that isn't grouped?

Without knowing the calculator details, I think you're wrong. I'm pretty sure the calculator always gives you the standard deviation and not the variance.

I'd guess the most likely reason you need to square here is because it's asking for the variance, and previous questions where you haven't need to have asked for the standard deviation.