Mixing
Alternate formula for sample variance
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I was studying for a test when I found the following formula for sample variance in my textbook:
$s^2text{ can also be expressed in this way:}$
$$s^2 = frac{1}{n-1}(sum_{i=1}^n x_i^2 - noverline{x})$$
I tried searching for this formula on the Internet, but I couldn't seem to find anything. I'm don't understand how that formula was derived from $s^2 = frac{1}{n-1}sum_{i=1}^n(x_i - overline{x})^2$ either. Is the above formula correct at all?
statistics
asked Jan 6 at 11:17
JamesJames
1
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add a comment |
$begingroup$
I was studying for a test when I found the following formula for sample variance in my textbook:
$s^2text{ can also be expressed in this way:}$
$$s^2 = frac{1}{n-1}(sum_{i=1}^n x_i^2 - noverline{x})$$
I tried searching for this formula on the Internet, but I couldn't seem to find anything. I'm don't understand how that formula was derived from $s^2 = frac{1}{n-1}sum_{i=1}^n(x_i - overline{x})^2$ either. Is the above formula correct at all?
statistics
asked Jan 6 at 11:17
JamesJames
1
$endgroup$
$begingroup$
No. $s^2=frac{1}{n-1}sum (x_i-bar x)^2=frac{1}{n-1}(sum x_i^2-nbar x^2)$.
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– StubbornAtom
Jan 6 at 12:23
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I see. How is the latter formula is derived? I'm still having some trouble understanding it.
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– James
Jan 6 at 12:42
1
$begingroup$
Just expand the square. Nothing more.
$endgroup$
– StubbornAtom
Jan 6 at 12:49
add a comment |
$begingroup$
I was studying for a test when I found the following formula for sample variance in my textbook:
$s^2text{ can also be expressed in this way:}$
$$s^2 = frac{1}{n-1}(sum_{i=1}^n x_i^2 - noverline{x})$$
I tried searching for this formula on the Internet, but I couldn't seem to find anything. I'm don't understand how that formula was derived from $s^2 = frac{1}{n-1}sum_{i=1}^n(x_i - overline{x})^2$ either. Is the above formula correct at all?
statistics
asked Jan 6 at 11:17
JamesJames
1
$endgroup$
I was studying for a test when I found the following formula for sample variance in my textbook:
$s^2text{ can also be expressed in this way:}$
$$s^2 = frac{1}{n-1}(sum_{i=1}^n x_i^2 - noverline{x})$$
I tried searching for this formula on the Internet, but I couldn't seem to find anything. I'm don't understand how that formula was derived from $s^2 = frac{1}{n-1}sum_{i=1}^n(x_i - overline{x})^2$ either. Is the above formula correct at all?
statistics
statistics
asked Jan 6 at 11:17
JamesJames
1
asked Jan 6 at 11:17
JamesJames
1
asked Jan 6 at 11:17
JamesJames
1
asked Jan 6 at 11:17
JamesJames
1
asked Jan 6 at 11:17
JamesJames
1
1
$begingroup$
No. $s^2=frac{1}{n-1}sum (x_i-bar x)^2=frac{1}{n-1}(sum x_i^2-nbar x^2)$.
$endgroup$
– StubbornAtom
Jan 6 at 12:23
$begingroup$
I see. How is the latter formula is derived? I'm still having some trouble understanding it.
$endgroup$
– James
Jan 6 at 12:42
1
$begingroup$
Just expand the square. Nothing more.
$endgroup$
– StubbornAtom
Jan 6 at 12:49
add a comment |
$begingroup$
No. $s^2=frac{1}{n-1}sum (x_i-bar x)^2=frac{1}{n-1}(sum x_i^2-nbar x^2)$.
$endgroup$
– StubbornAtom
Jan 6 at 12:23
$begingroup$
I see. How is the latter formula is derived? I'm still having some trouble understanding it.
$endgroup$
– James
Jan 6 at 12:42
1
$begingroup$
Just expand the square. Nothing more.
$endgroup$
– StubbornAtom
Jan 6 at 12:49
$begingroup$
No. $s^2=frac{1}{n-1}sum (x_i-bar x)^2=frac{1}{n-1}(sum x_i^2-nbar x^2)$.
$endgroup$
– StubbornAtom
Jan 6 at 12:23
$begingroup$
No. $s^2=frac{1}{n-1}sum (x_i-bar x)^2=frac{1}{n-1}(sum x_i^2-nbar x^2)$.
$endgroup$
– StubbornAtom
Jan 6 at 12:23
$begingroup$
I see. How is the latter formula is derived? I'm still having some trouble understanding it.
$endgroup$
– James
Jan 6 at 12:42
$begingroup$
I see. How is the latter formula is derived? I'm still having some trouble understanding it.
$endgroup$
– James
Jan 6 at 12:42
1
1
$begingroup$
Just expand the square. Nothing more.
$endgroup$
– StubbornAtom
Jan 6 at 12:49
$begingroup$
Just expand the square. Nothing more.
$endgroup$
– StubbornAtom
Jan 6 at 12:49
add a comment |
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$begingroup$
No. $s^2=frac{1}{n-1}sum (x_i-bar x)^2=frac{1}{n-1}(sum x_i^2-nbar x^2)$.
$endgroup$
– StubbornAtom
Jan 6 at 12:23
$begingroup$
I see. How is the latter formula is derived? I'm still having some trouble understanding it.
$endgroup$
– James
Jan 6 at 12:42
1
$begingroup$
Just expand the square. Nothing more.
$endgroup$
– StubbornAtom
Jan 6 at 12:49