Sample Standard Deviation
Calculate the standard deviation for the sample values: 4, 2, 9
Expand Hint
Sample standard deviation:
$$$s =\sqrt{\frac{1}{n-1}\sum_{i=1}^{n} (X_{1}-\mu )^{2}}$$$
where
$$n$$
is the number of items or observations,
$$X$$
is the value from the set, and
$$\mu$$
is the mean.
Hint 2
To find the mean:
$$$\mu=\frac{sum\:of\:terms}{number\:of\:terms}$$$
First, let's find the mean of all the values:
$$$\mu=\frac{sum\:of\:terms}{number\:of\:terms}=\frac{4+2+9}{3}=\frac{15}{3}=5$$$
Because these are sample values, the standard deviation formula is:
$$$s =\sqrt{\frac{1}{n-1}\sum_{i=1}^{n} (X_{1}-\mu )^{2}}$$$
where
$$n$$
is the number of items or observations,
$$X$$
is the value from the set, and
$$\mu$$
is the mean. (Note, do not confuse this with a population standard deviation.)
$$$s =\sqrt{\frac{(4-5)^{2}+(2-5)^{2}+(9-5)^{2}}{(3-1)}}$$$
$$$=\sqrt{\frac{(-1)^{2}+(-3)^{2}+(4)^{2}}{2}}=\sqrt{\frac{1+9+16}{2}}=\sqrt{\frac{26}{2}}=3.6$$$
3.6
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