Sample Standard Deviation
Calculate the standard deviation for the sample values: 4, 2, 9
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
We can set up the following table:
First, let's find the mean of all the values:
$$(4+2+9)/3=5$$
We can set up the following table:
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. Do not confuse this with a population standard deviation. Plugging the values from the table:
$$$\sigma =\sqrt{\frac{(1+9+16)}{3-1}}=\sqrt{\frac{26}{2}}=3.6$$$
3.6