Deviation
Find the sample standard deviation for this set of values: 0, 1, 5, 10, 7, 7.
Expand Hint
The sample standard deviation 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.
Hint 2
To find the mean:
$$$\mu=\frac{sum\:of\:terms}{number\:of\:terms}$$$
First, let’s find the mean of the values:
$$$\mu=\frac{sum\:of\:terms}{number\:of\:terms}=\frac{0+1+5+10+7+7}{6}=\frac{30}{6}=5$$$
The sample standard deviation 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. Thus,
$$$s=\sqrt{\frac{1}{6-1}\cdot[(X_1-\mu)^2+(X_2-\mu)^2+(X_3-\mu)^2+(X_4-\mu)^2+(X_5-\mu)^2+(X_6-\mu)^2]}$$$
$$$=\sqrt{\frac{1}{5}\times[(0-5)^2+(1-5)^2+(5-5)^2+(10-5)^2+(7-5)^2+(7-5)^2]}$$$
$$$=\sqrt{\frac{1}{5}\times[(-5)^2+(-4)^2+(0)^2+(5)^2+(2)^2+(2)^2]}$$$
$$$=\sqrt{\frac{1}{5}\times[25+16+25+4+4]}=\sqrt{\frac{74}{5}}=\sqrt{14.8}=3.8$$$
3.8
Time Analysis
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