Sample Coefficient Variant
Calculate the sample coefficient of variation (%) for the values: 2, 1, 10, 43, 34
Expand Hint
The sample coefficient of variation:
$$$CV=\frac{s}{\mu}$$$
where
$$s$$
is the sample standard deviation, and
$$\mu$$
is the arithmetic mean.
Hint 2
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.
First, let's find the mean of all the values:
$$$\mu=\frac{sum\:of\:terms}{number\:of\:terms}=\frac{2+1+10+43+34}{5}=\frac{90}{5}=18$$$
Next, let’s find the 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. (Note, do not confuse this with a population standard deviation.)
$$$s =\sqrt{\frac{(10-18)^{2}+(1-18)^{2}+(2-18)^{2}+(43-18)^{2}+(34-18)^{2}}{(5-1)}}$$$
$$$s=\sqrt{\frac{(-8)^{2}+(-17)^{2}+(-16)^{2}+(25)^{2}+(16)^{2}}{4}}$$$
$$$s=\sqrt{\frac{64+289+(2)256+625}{4}}=\sqrt{\frac{1490}{4}}=19.3$$$
Finally, the sample coefficient of variation:
$$$CV=\frac{s}{\mu}$$$
where
$$s$$
is the sample standard deviation, and
$$\mu$$
is the arithmetic mean.
$$$CV=\frac{19.3}{18}=1.07$$$
The sample coefficient of variation is
$$1.07 \times 100=107\%$$
.
107%
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