Question

If a set of data has mean 60 and variance 9 then it's coefficient of variation is

Answer 1

Coefficient of variation is calculated by dividing the standard deviation by the mean multiplied by 100. Given a data set with mean equal to 60 and variance equal to 9, we can calculate the coefficient of variation by finding the value of the standard deviation which is the square root of the variance. so standard deviation is equal to square root of 9 which is 3. Then, the coefficient of variation is equal to 3/60*100 which is equal to 5%.

Answer 2

The coefficient of variation $c_{v}$ is $\boxed{\bf 5\%}$.  

Further explanation:

The mean or average is used to derive the central tendency of the data.

Standard deviation is a measure that is used to quantify the amount of variation or dispersion of a data.

The coefficient of variation is the standard deviation divided by the mean and the formula for coefficient of variation is,

$\boxed{c_{v}=\dfrac{\sigma}{\mu}\cdot 100}$   .....(1)

where, $\sigma$ is the standard deviation and $\mu$ is the mean.

Also, standard deviation is equal to square root of variance.

Here, the set of data has mean $\mu=60$ and variance $\sigma=9$.

Now, the standard deviation $(\sigma)$ is equal to square root of variance and can be written as,

$\begin{aligned}\sigma&=\sqrt{9}\\&=3\end{aligned}$  

Thus, the standard deviation $\sigma=3$.

Substitute the values of mean and standard deviation to get the value of coefficient of variation as follows:

$\begin{aligned}c_{v}&=\dfrac{3}{60}\cdot 100\\&=\dfrac{1}{20}\cdot 100\\&=5\end{aligned}$  

Therefore, coefficient of variation $c_{v}$ is $\boxed{\bf 5\%}$.

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Answer details:

Grade: High school

Subject: Mathematics

Chapter: Statistics

Keywords: Coefficient of variation, mean, variation, standard deviation, median, mode, dispersion, geometric mean, harmonic mean, probability, probability distribution, normal distribution.