Question

find the coefficient of variation of first five prime numbers​

Answer 1

Answer:

Formula. The formula for the coefficient of variation is: Coefficient of Variation = (Standard Deviation / Mean) * 100.

Step-by-step explanation:

You solve yourself and get the right answer because many people don't give right answers

Answer 2

Given,

First five prime numbers.

To find,

Coefficient of variation of first five prime numbers.

Solution,

We can solve this problem simply by following the process given below.

Let's first understand what coefficient of variation is and the way to find it.

So, coefficient of variation is a type of dispersion measurement. A measure of dispersion is a quantity that tells us about the extent of variability of our data. The coefficient of variation is defined as the ratio of standard deviation to the mean. It is used to measure the dispersion of data from the mean or the average value. It is usually denoted by CV and represented as a percentage.

So mathematically,

$CV=\frac{standard \hspace{2}deviation(\sigma)}{mean(\bar x)}*100$

Now, we are required to find the CV for the first five prime numbers. These are,

2, 3, 5, 7, 11.

Let's first find out mean,

⇒ $\bar x=\frac{2+3+5+7+11}{5} =\frac{28}{5}$

⇒ $\bar x = 5.6$

Now, the standard deviation is given by,

$\sigma = \sqrt{\frac{\Sigma (x_i-\bar x)^{2} }{N}}$

Where $x_i$ is the value of data from the population, that is 2, 3, 5, 7, 11 here, $\bar x$ is the mean and $N$ is the number of elements.

⇒ $\sigma = \sqrt{\frac{(2-5.6)^{2}+(3-5.6)^2+(5-5.6)^2+(7-5.6)^2+(11-5.6)^2 }{5}}$

⇒ $\sigma = \sqrt{\frac{(-3.6)^{2}+(-2.6)^2+(-0.6)^2+(1.4)^2+(5.4)^2 }{5}}$

⇒ $\sigma = \sqrt{\frac{12.96+6.76+0.36+1.96+29.16 }{5}}$

⇒ $\sigma = \sqrt{\frac{51.2}{5}}$

⇒ $\sigma = \sqrt{\frac{51.2}{5}}=\sqrt{10.24}$

⇒ $\sigma=3.2$

As we now have found mean as well as standard deviation, CV can be calculated as,

$CV=\frac{\sigma}{\bar x} *100=\frac{3.2}{5.6} *100$

⇒ $CV = 57.14$%

Therefore, for the first five prime numbers, the coefficient of variation will be 57.14%.