Question

The coefficient of variation of a collection data is 57 and its S.D. is 6.84, then find the mean.

Answer 1

In this question, the coefficient of variation and standard deviation of the distribution is given, then in order to find its mean we will use the simple formula of the coefficient of variation which is given by $\dfrac{\sigma }{{\bar x}} \times 100$. Substitute the given values in the formula and do the calculation to get the desired result.

Complete step by step solution:
Mean is an average of the given numbers: a calculated central value of a set of numbers.
Standard deviation is defined as the deviation of the values or data from an average mean. A lower standard deviation concludes that the values are very close to their average. Whereas higher values mean the values are far from the mean value.
The coefficient of variation is a standardized measure of the dispersion of a probability distribution or frequency distribution. When the value of the coefficient of variation is lower, it means the data has less variability and high stability.
Given that coefficient of variation = 57 and standard deviation = 6.84.
Let the mean of the distribution be $x$.
We know if a distribution has mean $\bar x$ and standard deviation $\sigma$. Then,
Coefficient of variation $= \dfrac{\sigma }{{\bar x}} \times 100$
By substituting the values, we have,
$\Rightarrow 57 = \dfrac{{6.84}}{x}$
Cross-multiply the terms,
$\Rightarrow 57x = 6.84$
Divide both sides by 57,
$\Rightarrow x = \dfrac{{6.84}}{{57}}$
Divide the numerator by denominator,
$\therefore x = 0.12$

Hence, the mean is 0.12.

Note: Mean is the arithmetic average of the data given. Mean is also used to calculate the variance and standard deviation of the data in statistics. The mean is affected by extremely high or low values, called outliers.