Question

Suppose you have a population 1, 2, 3, 4, 5, 6 i. Suppose that a sample of 2 values is taken, what is the possible total number of samples? ii. What is the sample mean? iii. Obtain the standard error. What is its statistical implication? iv. Determine the percentage relative standard error v. Calculate the coefficient of variation. What is its statistical implication?

Answer 1

i)

$n=C^2_6=\frac{6!}{2!4!}=15$ samples

ii, iii, iv.

statistical implication of standard error:

The standard error (SE) of a statistic is the approximate standard deviation of a statistical sample population. The standard error is a statistical term that measures the accuracy with which a sample distribution represents a population by using standard deviation.

v.

coefficient of variation:

$CV=\sigma/\mu$

where $\sigma$ is population standard deviation,

$\mu$ is population mean.

$CV=1.71/3.5=0.49$

statistical implication of coefficient of variation:

The coefficient of variation (CV) is a statistical measure of the dispersion of data points in a data series around the mean. The coefficient of variation represents the ratio of the standard deviation to the mean, and it is a useful statistic for comparing the degree of variation from one data series to another, even if the means are drastically different from one another.