Chapter 4.1, Problem 1TY

Interpretation Introduction

Interpretation:

The change in mean, standard deviation and coefficient of variation when the given numbers are divided by two has to be given.

Concept Introduction:

Mean:

The Mean or the arithmetic mean ( $\overline{x}$) is given as the summation of measured values divided by the number of measurements (n). Mean is also called as average.

$\overline{x}=\frac{{\displaystyle \sum _i{x}_i}}{n}$

Standard deviation:

Standard deviation measures how closely the data are clustered about the mean.

The standard deviation (s) is given by the formula:

$s=\sqrt{\frac{{\displaystyle \sum _i{(x_i-\overline{x})}^2}}{n-1}}$

Coefficient of variation:

The standard deviation expressed as a percentage of the mean value is called the relative standard deviation or the coefficient of variation.

$\text{Coefficient of variation = 100}\times \frac{s}{\overline{x}}$

To Give: The change in mean, standard deviation and coefficient of variation when the given numbers are divided by two.