2.3 Measures of the Location of the Data

$i=\left(\frac{k}{100}\right)\left(n+1\right)$

where i = the ranking or position of a data value,

k = the kth percentile,

n = total number of data.

Expression for finding the percentile of a data value$\left(\frac{x\text{ + }0.5y}{n}\right)$(100)

where x = the number of values counting from the bottom of the data list up to but not including the data value for which you want to find the percentile,

y = the number of data values equal to the data value for which you want to find the percentile,

n = total number of data.

2.5 Measures of the Center of the Data

$\mu =\frac{{\displaystyle \sum fm}}{{\displaystyle \sum f}}$ where f = interval frequencies and m = interval midpoints.

2.7 Measures of the Spread of the Data

$s_x=\sqrt{\frac{{\displaystyle \sum f{m}^2}}{n}-{\overline{x}}^2}$ where $\begin{array}{l}{s}_x=\text{ sample standard deviation}\\ \overline{x}\text{ = sample mean}\end{array}$ $z=\frac{\overline{x}}{\text{s}}$ and $z=\frac{\mu }{\theta }\text{.}$