Data Analysis

Mode

Mode is the most frequently occurring number. A set of data can have more than one mode.

Mean

$\text{mean} = \dfrac{\text{sum of all numbers}}{\text{number of numbers}}$

Median

Median is the centre number when the numbers are arranged from smallest to largest.

Range

Range = maximum $-$ minimum

Quartiles & percentiles

0^th percentile: minimum
25^th percentile: lower quartile
50^th percentile: median
75^th percentile: upper quartile
100^th percentile: maximum

Interquartile range

Interquartile range = upper quartile $-$ lower quartile

Mean & standard deviation

Ungrouped
$\text{Mean}, \bar{x} =\frac{\sum x}{N}$
$\text{Standard deviation}, \sigma =\sqrt{\frac{\sum(x-\overline{x})^2}{N}}$

Grouped
$\text{Mean}, \overline{x}=\frac{\sum fx}{\sum f}$
$\text{Standard deviation}, \sigma =\sqrt{\frac{\sum fx^2}{\sum f}-\left(\frac{\sum fx}{\sum f}\right)^2}$