# 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
0th percentile: minimum
25th percentile: lower quartile
50th percentile: median
75th percentile: upper quartile
100th 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
$\text{Mean}, \overline{x}=\frac{\sum fx}{\sum f}$
$\text{Standard deviation}, \sigma =\sqrt{\frac{\sum fx^2}{\sum f}-\left(\frac{\sum fx}{\sum f}\right)^2}$

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