Mean, Median and mode for ungrouped data

Let $x_1,x_2, \cdots, x_n$ be $n$ observations.


Sample mean

The mean of $X$ is denoted by $\overline{x}$ and is given by

$\overline{x} =\frac{1}{n}\sum_{i=1}^{n}x_i$

Sample median

The median is the value of $x$ which divides the data into two equal parts.


$$ \begin{equation*} M= \left\{ \begin{array}{ll} \text{value of }\big(\frac{n+1}{2}\big)^{th}\text{ observation}, & \hbox{if $n$ is odd;} \\ \text{average of }\big(\frac{n}{2}\big)^{th}\text{ and }\big(\frac{n}{2}+1\big)^{th} \text{ observation}0, & \hbox{if $n$ is even.} \end{array} \right. \end{equation*} $$

Sample mode

The mode is the value of $x$ that occurs maximum number of times.

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