## Mean, Median and mode for ungrouped data

Let `$x_1,x_2, \cdots, x_n$`

be $n$ observations.

## Formula

## 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.

### a

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