# Standard Deviation — Definition, Formulae [Worked Examples]

by **Jack Bodeley** on *September 21, 2021*

## Definition

Median is the value of the middle item, or the mean of the values of the middle items, when data is arranged in an ascending or descending order of magnitude.

To determine the median, the data needs to be arranged in either an ascending or descending order first.

## Formulae

### Ungrouped Data — Odd Series

$$\frac{n+1}{2}$$

Where:

- n - no of items in the series

### Grouped Data

$$l_1+\frac{l_2+l_1}{f}(m-c)$$

Where:

- l1 - the lower limit of the class in which the median lies
- l2 - the upper limit of the class inc which the median lies
- f - the frequency of the class in which the median lies
- m - the middle item or (n + 1)/2th

## Example

Monthly Wages No.of Workers 800 - 1000 18 1000 - 1200 25