# Definition:Sample Statistic/Discrete

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## Contents

## Definition

Data which can be described with a discrete variable are known as **discrete data**.

## Examples

### Number of Children

The number $N$ of children in each of $1000$ families is an example of **discrete data**.

### Colors of Rainbow

The set $C$ of colors of the rainbow:

- $C = \set {\text {red}, \text {orange}, \text {yellow}, \text {green}, \text {blue}, \text {indigo}, \text {violet} }$

is an example of **discrete data**.

In such a circumstance where the discrete data are non-numerical, it is usually possible to assign (natural) numbers to each of the elements, for example:

\(\displaystyle \text {red}\) | \(\to\) | \(\displaystyle 1\) | |||||||||||

\(\displaystyle \text {orange}\) | \(\to\) | \(\displaystyle 2\) | |||||||||||

\(\displaystyle \text {yellow}\) | \(\to\) | \(\displaystyle 3\) | |||||||||||

\(\displaystyle \text {green}\) | \(\to\) | \(\displaystyle 4\) | |||||||||||

\(\displaystyle \text {blue}\) | \(\to\) | \(\displaystyle 5\) | |||||||||||

\(\displaystyle \text {indigo}\) | \(\to\) | \(\displaystyle 6\) | |||||||||||

\(\displaystyle \text {violet}\) | \(\to\) | \(\displaystyle 7\) |

and so the set $C'$ can be considered instead: $C' = \set {1, 2, 3, 4, 5, 6, 7}$

## Also see

## Linguistic Note

Be careful with the word **discrete**.

A common homophone horror is to use the word **discreet** instead.

However, **discreet** means **cautious** or **tactful**, and describes somebody who is able to keep silent for political or delicate social reasons.

## Sources

- 1972: Murray R. Spiegel and R.W. Boxer:
*Theory and Problems of Statistics*(SI ed.) ... (previous) ... (next): Chapter $1$: Discrete and Continuous Variables - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next): Entry:**discrete data**