Definition:Sample Statistic/Discrete
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:
| \(\ds \text {red}\) | \(\to\) | \(\ds 1\) | ||||||||||||
| \(\ds \text {orange}\) | \(\to\) | \(\ds 2\) | ||||||||||||
| \(\ds \text {yellow}\) | \(\to\) | \(\ds 3\) | ||||||||||||
| \(\ds \text {green}\) | \(\to\) | \(\ds 4\) | ||||||||||||
| \(\ds \text {blue}\) | \(\to\) | \(\ds 5\) | ||||||||||||
| \(\ds \text {indigo}\) | \(\to\) | \(\ds 6\) | ||||||||||||
| \(\ds \text {violet}\) | \(\to\) | \(\ds 7\) |
and so the set $C'$ can be considered instead:
- $C' = \set {1, 2, 3, 4, 5, 6, 7}$
The number of shares sold each day on the stock market is an example of discrete data.
Yearly Incomes
The yearly incomes of college professors is an example of discrete data.
Population Numbers
The number of males and number of females living in a city are examples of discrete data.
Personal Qualitative Attributes
The colour of hair and eyes for each of a number of individuals are examples of discrete data.
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
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): data (singular datum)
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): data (singular datum)
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): discrete data