Definition:Sample Statistic/Discrete

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


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.