Definition:Grouped Data
Definition
Grouped data is an arrangement of observations of continuous data into a subdivision of the range of that data.
The lengths of the subintervals of this subdivision are made equal, except for those at either end, which are generally left half-open to accommodate outliers.
Hence, with an appropriate choice of subdivision, the grouping gives an immediate intuitive guess for the distribution of the observations.
Bin
Each of the subintervals of the subdivision into which the grouped data is assigned is referred to as a bin.
Mid-Interval Value
Let $S$ be a set of grouped data.
The mid-interval values are the midpoints of the bins into which $S$ has been assigned.
For the bins at either end of the subdivision, the midpoints are calculated as though they are the same bin width as the rest of the bins.
Examples
Heights of People
For $200$ people, their exact height $x$ in centimetres is measured.
The observations are grouped as follows:
$\begin {array} {r|l} \hline \text {Height $x$ (cm)} & \text {Count} \\ \hline x < 165 & 6 \\ 165 \le x < 170 & 39 \\ 170 \le x < 175 & 93 \\ 175 \le x < 180 & 44 \\ 180 \le x < 185 & 15 \\ x \ge 185 & 3 \\ \hline \end {array}$
Also known as
Grouped data is also known as binned data, from the usage of the term bin.
Also see
- Results about grouped data can be found here.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): grouped data
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): grouped data