Definition:Grouped Data/Mid-Interval Value

Definition

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}$

The mid-interval values for the above data are:

$162.5, 167.5, 172.5, 177.5, 182.5, 187.5$

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