Mean of Grouped Data/Examples/Heights of People

Examples of Mean of Grouped Data

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:

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

Hence the mean for the above data is calculated as:

$\mu = \dfrac {6 \times 162.5 + 39 \times 167.5 + 93 \times 172.5 + 44 \times 177.5 + 15 \times 182.5 + 3 \times 187.5} {200} = 173.5$

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