The Spread of Data
We saw previously that the mean does not always give us an indication of what the data looks like.
Which of the following sets of data have a mean of $5$?
Range
The range looks at the maximum and minimum values of a data set.
$$\text{range}=maximum \; value - minimum \; value$$
$\begin{matrix} 5 & 5 & 5 & 5 & 5 & 5 & 5 & 5 & 5 & 5 & 5\phantom{0} \end{matrix}$
$\begin{matrix} 3 & 3 & 4 & 4 & 5 & 5 & 5 & 6 & 6 & 7 & 7\phantom{0} \end{matrix}$
$\begin{matrix} 0 & 3 & 4 & 4 & 5 & 5 & 5 & 6 & 6 & 7 & 10 \end{matrix}$
$\begin{matrix} 1 & 1 & 1 & 3 & 5 & 5 & 5 & 7 & 9 & 9 & 9\phantom{0} \end{matrix}$
$\begin{matrix} 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \end{matrix}$
$\begin{matrix} 1 & 1 & 1 & 1 & 1 & 5 & 9 & 9 & 9 & 9 & 9\phantom{0} \end{matrix}$
$\begin{matrix} 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 55 \end{matrix}$
The greater the range, the
the data is spread.
Interquartile Range
The interrange looks at the middle values of a data set.
$$\text{interquartile range (IQR)}=upper \; quartile \; (Q_3) - lower \; quartile \; (Q_1)$$
$\begin{matrix} 5 & 5 & 5 & 5 & 5 & 5 & 5 & 5 & 5 & 5 & 5\phantom{0} \end{matrix}$
$\begin{matrix} 3 & 3 & 4 & 4 & 5 & 5 & 5 & 6 & 6 & 7 & 7\phantom{0} \end{matrix}$
$\begin{matrix} 0 & 3 & 4 & 4 & 5 & 5 & 5 & 6 & 6 & 7 & 10 \end{matrix}$
$\begin{matrix} 1 & 1 & 1 & 3 & 5 & 5 & 5 & 7 & 9 & 9 & 9\phantom{0} \end{matrix}$
$\begin{matrix} 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \end{matrix}$
$\begin{matrix} 1 & 1 & 1 & 1 & 1 & 5 & 9 & 9 & 9 & 9 & 9\phantom{0} \end{matrix}$
$\begin{matrix} 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 55 \end{matrix}$
The greater the interquartile range, the
the middle of the data is spread.