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Processing math: 100%

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 $5$ ?

$\begin{matrix} 5 & 5 & 5 & 5 & 5 & 5 & 5 & 5 & 5 & 5 & 5 \end{matrix}$

$\begin{matrix} 3 & 3 & 4 & 4 & 5 & 5 & 5 & 6 & 6 & 7 & 7 \end{matrix}$

$\begin{matrix} 0 & 3 & 4 & 4 & 5 & 5 & 5 & 6 & 6 & 7 & 10 \end{matrix}$

$\begin{matrix} 1 & 1 & 1 & 3 & 5 & 5 & 5 & 7 & 9 & 9 & 9 \end{matrix}$

$\begin{matrix} 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \end{matrix}$

$\begin{matrix} 1 & 1 & 1 & 1 & 1 & 5 & 9 & 9 & 9 & 9 & 9 \end{matrix}$

$\begin{matrix} 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 55 \end{matrix}$

The mean was

$5$ for all of the data sets but the spread of the data was very different.
We can measure the spread of data using the , and .

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.

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.