Summarising Data - Measures of Centre
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For the given set of data
\[\begin{array}{ | c | c | c | c | c | }\hline -6 & 0 & -3 & 3 & 6 \\ \hline -2 & 4& -1& 5& -2 \\ \hline \end{array}\]
Find
a. The mean
b. The median
c. The mode
d. The Range
(a)
$$
\begin{aligned}
\text{Mean}&=\frac{-6+0+(-3)+3+6+(-2)+4+(-1)+5+(-2)}{10}\\
&=0.4
\end{aligned}
$$
(b) Arranging the scores in ascending order: \[-6,-3,-2,-2,-1,0,3,4,5,6\] There are 10 scores, so the median is the average of 5th and 6th scores.
\[\text{Median}=\frac{-1+0}{2}=-0.5\]
(c) \(\text{Mode}=-2\) (Highest Frequency)
(d) $$\begin{aligned}\text{Range}&=\text{Highest score}-\text{Lowest score}\\
&=6-(-6)\\
&=6+6\\
&=12 \end{aligned}$$
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