Question

Determine the mean and standard deviation of the following graph.
A. mean = 3, SD= 1.50
B. mean = 2.87, SD=1.58
C. mean= 3, SD= 1.41
D. mean= 2.87, SD= 1.50

Answer 1

You can put this graph in table form,

\[\begin{array}{cc}
x & f\\
1 & 30 \\
2 & 50 \\
3 & 20 \\
4 & 10 \\
5 & 40
\end{array}\]
And now, you can apply the definitions of the mean and standard deviation.
\[\overline{x}=\frac{\sum_{i=1}^nx_if_i}{\sum_{i=1}^nf_i}\ \ \mathrm{(Mean)}\]
\[\sigma=\sqrt{\frac{\sum_{i=1}^n(x_i-\overline{x})^2f_i}{\sum_{i=1}^nf_i}}\ \ \mathrm{(Standard\ \ deviation)}\]