To determine the expected value of a determined variable, x, given that you know the relative frequencies (P(xi)), you have to multiply each possible value of x by its corresponding relative frequency, then add all the results:
[tex]\text{Mean}=\Sigma x_iP(x_i)[/tex]
The possible values of the variable are the ones under column xi, and their corresponding relative frequencies are under column P(xi). The mean value can be calculated as:
[tex]\begin{gathered} \text{Mean}=(1\cdot0.34)+(2\cdot0.42)+(3\cdot0.01)+(4\cdot0.2)+(5\cdot0.03) \\ \text{Mean}=2.16 \end{gathered}[/tex]
The mean or expected value of the scenario shown on the frequency table is 2.16
