8.  Workers who are being trained to perform a certain job are given a test.
       The scores on this test vary from  1 (lowest) to 5 (highest).
       The distribution of scores is shown in the following table. Find the mean score. 

 Solution: 
      Note that finding the mean for data in a relative frequency table differs slightly from finding 
      the mean of data in a frequency table, because we don't know the size of the population
      (this would be the sum of the frequencies in a frequency table). In a relative frequency table like this,
      the sum of the proportions should always be 1. 

      To find the mean we find the sum of all terms formed by multiplying a value by its proportion.
      Mean = 1(0.10) + 2(0.28) + 3(0.24) + 4(0.22) + 5(0.16)
      Mean =  0.10 + 0.56 + 0.72 + 0.88 + 0.80
      Mean = 3.06