Using it's concept, it is found that the mean of the data-set is of [tex]\frac{3}{4}[/tex].
The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.
In this problem, the 4 observations are given by:
[tex]\left{\frac{1}{2}, \frac{1}{3}, \frac{2}{3}, 1\frac{1}{2} = 1 + \frac{1}{2} = \frac{3}{2}\right}[/tex]
Hence, the mean is given as follows:
[tex]M = \frac{\frac{1}{2} + \frac{1}{3} + \frac{2}{3} + \frac{3}{2}}{4} = \frac{\frac{3 + 2 + 4 + 9}{6}}{4} = \frac{18}{24} = \frac{3}{4}[/tex]
The mean of the data-set is of [tex]\frac{3}{4}[/tex].
More can be learned about the mean of a data-set at https://brainly.com/question/24628525