Using the histogram, the mean of the data-set is estimated to be of 31.
- The mean, given an histogram, is the sum of the halfway points of each interval multiplied by it's relative frequency.
In this problem, the intervals and relative frequencies are:
- The first interval has halfway point 23 and relative frequency [tex]\frac{4}{30}[/tex].
- The second interval has halfway point 28 and relative frequency [tex]\frac{8}{30}[/tex].
- The third interval has halfway point 33 and relative frequency [tex]\frac{14}{30}[/tex].
- The fourth interval has halfway point 38 and relative frequency [tex]\frac{4}{30}[/tex].
Hence, the mean is:
[tex]E(X) = 23\frac{4}{30} + 28\frac{8}{30} + 33\frac{14}{30} + 38\frac{4}{30} = \frac{23(4) + 28(8) + 33(14) + 38(4)}{30} = 31[/tex]
For more on mean of histograms, you can check https://brainly.com/question/24651197
