Hello there. To solve this question, we'll have to remember some properties about mean and median of a set of values.
Given a set of values, in this case, modelling the number of hours the people in the survey was asked they've been watching television last week:
[tex]\{20,5,14,11,18,19,15,14\}[/tex]
We have to determine the mean and the median of this set of values.
The mean of a set of values is the arithmetic mean. It is calculated by adding all the values in the set and dividing the result by the number of values:
[tex]\mu(x_1,x_2,\cdots,x_n)=\dfrac{\sum_{i=0}^nx_i}{n}[/tex]
In this case, we have 8 values, hence
[tex]\mu=\dfrac{20+15+14+19+11+18+14+5}{8}=\dfrac{116}{8}=14.5[/tex]
The median of a set of value is determined in two ways:
First we order the values, either in ascending or descending order and, using the number of values, we know if the median is the central value or the mean of the two values.
In this case, since we have an even number of values, we'll have two central values and we have to take the mean of them to determine the median:
Ordering the values:
[tex]\{5,11,14,14,15,18,19,20\}[/tex]
In this case, the two central values are 14 and 15. Adding them, we get
[tex]14+15=29[/tex]
Dividing it by 2, we find the median:
[tex]Median=\dfrac{29}{2}=14.5[/tex]
Notice the median is the same as the mean.
