Before we begin we will order the data set given
4, 6, 7, 9, 10, 11, 11, 12, 15, 16
Mean.
The mean of a data set is given by:
![\operatorname{mean}=\frac{\sum ^{}_{}x_i}{n}]()
where the denominator means that we have to add the points on the data and then divide them result by the number of points in the data. In this case we have:
![\begin{gathered} \operatorname{mean}=(4+6+7+9+10+11+11+12+15+16)/(10) \\ \operatorname{mean}=(101)/(10) \\ \operatorname{mean}=10.1 \end{gathered}]()
Hence the mean of the data set is 10.1
Median.
The median is the central value of the ordered data set. In this case we have an even number of values which means that the median is the average of the central values. The central values in this set are the the fifth and sixth term, that is, 10 and 11. The median is then:
![\begin{gathered} \operatorname{median}=(10+11)/(2) \\ \operatorname{median}=(21)/(2) \\ \operatorname{median}=10.5 \end{gathered}]()
Mode
The mode is value that occur most frequently. In this case only the 11 repeats itsefl, hence the mode is 11.
Summing up we have:
Mean 10.1
Median 10.5
Mode 11