Step 1: Write out the set
[tex]\mleft\lbrace12,12,18,19,19,21,23,23,23,23,32,32,41,50,50,50,82,82\mright\rbrace[/tex]
Step 2: Compute the mean
[tex]\text{Mean }=\frac{\text{ Sum of all the elements}}{\text{ the total number of the elements}}[/tex][tex]\text{the sum }=612[/tex][tex]the\text{ number of the elements }=18[/tex]
Hence, the mean is given by
[tex]\operatorname{mean}\text{ = }\frac{612}{18}=34[/tex]
The mean is 34
Step 3: Find the median
Median = [(n+1)/2]th element, if n is odd.
Median = mean of (n/2)th element and [(n/2)+1]th element, if n is even.
Where n is the number of elements in the set
In this case, n = 1 is even.
Therefore, the (n/2)th element is the 9th element, which is 23
and
the [(n/2)+1]th element is the 10th element, which is 23
[tex]\operatorname{median}\text{ }=\frac{23+23}{2}=\frac{46}{2}=23[/tex]
Thus, the median is 23
Step 4: Find the mode
The mode is the value that appears most frequently in a data set.
In this case, 23 appears the most often in the data set.
Therefore, the mode is 23
Step 5: Find the range.
The range is the positive difference between the largest element of the set and the smallest element.
The largest element is 82, and
the smallest element is 12
Hence, the range is given by
[tex]\text{range = }82-12=70[/tex]
The range is 70
