Answer:
The data set is:
S = {4.5, 4.5, 4.5, 4.5, 6, 8, 10, 12, 13.5, 13.5, 13.5, 13.5}
Step-by-step explanation:
Consider the ordered data set:
S = {4.5, 4.5, 4.5, 4.5, 6, 8, 10, 12, 13.5, 13.5, 13.5, 13.5}
The lower extreme is: 4.5
The upper extreme is: 13.5
The median for an even number of observations is the mean of the middle two values.
![\text{Median}=\frac{6^{th}+7^{th}}{2}=\frac{8+10}{2}=9](https://tex.z-dn.net/?f=%5Ctext%7BMedian%7D%3D%5Cfrac%7B6%5E%7Bth%7D%2B7%5E%7Bth%7D%7D%7B2%7D%3D%5Cfrac%7B8%2B10%7D%7B2%7D%3D9)
The first quartile (Q₁) is defined as the mid-value between the minimum figure and the median of the data set.
Q₁ = 4.5
The 3rd quartile (Q₃) is the mid-value between the median and the maximum figure of the data set.
Q₃ = 13.5
A box plot that has no whiskers has, Range = Interquartile Range.
Compute the range as follows:
![Rangw=Max.-Min.=13.5-4.5=9](https://tex.z-dn.net/?f=Rangw%3DMax.-Min.%3D13.5-4.5%3D9)
Compute the Interquartile Range as follows:
![IQR=Q_{3}-Q_{1}=13.5-4.5=9](https://tex.z-dn.net/?f=IQR%3DQ_%7B3%7D-Q_%7B1%7D%3D13.5-4.5%3D9)
Thus, the box pot for the provided data has no whiskers.