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.
[tex]\text{Median}=\frac{6^{th}+7^{th}}{2}=\frac{8+10}{2}=9[/tex]
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:
[tex]Rangw=Max.-Min.=13.5-4.5=9[/tex]
Compute the Interquartile Range as follows:
[tex]IQR=Q_{3}-Q_{1}=13.5-4.5=9[/tex]
Thus, the box pot for the provided data has no whiskers.
