Question

Write a set of data that contains 12 values for which the box plot has no whiskers. State the median, first and third quartiles, and lower and upper extreme

Answer 1

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.

$\text{Median}=\frac{6^{th}+7^{th}}{2}=\frac{8+10}{2}=9$

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:

$Rangw=Max.-Min.=13.5-4.5=9$

Compute the Interquartile Range as follows:

$IQR=Q_{3}-Q_{1}=13.5-4.5=9$

Thus, the box pot for the provided data has no whiskers.