answer the statistical measures and create a box and whiskers plot for the following set of data…

Explanation:

Step1: Find the minimum value

The minimum value in the data - set $1,4,5,8,11,11,11,15,15,15,16,16,18,18$ is $1$.

Step2: Find the maximum value

The maximum value in the data - set is $18$.

Step3: Find the median (Med)

There are $n = 14$ data points. The median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+1)$th ordered data points. $\frac{n}{2}=7$ and $\frac{n}{2}+1 = 8$. The 7th value is $11$ and the 8th value is $15$. So, $Med=\frac{11 + 15}{2}=13$.

Step4: Find the lower half of the data

The lower half of the data is $1,4,5,8,11,11,11$. There are $n_1=7$ data points. The median of the lower - half (Q1) is the 4th value. So, $Q1 = 8$.

Step5: Find the upper half of the data

The upper half of the data is $15,15,15,16,16,18,18$. There are $n_2 = 7$ data points. The median of the upper - half (Q3) is the 4th value. So, $Q3=16$.

Answer:

Min: $1$, Q1: $8$, Med: $13$, Q3: $16$, Max: $18$