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

Explanation:

Step1: Determine minimum and maximum

The minimum value (Min) of the data - set $3,5,6,9,9,11,11,12,13,15,16,16,18$ is $3$ (not $1$ as wrongly filled), and the maximum value (Max) is $18$.

Step2: Calculate the median (Med)

There are $n = 13$ data points. The median is the $\left(\frac{n + 1}{2}\right)$-th value. $\frac{13+1}{2}=7$ - th value. So, $Med = 11$.

Step3: Calculate the lower - quartile (Q1)

The lower half of the data set is $3,5,6,9,9,11$. There are $n_1=6$ data points. The median of the lower half is the average of the $\frac{6}{2}$-th and $\left(\frac{6}{2}+1\right)$-th values. The $3$-rd value is $6$ and the $4$-th value is $9$. So, $Q1=\frac{6 + 9}{2}=7.5$.

Step4: Calculate the upper - quartile (Q3)

The upper half of the data set is $12,13,15,16,16,18$. There are $n_2 = 6$ data points. The median of the upper half is the average of the $\frac{6}{2}$-th and $\left(\frac{6}{2}+1\right)$-th values. The $3$-rd value is $15$ and the $4$-th value is $16$. So, $Q3=\frac{15 + 16}{2}=15.5$.

Answer:

Min: $3$, Q1: $7.5$, Med: $11$, Q3: $15.5$, Max: $18$