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

Explanation:

Step1: Find the minimum

The minimum value in the data - set $3,4,4,5,7,7,10,10,12,16$ is $3$.

Step2: Find the first quartile (Q1)

First, find the median of the lower half of the data. The data set has $n = 10$ values. The lower half is $3,4,4,5,7$. The median of this lower - half (Q1) is the middle value. Since there are 5 values, the middle value is the 3rd one, so $Q1 = 4$.

Step3: Find the median (Med)

Since $n = 10$ (an even number of data points), the median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+1)$th ordered values. $\frac{n}{2}=5$ and $\frac{n}{2}+1 = 6$. The 5th and 6th values are 7 and 7, so $Med=\frac{7 + 7}{2}=7$.

Step4: Find the third quartile (Q3)

The upper half of the data is $7,10,10,12,16$. The median of this upper - half (Q3) is the middle value. Since there are 5 values, the middle value is the 3rd one, so $Q3 = 10$.

Step5: Find the maximum

The maximum value in the data - set is $16$.

Answer:

Min: $3$ Q1: $4$ Med: $7$ Q3: $10$ Max: $16$