Question

answer the statistical measures and create a box and whiskers plot for the following set of data. enter all values as whole numbers or decimals. 2,3,4,4,5,6,6,6,8,9,10,11 min: q1: med: q3: max: create the box plot by dragging the lines: answer attempt 1 out of 2 you must answer all questions above in order to submit.

Explanation:

Step1: Find the minimum value

The minimum value in the data - set $2,3,4,4,5,6,6,6,8,9,10,11$ is $2$.

Step2: Find the maximum value

The maximum value in the data - set is $11$.

Step3: Find the median (Med)

There are $n = 12$ data points. The median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+1)$th ordered data points. $\frac{n}{2}=6$ and $\frac{n}{2}+1 = 7$. The 6th and 7th values are $6$ and $6$, so $Med=\frac{6 + 6}{2}=6$.

Step4: Find the lower half of the data

The lower half of the data is $2,3,4,4,5,6$.

Step5: Find the first quartile (Q1)

There are $n_1=6$ data points in the lower - half. The median of the lower - half is the average of the $\frac{n_1}{2}$th and $(\frac{n_1}{2}+1)$th ordered data points. $\frac{n_1}{2}=3$ and $\frac{n_1}{2}+1 = 4$. The 3rd and 4th values are $4$ and $4$, so $Q1=\frac{4 + 4}{2}=4$.

Step6: Find the upper half of the data

The upper half of the data is $6,6,8,9,10,11$.

Step7: Find the third quartile (Q3)

There are $n_2 = 6$ data points in the upper - half. The median of the upper - half is the average of the $\frac{n_2}{2}$th and $(\frac{n_2}{2}+1)$th ordered data points. $\frac{n_2}{2}=3$ and $\frac{n_2}{2}+1 = 4$. The 3rd and 4th values are $8$ and $9$, so $Q3=\frac{8 + 9}{2}=8.5$.

Answer:

Min: $2$
Q1: $4$
Med: $6$
Q3: $8.5$
Max: $11$