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: 2 q1: 4 med: 6.5 q3: 9 max: 11
create the box plot by dragging the lines:

Explanation:

Step1: Find the minimum

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

Step2: Find the first quartile (Q1)

First, find the median of the lower half of the data. The data has $n = 12$ values. The lower half of the data is $2,3,4,4,5,6$. The median of this lower - half (Q1) is the average of the 3rd and 4th ordered values. $\frac{4 + 4}{2}=4$.

Step3: Find the median (Med)

Since $n = 12$ (an even number of data points), the median is the average of the 6th and 7th ordered values. $\frac{6+6}{2} = 6$.

Step4: Find the third quartile (Q3)

The upper half of the data is $6,8,9,10,11$. The median of this upper - half (Q3) is the average of the 3rd and 4th ordered values of the upper half. $\frac{9 + 9}{2}=9$.

Step5: Find the maximum

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

Answer:

Min: 2, Q1: 4, Med: 6, Q3: 9, Max: 11