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. 3,4,4,6,6,8,9,12,15 min: q1: med: q3: max: create the box plot by dragging the lines:

Explanation:

Step1: Arrange data in order

The data set $3,4,4,6,6,8,9,12,15$ is already in ascending - order.

Step2: Find the minimum value

The minimum value (Min) of the data set is the first value. So, Min = 3.

Step3: Find the first - quartile (Q1)

The number of data points $n = 9$. The position of Q1 is $\frac{n + 1}{4}=\frac{9+1}{4}=2.5$. So, Q1 is the average of the 2nd and 3rd ordered data points. Q1=$\frac{4 + 4}{2}=4$.

Step4: Find the median (Med)

The position of the median for $n = 9$ (odd number of data points) is $\frac{n + 1}{2}=\frac{9+1}{2}=5$. So, Med = 6.

Step5: Find the third - quartile (Q3)

The position of Q3 is $\frac{3(n + 1)}{4}=\frac{3\times(9 + 1)}{4}=7.5$. So, Q3 is the average of the 7th and 8th ordered data points. Q3=$\frac{9+12}{2}=10.5$.

Step6: Find the maximum value

The maximum value (Max) of the data set is the last value. So, Max = 15.

Answer:

Min: 3
Q1: 4
Med: 6
Q3: 10.5
Max: 15