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.
5,9,9,10,13,14,15,16,16
min: q1: med: q3: max:
create the box plot by dragging the lines

Explanation:

Step1: Arrange data in order

The data is already in ascending - order: 5, 9, 9, 10, 13, 14, 15, 16, 16.

Step2: Find the minimum value

The minimum (Min) value of the data - set is the first value. Min = 5.

Step3: Find the first quartile (Q1)

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

Step4: Find the median (Med)

The position of the median for $n = 9$ (odd number of data - points) is $\frac{n + 1}{2}=5$. So, Med = 13.

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 values. Q3=$\frac{15+16}{2}=15.5$.

Step6: Find the maximum value

The maximum (Max) value of the data - set is the last value. Max = 16.

Answer:

Min: 5
Q1: 9
Med: 13
Q3: 15.5
Max: 16