Question

1. you have been asked to represent this data in a box plot. answer the following questions: 16, 4, 20, 16, 36, 32, 44, 40, 60 3b construct a box plot for the data.

Explanation:

Step1: Sort the data

$4, 16, 16, 20, 32, 36, 40, 44, 60$

Step2: Find the minimum

The minimum value is $4$.

Step3: Find the first - quartile ($Q_1$)

There are $n = 9$ data points. The position of $Q_1$ is $\frac{n + 1}{4}=\frac{9+1}{4}=2.5$. So, $Q_1=\frac{16 + 16}{2}=16$.

Step4: Find the median ($Q_2$)

The position of the median is $\frac{n + 1}{2}=\frac{9+1}{2}=5$. So, $Q_2 = 32$.

Step5: Find the third - quartile ($Q_3$)

The position of $Q_3$ is $\frac{3(n + 1)}{4}=\frac{3\times(9 + 1)}{4}=7.5$. So, $Q_3=\frac{40+44}{2}=42$.

Step6: Find the maximum

The maximum value is $60$.

Answer:

On the box - plot:

• The left - most whisker starts at the minimum value $4$.
• The left side of the box is at $Q_1 = 16$.
• The line inside the box is at the median $Q_2=32$.
• The right side of the box is at $Q_3 = 42$.
• The right - most whisker ends at the maximum value $60$.