Question

find the following descriptive statistics of the boxplot below:
minimum value:
first quartile:
median:
third quartile:
maximum value:
range:
interquartile range:

Explanation:

Step1: Identify minimum value

The left - most point of the whisker is the minimum value. From the box - plot, it is \(12\).

Step2: Identify first quartile (\(Q_1\))

The left - hand side of the box is the first quartile. It is \(14\).

Step3: Identify median

The line inside the box is the median. It is \(16\).

Step4: Identify third quartile (\(Q_3\))

The right - hand side of the box is the third quartile. It is \(19\).

Step5: Identify maximum value

The right - most point of the whisker is the maximum value. It is \(20\).

Step6: Calculate range

Range is \( \text{Max}-\text{Min}\). So, \(20 - 12=8\).

Step7: Calculate inter - quartile range (IQR)

IQR is \(Q_3 - Q_1\). So, \(19 - 14 = 5\).

Answer:

Minimum Value: \(12\)
First Quartile: \(14\)
Median: \(16\)
Third Quartile: \(19\)
Maximum Value: \(20\)
Range: \(8\)
Interquartile Range: \(5\)