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 gives the minimum value. Looking at the box - plot, the minimum value is \(7\).

Step2: Identify First Quartile (\(Q_1\))

The left - hand side of the box gives the first quartile. Here, \(Q_1 = 12\).

Step3: Identify Median

The line inside the box gives the median. So, the median is \(14\).

Step4: Identify Third Quartile (\(Q_3\))

The right - hand side of the box gives the third quartile. Thus, \(Q_3=17\).

Step5: Identify Maximum Value

The right - most point of the whisker gives the maximum value. The maximum value is \(22\).

Step6: Calculate Range

Range is calculated as \( \text{Range}=\text{Max}-\text{Min}\). Substituting the values, \( \text{Range}=22 - 7=15\).

Step7: Calculate Inter - quartile Range (IQR)

IQR is calculated as \( \text{IQR}=Q_3 - Q_1\). Substituting the values, \( \text{IQR}=17-12 = 5\).

Answer:

Minimum Value: \(7\)
First Quartile: \(12\)
Median: \(14\)
Third Quartile: \(17\)
Maximum Value: \(22\)
Range: \(15\)
Interquartile Range: \(5\)