Question

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

Explanation:

Step1: Find Minimum Value

The left - most point of the boxplot is the minimum value. From the graph, it is \(7\).

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

The left - hand side of the box is the first quartile. Observing the graph, \(Q_1 = 12\).

Step3: Find Median

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

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

The right - hand side of the box is the third quartile. From the graph, \(Q_3=17\).

Step5: Find Maximum Value

The right - most point of the boxplot is the maximum value. It is \(22\).

Step6: Calculate Range

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

Step7: Calculate Inter - quartile Range (IQR)

The inter - quartile range is \(IQR = Q_3 - Q_1\). Substituting the values, \(IQR=17 - 12 = 5\).

Answer:

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