Question

Here is an ordered set of sample data.87 109 156 166 204210 279 416 500 534592 609 655 677 777837 873 998Identify the 5 number summary: (min, Q1, median, Q3, max).

Answer 1

A boxplot is a standardized way of displaying the dataset based on a five-number summary: the minimum, the maximum, the median, the first quartile, and the third quartile.

The general representation for a box plot is given below;

Comparing this to the box plot given in the question, the following can be deduced;

`\begin{gathered} \text{minimum, }\min =11 \\ lowerquartileQ_1=12 \\ \text{Median}=15 \\ \text{upper quartile, Q}_3=17 \\ \max imum,\text{ max=20} \end{gathered}`

Therefore, the answer as arranged is;

`(11,12,15,17,20)`

The interquartile range, IQR is given by;

`\begin{gathered} Q_3-Q_1 \\ \text{where;} \\ Q_3=17 \\ Q_1=12 \\ \\ \text{IQR}=17-12 \\ \text{IQR}=5 \end{gathered}`

Therefore, the interquartile range is 5.