Question

the data represent the age of world leaders on their day of inauguration. find the five - number summary, and construct a boxplot for the data. comment on the shape of the distribution.
the five - number summary is 41, 43, 47, 69

Explanation:

Step1: Sort the data

First, sort the data set: \(41,42,42,43,43,45,46,47,47,52,55,55,61,63,69\)

Step2: Find the median (\(Q_2\))

Since \(n = 15\) (odd), the median is the \(\frac{n + 1}{2}=\frac{15+ 1}{2}=8^{th}\) value. So \(Q_2=47\)

Step3: Find the lower half and \(Q_1\)

The lower half of the data is \(41,42,42,43,43,45,46\). Since \(n_1=7\) (odd), \(Q_1\) is the \(\frac{7 + 1}{2}=4^{th}\) value of the lower - half. So \(Q_1 = 43\)

Step4: Find the upper half and \(Q_3\)

The upper half of the data is \(47,52,55,55,61,63,69\). Since \(n_2 = 7\) (odd), \(Q_3\) is the \(\frac{7+1}{2}=4^{th}\) value of the upper - half. So \(Q_3=55\)

Answer:

The five - number summary is \(41\), \(43\), \(47\), \(55\), \(69\)