Questions: 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. 65 68 44 61 57 65 52 62 53 54 69 67 67 43 48 The five-number summary is .

Solution Steps

First, organize the given data in ascending order: \[ 43, 44, 48, 52, 53, 54, 57, 61, 62, 65, 65, 67, 67, 68, 69 \]

The five-number summary consists of the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum.

1. Minimum: The smallest value in the data set is \(43\).
2. First Quartile (Q1): The median of the first half of the data. Since there are 15 data points, the first quartile is the 4th value: \[ Q1 = 52 \]
3. Median (Q2): The middle value of the data set. For 15 data points, the median is the 8th value: \[ Q2 = 61 \]
4. Third Quartile (Q3): The median of the second half of the data. The third quartile is the 12th value: \[ Q3 = 67 \]
5. Maximum: The largest value in the data set is \(69\).

To construct the boxplot:

• Draw a box from \(Q1 = 52\) to \(Q3 = 67\).
• Draw a line inside the box at the median \(Q2 = 61\).
• Draw whiskers from the box to the minimum \(43\) and maximum \(69\).

The distribution appears to be slightly right-skewed, as the right whisker (from \(Q3\) to the maximum) is longer than the left whisker (from \(Q1\) to the minimum).

Final Answer