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. 57, 65, 44, 69, 65, 67, 52, 54, 53, 43, 48, 62, 67, 61, 63 The five-number summary is Choose the correct boxplot of the data below: A B. C. Choose the correct description of the shape of the distribution. A. The distribution is skewed to the left. B. The distribution is skewed to the right. C. The distribution is roughly symmetric. D. The shape of the distribution cannot be determined from the boxplot.

Solution Steps

First, we need to arrange 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, third quartile (Q3), and maximum.

• Minimum: The smallest number in the data set. \[ \text{Minimum} = 43 \]

• First Quartile (Q1): The median of the first half of the data. \[ Q1 = 52 \]

• Median: The middle number in the data set. \[ \text{Median} = 57 \]

• Third Quartile (Q3): The median of the second half of the data. \[ Q3 = 67 \]

• Maximum: The largest number in the data set. \[ \text{Maximum} = 69 \]

Using the five-number summary, we can construct the boxplot. The boxplot should have:

• A box from Q1 (52) to Q3 (67)
• A line at the median (57)
• Whiskers extending to the minimum (43) and maximum (69)

The correct boxplot is Option C.

To determine the shape of the distribution, we observe the boxplot:

• The box is slightly skewed to the left because the left whisker (43 to 52) is longer than the right whisker (67 to 69).

Thus, the correct description is: \[ \text{A. The distribution is skewed to the left.} \]

Final Answer