Exam Scores After giving a statistics exam, Professor Dang determined the following five-number summary for her class results: 60 68 77 89 98. Use this information to draw a boxplot of the exam scores.

Verified step by step guidance

1. Identify the five-number summary components: minimum = 60, first quartile (Q1) = 68, median (Q2) = 77, third quartile (Q3) = 89, and maximum = 98. These values define the key points of the boxplot.
2. Draw a number line that covers the range from the minimum value (60) to the maximum value (98) to provide a scale for the boxplot.
3. Draw a box starting at Q1 (68) and ending at Q3 (89). This box represents the interquartile range (IQR), which contains the middle 50% of the data.
4. Inside the box, draw a line at the median value (77) to show the center of the data distribution.
5. Draw 'whiskers' from the edges of the box to the minimum value (60) on the left and to the maximum value (98) on the right, completing the boxplot.

Key Concepts

Five-Number Summary

The five-number summary consists of the minimum, first quartile (Q1), median, third quartile (Q3), and maximum values of a data set. It provides a quick overview of the distribution and spread of the data, which is essential for constructing a boxplot.

Boxplot Construction

A boxplot visually represents the five-number summary by drawing a box from Q1 to Q3 with a line at the median, and whiskers extending to the minimum and maximum values. It helps identify the central tendency, variability, and potential outliers in the data.

Interquartile Range (IQR)

The interquartile range (IQR) is the difference between Q3 and Q1 and measures the spread of the middle 50% of the data. It is used to assess data variability and detect outliers, which can influence how the whiskers are drawn in a boxplot.