Speed Reading Jessica enrolled in a course that promised to increase her reading speed. To help judge the effectiveness of the course, Jessica measured the number of words per minute she could read prior to enrolling in the course. She obtained the following five-number summary: 110 140 157 173 205. Use this information to draw a boxplot of the reading speed.
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Identify the five-number summary components: minimum = 110, first quartile (Q1) = 140, median = 157, third quartile (Q3) = 173, and maximum = 205. These values will form the key points of the boxplot.
Draw a number line that covers the range from the minimum value (110) to the maximum value (205). This will serve as the scale for the boxplot.
Draw a box from Q1 (140) to Q3 (173). This box represents the interquartile range (IQR), which contains the middle 50% of the data.
Inside the box, draw a line at the median value (157) to show the center of the data distribution.
Draw 'whiskers' from the edges of the box to the minimum value (110) on the left and to the maximum value (205) on the right. These whiskers represent the spread of the data outside the interquartile range.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
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, central tendency, and spread of the data, which is essential for constructing a boxplot.
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 data’s spread, central value, and potential outliers.
Understanding the relative positions of the quartiles and median in the boxplot reveals the skewness and variability of the data. For example, if the median is closer to Q1 or Q3, it indicates asymmetry in the data distribution.