Speed Reading Jessica enrolled in a course that promised to in...

Question

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.

Accepted Answer

Hello. In this video, we want to construct a box and whisker plot for the given data set. Now, the data set represents the number of hours spent on leisurely activities per week by a sample of 15 individuals. So, the first thing we want to do is you want to organize our data from least to greatest, but our data is already given in the form of least to greatest. So, the first thing we're going to identify is the minimum value of our data set, which is the smallest value. Our minimum, in this case is going to be 12. Next, we need to identify the maximum value. The maximum value is the largest value in the data set, and that is going to be 50. Next, we are going to identify the median, and the median is going to be our second quartile for the box and whisker plot. Now, the median is the middlemost number in our sample data, and since we are working with 15 pieces of data, the middlemost number is going to be the 8th piece of data in the data set. That median is going to be 30. So we have a median or 2nd quartile of 30. Next, we are going to identify our 1st and our 3rd quartiles. Now, the first quartile is going to be the median of the first half of the data set, and the median of the first half of the data set is going to be 20. So we have a 1st quartile of 20. Next, we are going to identify the 3rd quartile, and that is going to be the median of the upper half of the data set. That median is going to be 40. So, we have a 3rd quartile of 40. Next, we are going to identify our interquartile range. The interquartile range is defined as the 3rd quartile minus the 1st quartile. That is going to be 40 minus 20, and that is going to give us 20. So we have an interquartile range of 20. Now what we want to do is you want to identify our upper and lower bounds for the box and whisker plot. Starting with the lower bound, the lower bound is defined as the first quartile minus 1.5, multiplied by our interquartile range. That is going to give us a lower bound of 20 minus 1.5, multiplied by 20, and that is going to give us a lower bound of -10. Next, we are going to identify our upper bound. The upper bound is defined as our third quartile, plus 1.5, multiplied by our interquartile range. That is going to give us 40 plus 1.5 multiplied by 20, and we're going to have an upper bound of 70. So, the next thing we want to do is we want to check for any outliers in our box and whisker plot. In order to check for outliers, we want to check and see if our maximum and minimum values are on the interval from -10 to 70. So, is 12 and 50 between the values of -10 and 70? And the answer to that is yes, so we're not going to have any outliers for a box and whisker plot. Now what we want to do is we want to go ahead and plot the data for our box and whisker plot. So that is going to give us the following. So this is going to be the following box and whisker plot that is produced by plotting the three quartiles, the minimum and maximum value, and this is going to be the solution to the problem. So I hope this video helps you in understanding how to plot this box and whisker plot, and we will go ahead and see you all in the next video.

Key Concepts

Five-Number Summary

Boxplot Construction

Interpreting Data Distribution

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