A group of 15 students were assigned a novel to read during class. The data below represents the number of pages each student read.
8, 8, 10, 11, 12, 12, 13, 14, 16, 16, 18, 18, 18, 20, 24
Which of the following box plots correctly summarizes the data?
There are multiple ways to create box plots for this data set, as there is not a unique correct answer. However, one possible box plot that could accurately summarize the data is as follows:
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8 10 12 14 16 18 20
The box plot is created by first finding the median, which is the middle value when the data is arranged in order. In this case, the median is 14.
Next, find the lower quartile (Q1), which represents the lower 25% of the data. In this case, Q1 is 10.
Find the upper quartile (Q3), which represents the upper 25% of the data. In this case, Q3 is 18.
Plotting these values on the number line, we get the boxes as shown in the box plot.
Finally, find the minimum and maximum values in the data set, which are 8 and 24, respectively. These are denoted with vertical lines (whiskers) extending from the boxes.
Note that this is just one possible way to create a box plot for the given data. Other valid box plots could be derived by using different calculations or choosing different quartiles.