Question

The five-number summary for a distribution of final exam scores is 44, 75, 82, 87, 06. Explain why it is not possible to draw a boxplot based on this information. (Hint: What more do you need to know?)

A) It isn't possible to draw a boxplot based on the five-number summary because the five-number summary is used to summarize symmetric distributions, not asymmetric distributions. The boxplot cannot be constructed with the information in the five-number summary .
B) Isn't possible to draw a boxplot based on the five-number summary because the five-number summary doesn't contain the interquartile range (QR), which is necessary to draw the boxplot
C) It isn't possible to draw a boxplot based on the five number summary because the five-number summary doesn't contain all observations from the distribution of final exam scores
D) It is possible to draw a boxplot based on the five number summary because the boxplot must mark all potential outliers. Since the minimum is lower than the left limit, there may be other unknown outiers between the minimum and left limit, and so the bosplot cannot mark all potential outlers.

Answer 1

A box plot can be constructed from the five-number summary; however, there appears to be a mistake in the values provided, as the last number is out of order. The correct five numbers should all be in ascending order to use them for constructing the box plot.

Step-by-step explanation:

A box plot, also known as a box-and-whisker plot, can indeed be constructed using the five-number summary. However, the five-number summary provided in the question seems to be incorrect or typographically in error: 44, 75, 82, 87, 06. There's an issue with the last number '06', which appears to be out of order and may represent '6' being out of place as the minimum value. For a valid five-number summary, the values should be in ascending order: the minimum, the first quartile (Q1), the median (Q2), the third quartile (Q3), and the maximum.

To plot a box plot, we need to know the following points: the minimum score, Q1, the median (Q2), Q3, and the maximum score. The whiskers of the box plot extend from Q1 to the minimum value and from Q3 to the maximum value, while the box itself represents the interquartile range (IQR), with the median marked inside it. The presence of potential outliers can also be determined using the IQR by checking if any values fall more than 1.5 times the IQR below Q1 or above Q3, but a complete set of data is not necessary for constructing the box plot itself, just the correct five-number summary.