Statistics: Box-and-Whisker Plots
Summarizing data with quartiles, medians, and spread
Statistics: Box-and-Whisker Plots
Summarizing data with quartiles, medians, and spread
Statistics - Grade 6-8
- 1
Find the five-number summary for this data set: 4, 6, 7, 8, 10, 12, 15.
The five-number summary includes the minimum, Q1, median, Q3, and maximum.
The five-number summary is minimum 4, first quartile 6, median 8, third quartile 12, and maximum 15. - 2
A data set has this five-number summary: minimum 2, Q1 5, median 9, Q3 14, maximum 18. Describe how to draw its box-and-whisker plot.
Draw a number line from 0 to 20. Draw a box from 5 to 14, draw a vertical line inside the box at 9, and draw whiskers from 5 down to 2 and from 14 up to 18. - 3
A box-and-whisker plot has Q1 at 12 and Q3 at 20. What is the interquartile range, or IQR?
Use IQR = Q3 - Q1.
The interquartile range is 8 because Q3 minus Q1 is 20 minus 12. - 4
A box-and-whisker plot has a minimum of 6 and a maximum of 31. What is the range of the data?
The range is 25 because 31 minus 6 equals 25. - 5
Look at a box-and-whisker plot with minimum 10, Q1 15, median 18, Q3 25, and maximum 30. What does the median tell you about the data?
The median is the middle value of the data set.
The median tells us that about half of the data values are 18 or less and about half are 18 or greater. - 6
Find the five-number summary for this data set: 18, 20, 22, 22, 25, 27, 30, 31, 33, 35, 36, 40.
There are 12 values, so the median is the average of the 6th and 7th values.
The five-number summary is minimum 18, Q1 22, median 28.5, Q3 34, and maximum 40. - 7
Use the 1.5 times IQR rule to check for outliers in this data set: 3, 5, 6, 6, 7, 8, 8, 9, 30.
Find Q1 and Q3 first, then calculate the lower and upper fences.
The median is 7, Q1 is 5.5, and Q3 is 8.5, so the IQR is 3. The lower fence is 1 and the upper fence is 13. Since 30 is greater than 13, 30 is an outlier. - 8
Class A has a five-number summary of 60, 70, 78, 86, 95. Class B has a five-number summary of 65, 75, 80, 83, 90. Which class has scores that are more consistent, and why?
A smaller spread means the data values are more consistent.
Class B has scores that are more consistent because its IQR is 8 and its range is 25, while Class A has an IQR of 16 and a range of 35. - 9
In a box-and-whisker plot, about what percent of the data values are at or below Q3?
About 75 percent of the data values are at or below Q3 because Q3 is the third quartile. - 10
A box-and-whisker plot has minimum 2, Q1 4, median 5, Q3 9, and maximum 20. Is the data more spread out on the lower side or the upper side? Explain.
Compare the lengths of the whiskers and the distances on each side of the median.
The data is more spread out on the upper side because the distance from the median to the maximum is much larger than the distance from the minimum to the median. - 11
A town recorded daily rainfall amounts in millimeters: 0, 0, 1, 2, 2, 3, 3, 4, 10, 12. Find the five-number summary.
The five-number summary is minimum 0, Q1 1, median 2.5, Q3 4, and maximum 12. - 12
A student says a box-and-whisker plot has Q1 at 8, median at 7, and Q3 at 12. Explain the mistake.
Check whether the numbers are in the correct order.
The mistake is that the median cannot be less than Q1. The values in a five-number summary must go in order from least to greatest. - 13
A dot plot shows this data set: 1, 2, 2, 3, 4, 4, 4, 5, 6, 7, 7. Find the five-number summary that would be used to make a box-and-whisker plot.
The five-number summary is minimum 1, Q1 2, median 4, Q3 6, and maximum 7. - 14
A box-and-whisker plot for test scores has a median of 84. What does this mean? What does it not mean?
The median describes the middle of the ordered data, not the most common value.
It means about half of the test scores are 84 or lower and about half are 84 or higher. It does not mean that half of the students scored exactly 84. - 15
Which data set matches a box-and-whisker plot with minimum 10, Q1 15, median 20, Q3 24, and maximum 30? A: 10, 15, 15, 20, 22, 24, 30. B: 10, 12, 15, 20, 24, 28, 30. C: 10, 15, 18, 20, 24, 24, 30.
Data set A matches the box-and-whisker plot. Its minimum is 10, Q1 is 15, median is 20, Q3 is 24, and maximum is 30.