Math: Box Plots and Data Analysis
Reading quartiles, medians, and spread in data
Math: Box Plots and Data Analysis
Reading quartiles, medians, and spread in data
Math - Grade 6-8
- 1
Find the median of this data set: 4, 7, 9, 10, 12, 15, 18.
The median is the middle number when the data are already in order.
The median is 10 because it is the middle value in the ordered list. - 2
Find the median of this data set: 6, 8, 11, 13, 17, 20.
The median is 12 because the two middle values are 11 and 13, and their average is 12. - 3
Find the first quartile, median, and third quartile for this ordered data set: 3, 5, 8, 9, 12, 14, 16, 20, 21.
Do not include the median in either half when there is an odd number of data values.
The first quartile is 6.5, the median is 12, and the third quartile is 18. The lower half is 3, 5, 8, 9 and its median is 6.5. The upper half is 14, 16, 20, 21 and its median is 18. - 4
Find the five-number summary for this ordered data set: 2, 4, 6, 8, 10, 12, 14, 16, 18.
The five-number summary is minimum 2, first quartile 5, median 10, third quartile 15, and maximum 18. - 5
A box plot has minimum 5, first quartile 9, median 12, third quartile 18, and maximum 22. What is the interquartile range?
The interquartile range is third quartile minus first quartile.
The interquartile range is 9 because 18 minus 9 equals 9. - 6
A box plot has minimum 1, first quartile 4, median 7, third quartile 11, and maximum 15. What is the range?
The range is 14 because 15 minus 1 equals 14. - 7
This box plot summary describes quiz scores: minimum 50, first quartile 60, median 72, third quartile 85, maximum 95. What percent of the scores are at or below 72?
The median marks the halfway point in the data.
About 50 percent of the scores are at or below 72 because the median splits the data into two equal halves. - 8
This box plot summary describes plant heights in centimeters: minimum 12, first quartile 18, median 24, third quartile 30, maximum 36. Between which two values is the middle 50 percent of the data?
The middle 50 percent of the data is between 18 and 30 because those are the first and third quartiles. - 9
Two classes took the same test. Class A has five-number summary 55, 68, 74, 82, 96. Class B has five-number summary 50, 70, 74, 78, 90. Which class has the greater range?
Compare maximum minus minimum for each class.
Class A has the greater range. Class A has a range of 41 because 96 minus 55 equals 41. Class B has a range of 40 because 90 minus 50 equals 40. - 10
Two teams recorded the number of points scored in games. Team X has five-number summary 10, 14, 20, 25, 29. Team Y has five-number summary 8, 15, 20, 23, 31. Which team has the greater interquartile range?
Team X has the greater interquartile range. Team X has an interquartile range of 11 because 25 minus 14 equals 11. Team Y has an interquartile range of 8 because 23 minus 15 equals 8. - 11
A data set has minimum 7, first quartile 10, median 13, third quartile 19, and maximum 24. Draw conclusions about whether the data are more spread out above or below the median.
Compare the distances on each side of the median.
The data are more spread out above the median because the distance from the median to the maximum is 11, while the distance from the minimum to the median is 6. The upper half also includes a wider quartile from 13 to 19 than the lower quartile from 10 to 13. - 12
The ordered data set is 5, 6, 8, 9, 10, 11, 14, 15, 18, 20. Find the first quartile, median, third quartile, and interquartile range.
The first quartile is 8, the median is 10.5, the third quartile is 15, and the interquartile range is 7. The lower half is 5, 6, 8, 9, 10 with median 8, and the upper half is 11, 14, 15, 18, 20 with median 15. - 13
A box plot for daily temperatures shows minimum 60, first quartile 65, median 70, third quartile 80, and maximum 90. Explain what the box part of the plot represents.
The ends of the box are the first and third quartiles.
The box represents the middle 50 percent of the data. In this example, it shows that the middle half of the temperatures are between 65 and 80. - 14
A student says, "If two box plots have the same median, then the data sets have the same spread." Is the student correct? Explain.
The student is not correct. Two data sets can have the same median but different ranges or different interquartile ranges, so their spreads can still be different. - 15
A set of running times has five-number summary 18, 22, 25, 31, 40. Write two true statements about this data set.
Use the minimum, quartiles, median, and maximum to describe the data.
One true statement is that the median running time is 25. Another true statement is that the middle 50 percent of the times are between 22 and 31. It is also true that the range is 22.