Quartiles and box plots: practice problems
Quartiles split sorted data into four parts. Box plots make it easy to compare how spread out data sets are.
Basic, Standard, Advanced: Grade 8 · Term 3
Math problem generator
Finding quartiles
Sort the data and find the median (Q2). Split the data into a lower and an upper half (leave out the median when the number of values is odd). The median of the lower half is Q1 and the median of the upper half is Q3.
For : Q2 = 7, Q1 = 4, Q3 = 10.
Range and interquartile range
The interquartile range describes the spread of the middle half of the data and is not affected much by extreme values.
Reading box plots
The box runs from Q1 to Q3 with a line at the median; the whiskers reach the minimum and maximum. About half the data lie inside the box. A box plot does not show the mean or the individual values.
Worked examples
The data below are the handball throw distances of 9 students (in metres). Find the five values needed to draw a box plot.
Hint
Find the minimum, Q1, median, Q3 and maximum (the five-number summary).
Answer
- minimum
- Q1
- median
- Q3
- maximum
Solution
In increasing order:
The five values are
The data below are the quiz scores of 11 students in a group (in points). Which of the box plots (1)–(3) shows these data? Answer with the number.
Hint
Find the minimum, quartiles, median and maximum and compare with the plots.
Answer
Solution
In increasing order:
The five values are
The matching plot is
The box plots show the maths test scores (out of 100) of class A and class B (30 students each). Which statement is correct?
- AIn class A, at least 15 students scored 55 or more.
- BClass A has the larger range.
- CClass B has the larger median.
- DClass A has the larger interquartile range.
Hint
With 30 students the median is the mean of the 15th and 16th scores, so at least half the students score at or above the median.
Answer
Solution
Class A:
Class B:
Ranges: A 65, B 80. IQRs: A 20, B 35. So the correct statement is: "In class A, at least 15 students scored 55 or more."
Practice problems
The data below are the quiz scores of 7 students in a group (in points). Find the range and the interquartile range.
Hint
Range = max − min; interquartile range = Q3 − Q1.
Answer
- range
- interquartile range
Solution
In increasing order:
Range:
Quartiles:
Interquartile range:
The data below are the quiz scores of 11 students in a group (in points). Which of the box plots (1)–(3) shows these data? Answer with the number.
Hint
Find the minimum, quartiles, median and maximum and compare with the plots.
Answer
Solution
In increasing order:
The five values are
The matching plot is
The third quartile of the 8 values below is 20.5. Find the integer .
Hint
With 8 values, Q3 is the mean of the 6th and 7th values in order.
Answer
Solution
The other 7 values in order:
The quartile is the mean of the 6th and 7th values; consider where fits in the order.
The only integer that works is