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Quartiles and box plots
Dynamic tasks on medians, quartiles, interquartile range, outliers and reading box-and-whisker plots.
Questions: 10Estimated time: 18 minutes
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Question 1out of 10
For data with Q1 = 9 and Q3 = 16, using the 1.5·IQR rule, is 28 an upper outlier?
First calculate IQR = Q3 − Q1. The upper outlier fence is Q3 + 1.5 × IQR. A value is an upper outlier if it is strictly greater than this fence.
Question 2out of 10
Find the first quartile Q1: 7, 9, 11, 13, 16, 19, 22, 25.
Sort the data. Q2 is the overall median; Q1 is the median of the lower half and Q3 the median of the upper half. In these tasks, an even-length list is split into two equal halves; the median of an even-sized group is the average of its two middle values.
Question 3out of 10
What median is shown in the box plot?
In a box plot, the median is the line inside the box. Read its position on the number scale. The box edges mark Q1 and Q3 rather than the median.
Question 4out of 10
Find the second quartile Q2: 18, 12, 10, 16, 23, 14, 20.
Sort the data. Q2 is the overall median; Q1 is the median of the lower half and Q3 the median of the upper half. In these tasks, an even-length list is split into two equal halves; the median of an even-sized group is the average of its two middle values.
Question 5out of 10
Approximately what percentage of data lies between the first and third quartiles?
Interquartile range IQR = Q3 − Q1. It describes the spread of the middle approximately 50% of the data. A greater IQR means greater spread in this middle portion.
Question 6out of 10
The first quartile is 19 and the third is 30. Find the interquartile range.
Interquartile range IQR = Q3 − Q1. It describes the spread of the middle approximately 50% of the data. A greater IQR means greater spread in this middle portion.
Question 7out of 10
Find the third quartile Q3: 9, 11, 13, 15, 17, 19, 21, 23.
Sort the data. Q2 is the overall median; Q1 is the median of the lower half and Q3 the median of the upper half. In these tasks, an even-length list is split into two equal halves; the median of an even-sized group is the average of its two middle values.
Question 8out of 10
Find the second quartile Q2: 25, 16, 14, 20, 22, 12, 18.
Sort the data. Q2 is the overall median; Q1 is the median of the lower half and Q3 the median of the upper half. In these tasks, an even-length list is split into two equal halves; the median of an even-sized group is the average of its two middle values.
Question 9out of 10
For data with Q1 = 5 and Q3 = 9, using the 1.5·IQR rule, is 17 an upper outlier?
First calculate IQR = Q3 − Q1. The upper outlier fence is Q3 + 1.5 × IQR. A value is an upper outlier if it is strictly greater than this fence.
Question 10out of 10
Set A has interquartile range 6, and set B has 10. Which set has more spread in its middle 50%?
Interquartile range IQR = Q3 − Q1. It describes the spread of the middle approximately 50% of the data. A greater IQR means greater spread in this middle portion.
Time left: 00:00:00
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Sample questions
- Find the second quartile Q2: ___.
- Find the first quartile Q1: ___.
- Find the third quartile Q3: ___.
- The first quartile is ___ and the third is ___. Find the interquartile range.
- For data with Q1 = ___ and Q3 = ___, using the 1.5·IQR rule, is ___ an upper outlier?
Quartiles and box plots
For ordered data, the median Q2 divides the values into two parts, while Q1 and Q3 divide them into quarters. The interquartile range IQR = Q3 − Q1 measures the spread of the middle 50% and is less sensitive to extreme values than the full range.
Plots and outliers
A box plot displays the minimum, Q1, median, Q3 and maximum, with outliers shown separately under the chosen convention. A common outlier rule is below Q1 − 1.5IQR or above Q3 + 1.5IQR. Compare both centre and spread when interpreting groups.
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