Work through the levels in order. Type your answer and press Check — open the worked solution if you get stuck. Answers like -6, 3/4 or 0.25 are typed exactly as shown. A ⭐ Bonus Challenge at the end is extra credit — skip it if the rest was hard work.
Level 1 · Warm-up
1 Which is the five-number summary of 14, 9, 21, 6, 17, 11, 25?
Show worked solution
In order: 6, 9, 11, 14, 17, 21, 25. Median 14; lower half 6, 9, 11 gives Q1 = 9; upper half 17, 21, 25 gives Q3 = 21. Summary: 6, 9, 14, 21, 25. 6, 10, 14, 19, 25 puts the median into both halves; 6, 11, 14, 17, 25 takes the values next to the median as quartiles; 9, 11, 14, 17, 21 drops the min and max.
2 Find Q1, Q3 and the interquartile range of these 12 values.
Show worked solution
In order: 3, 5, 6, 8, 10, 11 | 13, 14, 16, 19, 20, 24. Q1 = (6 + 8) ÷ 2 = 7; Q3 = (16 + 19) ÷ 2 = 17.5; IQR = 17.5 − 7 = 10.5.
3 The box plot shows the scores of 60 students in a test. About how many students scored from 31 to 47?
Show worked solution
31 is Q1 and 47 is Q3, so the box holds about 50% of the scores. 50% of 60 = 30.
Level 2 · Core
4 Which statement about this data set must be true?
Show worked solution
15 is Q1 and 35 is Q3, so About half of the values lie between 15 and 35. Each whisker holds about 25%, whatever its length; 20 is the median, so only about 50% lie below it; and a box plot shows the median, not the mean.
5 For the data 6, 23, 25, 26, 28, 30, 31, 33, 35, 52, find the fences for the outlier rule.
Show worked solution
Halves 6, 23, 25, 26, 28 and 30, 31, 33, 35, 52 give Q1 = 25 and Q3 = 33. IQR = 8 and 1.5 × 8 = 12. Fences: 25 − 12 = 13 and 33 + 12 = 45, so 6 and 52 are outliers.
6 A large data set has the five-number summary 4, 12, 17, 20, 29. Its maximum is raised but nothing else changes. What is the smallest whole number the maximum could be raised to so that it becomes an outlier?
Show worked solution
IQR = 20 − 12 = 8 and 1.5 × 8 = 12, so the upper fence is 20 + 12 = 32. An outlier must be more than 32, so the smallest whole number is 33. (32 itself is on the fence, not beyond it.)
Level 3 · Challenge
7 Three statements about the data 2, 5, 7, 8, 9, 12, 14, 15, 30:
1 The interquartile range is 8.5.
2 The value 30 is an outlier.
3 If the 30 were changed to 16, the interquartile range would change.
Which statements are correct?
1 The interquartile range is 8.5.
2 The value 30 is an outlier.
3 If the 30 were changed to 16, the interquartile range would change.
Which statements are correct?
Show worked solution
Median 9; halves 2, 5, 7, 8 and 12, 14, 15, 30 give Q1 = 6 and Q3 = 14.5, so IQR = 8.5 (1 ✓). Upper fence = 14.5 + 1.5 × 8.5 = 14.5 + 12.75 = 27.25, and 30 is above it (2 ✓). With 16 instead of 30 the upper half is 12, 14, 15, 16, and Q3 is still 14.5, so the IQR does not change (3 ✗). 1 and 2.
8 Eight values in order are 2, 4, a, 9, 11, 13, b, 21. Their lower quartile is 5 and their upper quartile is 16. Find a and b.
Show worked solution
Q1 = (4 + a) ÷ 2 = 5, so a = 6. Q3 = (13 + b) ÷ 2 = 16, so b = 19. Both keep the list in order: 4 ≤ 6 ≤ 9 and 13 ≤ 19 ≤ 21.
9 A data set has median 30 and interquartile range 10. Its upper quartile is 4 more than its median. Below what value is a data point an outlier?
Show worked solution
Q3 = 30 + 4 = 34, so Q1 = 34 − 10 = 24. 1.5 × 10 = 15, so the lower fence is 24 − 15 = 9.