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.
15 questions · official format, shuffled order
1 Find the interquartile range of these nine values. (With an odd count, leave the median out of both halves.)
Show worked solution
Median 14. Lower half 4, 7, 9, 11 gives Q1 = 8; upper half 17, 20, 23, 31 gives Q3 = 21.5. IQR = 13.5. (27 is the range.)
2 A data set has Q1 = 16 and Q3 = 28. Using the rule "more than 1.5 × IQR above Q3", which is the smallest whole number that would be an outlier at the top end?
Show worked solution
The fence is 28 + 18 = 46, so the smallest whole-number outlier is 47. (40 adds one IQR instead of 1.5 IQRs.)
3 Six numbers have a mean of 15. One of them, 21, is removed. What is the mean of the other five?
Show worked solution
90 − 21 = 69, and 69 ÷ 5 = 13.8.
4 The data 4, 7, 9, 10, 15 was typed in wrongly: the 15 should have been 55. What is the correct mean?
Show worked solution
Old total 45; new total 85; mean 17. (9 is the old mean — and the median, which does not change at all.)
5 y varies directly as x2, and y = 20 when x = 2. What is y when x = 5?
Show worked solution
20 = 4k, so k = 5 and y = 5 × 25 = 125. (50 treats it as y varying directly as x.)
6 Four identical machines finish a job in 15 hours. How many machines are needed to finish it in 6 hours?
Show worked solution
The job is 4 × 15 = 60 machine-hours, and 60 ÷ 6 = 10.
7 A car trip goes like this. What was the average speed for the whole 3 hours?
Show worked solution
100 km ÷ 3 h = 33⅓ km/h. (40 km/h divides by the 2.5 hours of moving time, leaving out the stop.)
8 y varies inversely as x. Find the missing value of x.
Show worked solution
xy = 60 each time, so x = 60 ÷ 6 = 10. (9 continues the table as if the x-values went up evenly.)
9 Which statement about these two box plots is correct?
Show worked solution
Medians 20 and 24; IQRs 13 and 8; ranges 25 and 28. So B has the larger median and the smaller interquartile range.
10 Find the interquartile range from this stem-and-leaf plot (2 | 3 means 23).
Show worked solution
Values 23, 25, 28, 30, 34, 34, 37, 41, 46. Q1 = 26.5 and Q3 = 39, so IQR = 12.5. (23 is the range.)
11 1 If y varies directly as x and x doubles, y doubles.
2 If y varies inversely as x and x doubles, y halves.
3 If y varies directly as x2 and x triples, y triples.
Which statements are correct?
2 If y varies inversely as x and x doubles, y halves.
3 If y varies directly as x2 and x triples, y triples.
Which statements are correct?
Show worked solution
y = kx doubles with x (1 ✓); y = k/x halves (2 ✓); y = kx2 goes up 32 = 9 times, not 3 (3 ✗). 1 and 2.
12 Ana and Ben walk the same 18 km path (x = time in hours, y = distance in km). Ana leaves at time 0 and arrives after 6 hours. Ben leaves 1 hour later and arrives at the 4-hour mark. How much faster is Ben, in km/h?
Show worked solution
Ana 18 ÷ 6 = 3 km/h; Ben 18 ÷ 3 = 6 km/h. Ben is 3 km/h faster. (6 is Ben’s speed, not the difference; 4.5 would come from using Ben’s 4-hour finishing time as his walking time.)
13 Ten students scored as shown. What is the mean score?
Show worked solution
(3 + 10 + 6) ÷ 10 = 1.9. (2 is the median and the mode.)
14 Class P has 20 students with a mean mark of 70. Class Q has 30 students with a mean mark of 80. What is the mean mark of all 50 students?
Show worked solution
(20 × 70 + 30 × 80) ÷ 50 = 3800 ÷ 50 = 76. (75 averages the two means.)
15 Look at the data 2, 3, 3, 4, 5, 6, 30.
1 The median is 4.
2 30 is an outlier by the 1.5 × IQR rule.
3 Removing 30 changes the median more than it changes the mean.
Which statements are correct?
1 The median is 4.
2 30 is an outlier by the 1.5 × IQR rule.
3 Removing 30 changes the median more than it changes the mean.
Which statements are correct?
Show worked solution
The middle value is 4 (1 ✓). IQR = 3, fence 6 + 4.5 = 10.5, and 30 is far above it (2 ✓). The mean falls from about 7.6 to about 3.8, the median only from 4 to 3.5 (3 ✗). 1 and 2.