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 The box plots compare goals scored per season by two teams. Which statement is correct?
Show worked solution
Medians: R 15, S 18, so S is higher. IQRs: R 21 − 12 = 9, S 20 − 14 = 6, so S is smaller. Ranges: R 17, S 20, not equal. S has the higher median and the smaller IQR. "The larger IQR" compares the ranges or the whisker lengths instead.
2 Reaction times (hundredths of a second) before and after training. Find the median of each set.
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Before (7 values): 12, 15, 21, 24, 26, 33, 38, so the median is the 4th, 24. After (9 values): 18, 22, 27, 29, 31, 35, 36, 41, 44, so the median is the 5th, 31.
3 Five scores have a mean of 14. One score, 22, is removed. What is the mean of the other four scores?
Show worked solution
Total = 5 × 14 = 70. Without 22: 70 − 22 = 48. Mean = 48 ÷ 4 = 12.
Level 2 · Core
4 For the data 3, 4, 4, 5, 6, 7, 41, which measure of centre describes the data best, and what is its value?
Show worked solution
The mean is 70 ÷ 7 = 10, larger than six of the seven values, because the outlier 41 drags it up. The median is the 4th value, 5. So median, 5. 4 is the mode, not the median.
5 The mean of 7 numbers is 9. Find their total, and the eighth number that would make the mean of all 8 equal to 10.
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Total = 7 × 9 = 63. New total needed = 8 × 10 = 80, so the eighth number is 80 − 63 = 17.
6 Group P has 80 students. About how many students in P scored more than the median of group Q?
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Q’s median is 35, which is P’s lower quartile. About 75% of P is above Q1, and 75% of 80 = 60.
Level 3 · Challenge
7 Three statements about L and R:
1 R has the higher median.
2 The range of L is larger than the IQR of R.
3 R has the smaller IQR.
Which statements are correct?
1 R has the higher median.
2 The range of L is larger than the IQR of R.
3 R has the smaller IQR.
Which statements are correct?
Show worked solution
L: 15, 22, 26, 28, 31, 34, 39, so median 28, Q1 22, Q3 34, IQR 12, range 24. R: 18, 19, 24, 30, 35, 41, 47, so median 30, Q1 19, Q3 41, IQR 22. 30 > 28 (1 ✓). 24 > 22 (2 ✓). R’s IQR, 22, is larger than L’s, 12 (3 ✗). 1 and 2.
8 Five numbers have a mean of 12 and a median of 10. The largest number, 25, is changed to 40. Find the new mean and the new median.
Show worked solution
The total rises by 40 − 25 = 15, from 60 to 75, so the new mean is 75 ÷ 5 = 15. The largest value stays the largest, so the middle value does not change: the median is still 10.
9 Ten students have a mean mark of 64. Two more students join, and the mean of all twelve becomes 66. What is the mean mark of the two new students?
Show worked solution
Old total = 10 × 64 = 640. New total = 12 × 66 = 792. The two new marks total 792 − 640 = 152, so their mean is 152 ÷ 2 = 76.