∑ DANEMATHICS
FREE CAPS MATHS RESOURCES
Grade 8–9 · Data Handling
Mean, Median, Mode and Range: Complete Guide
MEMORANDUM
Name:
Class:
Date:
Mark
/ 29
Answer all questions. Show all your working — marks are awarded for method as well as the final answer. Teacher copy: accept any correct equivalent method.
- 1The mean of 7, 11, 9, 13 and x is 11. Solve for x.(3)(7 + 11 + 9 + 13 + x)/5 = 11 (1)
40 + x = 55 (1)
x = 15 (1)✓✓✓ (3) - 2The mean of 14, 22, 18 and x is 20. Solve for x.(3)(14 + 22 + 18 + x)/4 = 20 (1)
54 + x = 20 × 4 = 80 (1)
x = 80 − 54 = 26 (1)✓✓✓ (3) - 3The mean of 8, 10, 15, 9 and x is 12. Solve for x.(3)(8 + 10 + 15 + 9 + x)/5 = 12 (1)
42 + x = 12 × 5 = 60 (1)
x = 60 − 42 = 18 (1)✓✓✓ (3) - 4Find the mean of 3, 5, 10, 2 (mean)(2)20 ÷ 4 = 5✓✓ (2)
- 5Find the mean of 12, 15, 18, 15 (mean)(2)60 ÷ 4 = 15✓✓ (2)
- 6Find the median of 8 ; 3 ; 9 ; 5 ; 6 (median, odd)(1)Order: 3 ; 5 ; 6 ; 8 ; 9 → 6✓ (1)
- 7Find the median of 4 ; 10 ; 6 ; 8 (median, even)(2)Order: 4 ; 6 ; 8 ; 10 → (6 + 8) ÷ 2 = 7✓✓ (2)
- 8Find the mode of 2, 4, 4, 4, 7, 9 (mode)(1)4 (appears three times)✓ (1)
- 9Find the range of 15, 22, 9, 30 (range)(1)30 − 9 = 21✓ (1)
- 10The mean of 4, 8, x, 6 is 7. Find x. (missing value)(3)Total 7 × 4 = 28; 28 − 18 = 10✓✓✓ (3)
- 11The mean of 5 numbers is 12. What is their total? (work back)(2)12 × 5 = 60✓✓ (2)
- 12Data: 6, 6, 7, 8, 40. Which is more typical, mean or median? (outlier)(2)Mean 13,4 vs median 7 → median (40 is an outlier)✓✓ (2)
- 13Find all four (mean, median, mode, range) for 2, 3, 3, 6 (all four)(4)Mean 14 ÷ 4 = 3,5; median (3 + 3) ÷ 2 = 3; mode 3; range 6 − 2 = 4✓✓✓✓ (4)
TOTAL: 29 marks