A-LevelMathematicsProbability and statistics9709/63 · Oct/Nov 2017 · Q23 Marks
Tien measured the arm lengths, x cm, of 20 people in his class. He found that Σx = 1218 and the standard deviation of x was 4.2. Calculate Σ(x – 45) and Σ(x – 45)².
- Tien measured the arm lengths, x cm, of 20 people in his class. He found that Σx = 1218 and the standard deviation of x was 4.2. Calculate Σ(x – 45) and Σ(x – 45)². [3]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2017). The mark or mark type is shown in brackets.
- [B1] Σ(x – 45) = 1218 – 20 × 45 = 318
- [M1] Fully correct substitution in the correct coded variance formula with their Σ(x – 45)
- [M1] OR valid method for Σx² = 74 529 (4.2² = Σx²/20 – (1218/20)²) and expanding Σ(x−45)² correctly = Σx² – 902x + 20×45² = '74 529'–90×1218+ 40 500 = 5409
- [A1] Σ(x – 45)² = 5409
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