A-LevelMathematicsProbability and statistics9709/61 · May/June 2019 · Q14 Marks
The times, t seconds, taken to swim 100m were recorded for a group of 9 swimmers and were found to be as follows. 95 126 117 135 120 125 114 119 136
- (i)Find the values of ∑(t – 120) and ∑(t − 120)2.[2]
- (ii)Using your values found in part (i), calculate the variance of t.[2]
Mark scheme
Marking points from the official mark scheme (May/June 2019). The mark or mark type is shown in brackets.
- [2] Σ(t − 120) = −25 + 6 - 3 + 15 + 0 + 5 - 6 - 1+ 16 = 7. Attempt to sum both (t – 120) and (t – 120)² Correct ans using Σt − 9 × 120 and ∑ (t − 120)² M1A1. Σ(t − 120)² = 25² + 6² + 3² + 15² + 0² + 5² + 6² + 1² + 16² = 1213. Both correct, www, SC correct ans no working B1B1
- [2] Var = (Σ(t − 120)²) / 9 - (Σ(t − 120) / 9)² = their 1213 / 9 - (their 7 / 9)². Using two coded values in correct formula including finding Σt from 7 etc. = 134(.2). Correct answer SC if correct variance obtained by another method from raw data give SCB1
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