Easy -1.2 This is a straightforward application of coding formulas for sums. Students need to apply the linear transformation properties: Σ(x-10) = Σx - 10n and Σ(x-10)² can be found using the variance formula. It requires recall of standard results and basic algebraic manipulation, but no problem-solving insight or complex multi-step reasoning.
1 In a statistics lesson 12 people were asked to think of a number, \(x\), between 1 and 20 inclusive. From the results Tom found that \(\Sigma x = 186\) and that the standard deviation of \(x\) is 4.5. Assuming that Tom's calculations are correct, find the values of \(\Sigma ( x - 10 )\) and \(\Sigma ( x - 10 ) ^ { 2 }\).
Consistent substituting in the correct coded variance formula OR valid method for \(\Sigma x^2\) then expanding \(\Sigma(x-10)^2\), 3 terms with at least 2 correct
\(\Sigma(x-10)^2 = 606\)
B1
Correct answer
Total: 3
## Question 1:
| Answer | Marks | Guidance |
|--------|-------|----------|
| $\Sigma(x-10) = 186 - 12 \times 10 = 66$ | **B1** | Correct answer |
| $\frac{\Sigma(x-10)^2}{12} - \left(\frac{\Sigma(x-10)}{12}\right)^2 = 4.5^2$ | **M1** | Consistent substituting in the correct coded variance formula OR valid method for $\Sigma x^2$ then expanding $\Sigma(x-10)^2$, 3 terms with at least 2 correct |
| $\Sigma(x-10)^2 = 606$ | **B1** | Correct answer |
| | **Total: 3** | |
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1 In a statistics lesson 12 people were asked to think of a number, $x$, between 1 and 20 inclusive. From the results Tom found that $\Sigma x = 186$ and that the standard deviation of $x$ is 4.5. Assuming that Tom's calculations are correct, find the values of $\Sigma ( x - 10 )$ and $\Sigma ( x - 10 ) ^ { 2 }$.\\
\hfill \mbox{\textit{CAIE S1 2018 Q1 [3]}}