OCR S1 2012 June — Question 2 6 marks

Exam BoardOCR
ModuleS1 (Statistics 1)
Year2012
SessionJune
Marks6
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Mark schemeDownload PDF ↗
TopicMeasures of Location and Spread
TypeCalculate variance/SD from coded sums
DifficultyEasy -1.2 This is a straightforward application of standard formulas for converting coded sums back to mean and variance. It requires only direct substitution into well-practiced formulas (mean = 1.5 + 1.4/50, variance from the coded variance formula) with minimal calculation steps. This is easier than average as it's purely procedural with no problem-solving or conceptual challenge.
Spec2.02g Calculate mean and standard deviation
2 The masses, \(x \mathrm {~kg}\), of 50 bags of flour were measured and the results were summarised as follows. $$n = 50 \quad \Sigma ( x - 1.5 ) = 1.4 \quad \Sigma ( x - 1.5 ) ^ { 2 } = 0.05$$ Calculate the mean and standard deviation of the masses of these bags of flour.
Question 2:
AnswerMarks Guidance
AnswerMarks Guidance
\(\frac{1.4}{50}\) \((= 0.028)\)M1 \(1.4 + 50 \times 1.5\) \((= 76.4)\)
\(1.5 + \frac{1.4}{50}\)M1 dep M1 \(\frac{76.4}{50}\). eg \(\frac{1.4+1.5}{50}\) M0M0A0
\(= 1.528\) or \(\frac{191}{125}\) or 1.53 (3 sf)A1 \((\Sigma x^2 - 2 \times 1.5 \times 76.4 + 50 \times 1.5^2 = 0.05)\) \((\Rightarrow \Sigma x^2 = 116.75\); no marks yet)
\(\frac{0.05}{50} - \left(\frac{1.4}{50}\right)^2\) or 0.000216 seenM1 \(\frac{0.05 + 2\times1.5\times76.4 - 50\times1.5^2}{50} - 1.528^2\) all correct. Not \(\frac{0.05}{50} - 1.528^2\)
\(\sqrt{0.000216}\)M1 Fully correct method, ie nothing added etc
\(= 0.0147\) (3 sf)A1 cao not isw 
## Question 2:

| Answer | Marks | Guidance |
|--------|-------|----------|
| $\frac{1.4}{50}$ $(= 0.028)$ | M1 | $1.4 + 50 \times 1.5$ $(= 76.4)$ |
| $1.5 + \frac{1.4}{50}$ | M1 dep M1 | $\frac{76.4}{50}$. eg $\frac{1.4+1.5}{50}$ M0M0A0 |
| $= 1.528$ or $\frac{191}{125}$ or 1.53 (3 sf) | A1 | $(\Sigma x^2 - 2 \times 1.5 \times 76.4 + 50 \times 1.5^2 = 0.05)$ $(\Rightarrow \Sigma x^2 = 116.75$; no marks yet) |
| $\frac{0.05}{50} - \left(\frac{1.4}{50}\right)^2$ or 0.000216 seen | M1 | $\frac{0.05 + 2\times1.5\times76.4 - 50\times1.5^2}{50} - 1.528^2$ all correct. Not $\frac{0.05}{50} - 1.528^2$ |
| $\sqrt{0.000216}$ | M1 | Fully correct method, ie nothing added etc |
| $= 0.0147$ (3 sf) | A1 | cao not isw |

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2 The masses, $x \mathrm {~kg}$, of 50 bags of flour were measured and the results were summarised as follows.

$$n = 50 \quad \Sigma ( x - 1.5 ) = 1.4 \quad \Sigma ( x - 1.5 ) ^ { 2 } = 0.05$$

Calculate the mean and standard deviation of the masses of these bags of flour.

\hfill \mbox{\textit{OCR S1 2012 Q2 [6]}}
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