OCR S1 2010 June — Question 6 6 marks

Exam BoardOCR
ModuleS1 (Statistics 1)
Year2010
SessionJune
Marks6
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Mark schemeDownload PDF ↗
TopicMeasures of Location and Spread
TypeAdding data values
DifficultyModerate -0.8 This is a straightforward application of standard formulas for updating mean and variance when adding a data point. It requires recall of the variance formula and careful arithmetic, but involves no problem-solving insight or conceptual difficulty—simpler than the average A-level question which typically demands more integrated reasoning.
Spec5.02b Expectation and variance: discrete random variables
There are 10 numbers in a list. The first 9 numbers have mean 6 and variance 2. The 10th number is 3. Find the mean and variance of all 10 numbers. [6]
AnswerMarks Guidance
Answer/Working: \(m = (9×6+3)÷10\) = 5.7M1, A1 or ((Sum of any 9 nos totalling 54) + 3) ÷ 10
\(\Sigma x^2\) = \(\frac{\Sigma x^2}{9}-6^2\)M1 or \(\frac{\Sigma(x-6)^2}{9}\) = 2 M1
\(\Sigma x^2 = 2×9 + 6^2×9\) or 342A1 or \(\Sigma x^2 = 18 + 12×54 -36×9\) or 342 A1
\(v = \frac{(342+3^2)}{10}-5.7^2\)M1 dep \(\Sigma x^2\) attempted, eg \((\Sigma x)^2\) (= 3249) or just state "\(\Sigma x^2\)"; allow \(\sqrt{}\)
= 2.61 oeA1 6 CAO
Total: 6 marks
**Answer/Working:** $m = (9×6+3)÷10$ = 5.7 | **M1, A1** | or ((Sum of any 9 nos totalling 54) + 3) ÷ 10

$\Sigma x^2$ = $\frac{\Sigma x^2}{9}-6^2$ | **M1** | or $\frac{\Sigma(x-6)^2}{9}$ = 2 M1

$\Sigma x^2 = 2×9 + 6^2×9$ or 342 | **A1** | or $\Sigma x^2 = 18 + 12×54 -36×9$ or 342 A1

$v = \frac{(342+3^2)}{10}-5.7^2$ | **M1** | dep $\Sigma x^2$ attempted, eg $(\Sigma x)^2$ (= 3249) or just state "$\Sigma x^2$"; allow $\sqrt{}$

= 2.61 oe | **A1 6** | CAO

**Total: 6 marks**

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There are 10 numbers in a list. The first 9 numbers have mean 6 and variance 2. The 10th number is 3. Find the mean and variance of all 10 numbers. [6]

\hfill \mbox{\textit{OCR S1 2010 Q6 [6]}}
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Q1 9 Q2 7 Q3 10 Q4 8 Q5 12 Q6 6 Q7 8 Q8 12