OCR S2 2016 June — Question 1 4 marks

Exam BoardOCR
ModuleS2 (Statistics 2)
Year2016
SessionJune
Marks4
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Mark schemeDownload PDF ↗
TopicMeasures of Location and Spread
TypeStandard unbiased estimates calculation
DifficultyEasy -1.2 This is a straightforward application of standard formulas for unbiased estimates of mean and variance. It requires only direct substitution into memorized formulas (mean = Σv/n, variance = Σv²/(n-1) - n(mean)²/(n-1)) with no problem-solving, conceptual understanding, or multi-step reasoning required.
Spec5.05b Unbiased estimates: of population mean and variance
The results of 14 observations of a random variable \(V\) are summarised by $$n = 14, \quad \sum v = 3752, \quad \sum v^2 = 1007448.$$ Calculate unbiased estimates of E\((V)\) and Var\((V)\). [4]
AnswerMarks Guidance
\(\mu = \bar{x} = \frac{3752}{14} = 268\)B1 268 only, must be stated separately, not isw
\(\frac{1007448}{14}x^2 = [=136.57...]\)M1 If single formula used, give M1 for divisor 13 anywhere
\(\times \frac{14}{13}\)M1 Multiply by 14/13
\(= 147(07\ldots)\)A1 Answer, a.r.t. 147, or \(\frac{1012}{6} = 147\frac{1}{6}\) (4 marks) 
$\mu = \bar{x} = \frac{3752}{14} = 268$ | B1 | 268 only, must be stated separately, not isw

$\frac{1007448}{14}x^2 = [=136.57...]$ | M1 | If single formula used, give M1 for divisor 13 anywhere

$\times \frac{14}{13}$ | M1 | Multiply by 14/13

$= 147(07\ldots)$ | A1 | Answer, a.r.t. 147, or $\frac{1012}{6} = 147\frac{1}{6}$ (4 marks) | MR 3572: 255.14, 7390.6 gets B0M1M1A1
The results of 14 observations of a random variable $V$ are summarised by
$$n = 14, \quad \sum v = 3752, \quad \sum v^2 = 1007448.$$
Calculate unbiased estimates of E$(V)$ and Var$(V)$. [4]

\hfill \mbox{\textit{OCR S2 2016 Q1 [4]}}
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