CAIE S1 2015 November — Question 1 3 marks

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2015
SessionNovember
Marks3
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Mark schemeDownload PDF ↗
TopicMeasures of Location and Spread
TypeCalculate mean from coded sums
DifficultyEasy -1.2 This is a straightforward algebraic manipulation question involving coded data. Students need to expand Σ(x-100) = Σx - 100n and solve for n using the given values. It requires only basic understanding of summation notation and one-step algebra, making it easier than average A-level content.
Spec2.02f Measures of average and spread
1 For \(n\) values of the variable \(x\), it is given that \(\Sigma ( x - 100 ) = 216\) and \(\Sigma x = 2416\). Find the value of \(n\).
Question 1:
AnswerMarks Guidance
Answer/WorkingMarks Guidance
\(\Sigma x - 100n = 216\)B1 \(\Sigma x - 100n\) seen
\(2416 - 100n = 216\)B1 Subst 2416 for their \(\Sigma x\)
\(n = 22\)B1 (3) Correct answer
OR: \(\frac{2416}{n} = \frac{216}{n} + 100\)B1 \(2416/n\) seen or \(216/n + 100\) oe, e.g. \(\Sigma x/n - 100 = 216/n\)
correct equationB1 Correct equation
\(n = 22\)B1 Correct answer 
## Question 1:

| Answer/Working | Marks | Guidance |
|---|---|---|
| $\Sigma x - 100n = 216$ | B1 | $\Sigma x - 100n$ seen |
| $2416 - 100n = 216$ | B1 | Subst 2416 for their $\Sigma x$ |
| $n = 22$ | B1 (3) | Correct answer |
| OR: $\frac{2416}{n} = \frac{216}{n} + 100$ | B1 | $2416/n$ seen or $216/n + 100$ oe, e.g. $\Sigma x/n - 100 = 216/n$ |
| correct equation | B1 | Correct equation |
| $n = 22$ | B1 | Correct answer |

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1 For $n$ values of the variable $x$, it is given that $\Sigma ( x - 100 ) = 216$ and $\Sigma x = 2416$. Find the value of $n$.

\hfill \mbox{\textit{CAIE S1 2015 Q1 [3]}}
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Q1 3 Q2 3 Q3 6 Q4 7 Q5 9 Q6 9 Q7 13