CAIE S1 2007 June — Question 1 4 marks

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2007
SessionJune
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicMeasures of Location and Spread
TypeCalculate variance/SD from coded sums
DifficultyEasy -1.2 This is a straightforward application of the coded data formulas for mean and standard deviation. Students need to recall that mean = 35 + (-15)/12 and use the variance formula with coded sums, requiring only direct substitution into standard formulas with no problem-solving or conceptual insight.
Spec2.02g Calculate mean and standard deviation

1 The length of time, \(t\) minutes, taken to do the crossword in a certain newspaper was observed on 12 occasions. The results are summarised below. $$\Sigma ( t - 35 ) = - 15 \quad \Sigma ( t - 35 ) ^ { 2 } = 82.23$$ Calculate the mean and standard deviation of these times taken to do the crossword.

Question 1:
AnswerMarks Guidance
Answer/WorkingMark Guidance
mean \(= 35 - \frac{15}{12}\)M1 For \(-\frac{15}{12}\) seen
\(= 33.75\) (33.8) minutesA1 Correct answer
\(sd = \sqrt{82.23/12 - (-15/12)^2}\)M1 \(82.23/12 - (\pm \text{ their coded mean})^2\)
\(= 2.3\) minutesA1 4 Correct answer
## Question 1:

| Answer/Working | Mark | Guidance |
|---|---|---|
| mean $= 35 - \frac{15}{12}$ | M1 | For $-\frac{15}{12}$ seen |
| $= 33.75$ (33.8) minutes | A1 | Correct answer |
| $sd = \sqrt{82.23/12 - (-15/12)^2}$ | M1 | $82.23/12 - (\pm \text{ their coded mean})^2$ |
| $= 2.3$ minutes | A1 **4** | Correct answer |

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1 The length of time, $t$ minutes, taken to do the crossword in a certain newspaper was observed on 12 occasions. The results are summarised below.

$$\Sigma ( t - 35 ) = - 15 \quad \Sigma ( t - 35 ) ^ { 2 } = 82.23$$

Calculate the mean and standard deviation of these times taken to do the crossword.

\hfill \mbox{\textit{CAIE S1 2007 Q1 [4]}}