CAIE S1 2010 November — Question 4 6 marks

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2010
SessionNovember
Marks6
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicMeasures of Location and Spread
TypeFind coded sums from raw data
DifficultyEasy -1.2 This is a straightforward application of coding formulas for mean and variance. Part (i) requires simple algebraic manipulation of Σ(x-60) to find the mean. Parts (ii) and (iii) use standard results about how sums change under linear transformations. All steps are routine recall with minimal problem-solving, making this easier than average.
Spec2.02g Calculate mean and standard deviation

4 Delip measured the speeds, \(x \mathrm {~km}\) per hour, of 70 cars on a road where the speed limit is 60 km per hour. His results are summarised by \(\Sigma ( x - 60 ) = 245\).
  1. Calculate the mean speed of these 70 cars. His friend Sachim used values of \(( x - 50 )\) to calculate the mean.
  2. Find \(\Sigma ( x - 50 )\).
  3. The standard deviation of the speeds is 10.6 km per hour. Calculate \(\Sigma ( x - 50 ) ^ { 2 }\).

4 Delip measured the speeds, $x \mathrm {~km}$ per hour, of 70 cars on a road where the speed limit is 60 km per hour. His results are summarised by $\Sigma ( x - 60 ) = 245$.\\
(i) Calculate the mean speed of these 70 cars.

His friend Sachim used values of $( x - 50 )$ to calculate the mean.\\
(ii) Find $\Sigma ( x - 50 )$.\\
(iii) The standard deviation of the speeds is 10.6 km per hour. Calculate $\Sigma ( x - 50 ) ^ { 2 }$.

\hfill \mbox{\textit{CAIE S1 2010 Q4 [6]}}