Moderate -0.8 This is a straightforward application of coding formulas for mean and standard deviation. Students need to reverse the linear transformation using standard formulas (mean_x = a + b*mean_y, SD_x = |b|*SD_y), requiring only algebraic manipulation and calculator work with no conceptual challenges or problem-solving insight.
2.
Data relating to the lifetimes (to the nearest hour) of a random sample of 200 light bulbs from the production line of a manufacturer were summarised in a grouped frequency table. The mid-point of each class in the table was represented by \(x\) and the corresponding frequency for that class by \(f\). The data were then coded using:
$$y = \frac { ( x - 755.0 ) } { 2.5 }$$
and summarised as follows:
$$\sum f y = - 467 , \sum f y ^ { 2 } = 9179$$
Calculate estimates of the mean and the standard deviation of the lifetimes of this sample of bulbs.
(4 marks) [0pt]
2.
Data relating to the lifetimes (to the nearest hour) of a random sample of 200 light bulbs from the production line of a manufacturer were summarised in a grouped frequency table. The mid-point of each class in the table was represented by $x$ and the corresponding frequency for that class by $f$. The data were then coded using:
$$y = \frac { ( x - 755.0 ) } { 2.5 }$$
and summarised as follows:
$$\sum f y = - 467 , \sum f y ^ { 2 } = 9179$$
Calculate estimates of the mean and the standard deviation of the lifetimes of this sample of bulbs.\\
(4 marks)\\[0pt]
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\hfill \mbox{\textit{SPS SPS SM Statistics 2021 Q2 [4]}}