A sports coach measured the reaction times (in milliseconds) of 80 athletes and…

MATHEMATICS · Multi-part · A Level · Mathematics · Data presentation and interpretation · Data presentation and interpretation

Problem

A sports coach measured the reaction times (in milliseconds) of 80 athletes and organised the data as follows: (i) Find the arithmetic mean of the reaction times by any method of your choice.
Reaction time (ms)140–160160–180180–200200–220220–240240–260
Number of athletes6112418129
(ii) Re-calculate the mean after first transforming every class mark by subtracting 200 and then dividing the result by 20. Show all the working clearly. (iii) Verify that the two means obtained in parts (i) and (ii) are equal. State, in not more than two sentences, what advantage the transformation in part (ii) offered during the calculation.

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