A sports coach measured the reaction times (in milliseconds) of 80 athletes and organised the data as follows:
a. (i) Find the arithmetic mean of the reaction times by any method of your choice.
Reaction time (ms)
140–160
160–180
180–200
200–220
220–240
240–260
Number of athletes
6
11
24
18
12
9
b. (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.
c. (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.