MATHEMATICS · Multi-part · A Level · Mathematics · Data presentation and interpretation · Data presentation and interpretation
Problem
Two bakeries, Bakery A and Bakery B, supply packets of bread to a supermarket. During an inspection, the quality manager records the following summary statistics for the mass of the packets:
Bakery A: mean 489 g, range 9 g, standard deviation 2.3 g
Bakery B: mean 489 g, range 26 g, standard deviation 7.1 g
Assume the masses are normally distributed around the stated mean.
(i) State the meaning of (a) range and (b) standard deviation in the above context of packet mass.
(ii) Using the statistics provided, identify which bakery produces packets with more consistent mass. Give two numerical reasons for your choice.
(iii) The supermarket demands that at least 95 % of packets lie within ±6 g of the mean mass. Without carrying out further calculations, explain which of the two measures—range or standard deviation—gives a more reliable basis for deciding whether a bakery meets this demand and justify your answer.