A factory records the diameters (in mm) of bolts

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

Problem

A factory records the diameters (in mm) of

50

bolts. The arithmetic mean of the diameters is

12.4\ \text{mm}

and the arithmetic mean of the squares of the diameters is

155.96\ \text{mm}^{2}

. (i) Calculate the variance of the diameters. (ii) State whether the batch meets the production standard if the allowable variance must not exceed

2\ \text{mm}^{2}