A factory manufactures steel rods whose diameters (in mm) are summarised in the frequency distribution below.
Diameter (mm) Number of rods
9.90 – 9.94 6
9.95 – 9.99 18
10.00 – 10.04 32
10.05 – 10.09 22
10.10 – 10.14 12
The nominal diameter is 10.00 mm.
(i) Determine the mean diameter of the rods, taking the class mid-point for each class interval.
(ii) Calculate the population standard deviation of the diameters.
(iii) Compute the overall range of the diameters.
(iv) The rods are acceptable if their diameter lies within ±0.10 mm of the nominal value. Using your numerical results, comment on whether the manufacturing process is adequately controlled.