Measurement: Precision, Accuracy and Tolerance

What a measuring instrument can and cannot tell you: precision, accuracy, uncertainty and tolerance.

10 questions, free, marked as you go with a worked explanation on every one.

What this covers

A machine shop specification calls for a bolt diameter of 12.50 mm with a tolerance of ± 0.05 mm. What is the largest diameter that still passes inspection, in millimetres?
For that same bolt, specified at 12.50 mm ± 0.05 mm, what is the full width of the acceptable range, in millimetres?
Four measurements of a rod whose true length is 50.00 cm read 50.31, 50.29, 50.30 and 50.32 cm. How would you describe this set of measurements?
A ruler is graduated in millimetres. What is the usual stated uncertainty of a single reading taken with it?
A technician measures a length as 24.6 cm when the true value is 25.0 cm. What is the percent error of the measurement?
A part is specified at 8.40 cm with a tolerance of ± 0.02 cm. A batch measures 8.39, 8.43, 8.41 and 8.38 cm. How many of the four parts fall within tolerance?
A digital caliper reads 4.72 mm, 4.75 mm and 4.73 mm on three passes over the same part. What is the mean of these readings, in millimetres, rounded to two decimal places?
A pipe must be cut to 240 cm with a tolerance of ± 1.5 cm before it is rejected. A cut piece measures 242.0 cm. By how many centimetres does it exceed the upper tolerance limit?
A recipe calls for 250 mL of milk. A cook measures out 238 mL. What is the absolute error, in millilitres?
Which instrument gives the most precise measurement of a pencil's diameter: a metre stick marked in centimetres, or a digital caliper reading to 0.01 mm?