Question

Three apprentice tailors (X, Y, and Z) are assigned the task of measuring the seam of a pair of trousers. Each one makes three measurements. The results in inches are X (26.5, 26.6, 26.4); Y (27.8, 27.3, 27.7); Z (26.9, 27.2, 27.1). The true length is 27.0 in. Comment on the precision and the accuracy of each tailor's measurements.

Answer 1

Answer:

Explanation:

Precision generally refers to the repeatability of measurements. That is, the closeness of repeated meaurements in values. Accuracy, on the other hand, refers to the closeness of a measured value to the true value.

For apprentice X, the three measurements taken (26.5, 26.6, 26.4) were close in values with an average of 26.5 and a mean deviation of 0.07. Hence, the apprentice is said to be precise in measurement. However, the average of the measurement is quite far from the true length of meaurement. Hence, the apprentice is inaccurate.

Apprentice Y had a mean measurement value of 27.6 and a mean deviation of 0.2. The measurements are far from each other and the apprentice is therefore said to be far from being precise. The mean measurement value is also far from true value. Hence the apprentice is also inaccurate in his/her measurement.

Apprentice Z has a mean measurement of 27.07 and a mean deviation of 0.11.  The repeated measurements were close enough to be precise while the average is also close to the true length, and hence, the measurement is said to be accurate.