Question

Q1. Mazan Computer Services LLC has employed two typists Mr. Khalid and Mr. Ibrahim. Mr. Khalid types, on an average, 30 pages per day with a standard deviation of 6 while Mr. Ibrahim types, on an average, 45 pages per day with a standard deviation of 10.

1. If you want to measure the consistency in the outputs of both the typists, which method you can use and why? What does a higher standard deviation denote in the above case?
2. Apply the method suggested by you and explain which typist Khalid or Ibrahim shows greater consistency in his output and why?                                                              

Answer 1

Answer a.

In order to measure the consistency in the outputs of both the typists we will use the Coefficient of Variation which is defined as the standardized measure of dispersion, which measures the spread of the data points around the mean. It is given as:

So, for the typist whose coefficient of variation is less, gives more consistent output.

In this case, higher standard deviation means that the number of pages typed by them lies within of the mean, that is,

For Mr. Khalid, standard deviation of 6 means that the number of pages typed by him lies within pages

For Mr. Ibrahim, standard deviation of 10 means that the number of pages typed by him lies within pages

Answer b.

For Mr. Khalid, Coefficient of Variation = (6/30) = (1/5) = 0.2

and For Mr. Ibrahim, Coefficient of Varition = (10/45) = (2/9) = 0.222

Since, Coefficient of Variation for Mr. Khalid = 0.2 < 0.22 of Mr. Ibrahim, we say that Ibrahim shows more consistency in his output.