Question

The following data relates to the age of 10 employees and the number of days which they reported sick in a month: Age   Sick days 20   11 30   12 32   10 35   13 40   14 46   16 52   15 55   17 58   18 62   19 Required: i) Calculate the Karl Pearson’s coefficient of correlation                   (5 marks) ii) What observation can you make from (i) above and interpret the results       (4 marks)

Answer 1

Age 20 30 32 35 40 46 52 55 58 162 sick days 11 12 10 13 14 16 45 17 18 19 3) Let considen age by variable x and sick days by variable y. Karl Pearson's correlation coefficient is, (x-x)(y - 5) Pxy I (x-3)? ICY-7) - Age sick days X-X (x-7)2 y (y-7)(y-7)" x-7)(y-7) Х 20 - 23 529 -3.5 12.25 80-5 30 -13 169 12 -2.5 6.25 32.5 32 10 -11 -8 20.25 121 64 -4.5 -1.5 49.5 35 13 2.25 12 40 -3 9 14 -0.5 0.25 1.5 46 3 9 16 1.5 2.25 4-5 52 5 9 81 15 0.5 0.25 er 55 12 144 17 6.25 30 er 15 225 18 3.5 1.2.25 52.5 20.25 62 19 361 19 Ex = [X-5) 2(x-2)2=ZY - 430 = 0 1712 145 SX 430 X= 13, 9 ช 10 4.5 85.5 El - Y) = (1-7): XLx2y-) 82.50 у 145 14.5 10 0 = 353

Nxy [(x-1) (y-7) [(x-)2 Ily-7)? 353 = 1712 X 82.50 = 0.939 Pxy =0.939 is is Here, coefficient of comelation is OLPX, L1 that closer to 1 and positive. So, the two variables, age of employees and number of sick days are positively to a high degree. conclude that as the age of an employee increases, he is likely to go on sick leave more others. We can often than

Since the coefficient of correlation is positive and closer to one so age of employees and number of sick days are positively correlated to a high degree.