Question

2) Ages of Workers Group 1 18 25 56 42 29 38 54 47 35 30 Ages of Workers Group 2 23 19 50 49 67 34 30 59 40 33 Ages of Workers Group 3 19 22 24 40 45 29 33 29 39 59 Ages of Workers Group 4 21 23 25 40 35 19 70 40 22 23 The ages of four groups of 10 workers at a factory are shown. Which group has the largest mean absolute deviation? A) Group 1 B) Group 2 C) Group 3 D) Group 4

Answer 1

Answer: B) Group 2

Step-by-step explanation:

Given the data:

Group 1 : 18 25 56 42 29 38 54 47 35 30

Group 2 : 23,19,50,49,67,34,30,59,40,33

Group 3 : 19,22,24,40,45,29,33,29,39,59

Group 4 : 21,23,25,40,35,19,70,40,22,23

The mean absolute deviation (MAD) :

Σ(x - m) / n

Where :

m = mean ; n = number of observations

Using calculator to save computation time :

GROUP 1:

m = 37.4 ; n = 10

Mean Absolute deviation = 10

GROUP 2:

m = 40.4 ; n = 10

Mean Absolute deviation = 12.68

GROUP 3:

m = 33.9 ; n = 10

Mean Absolute deviation = 9.48

GROUP 4:

m = 31. 8; n = 10

Mean Absolute deviation = 11.56

9.48 < 10 < 11.56 < 12.68

Group 3 < group 1 < group 4 < group 2

Group 2 has the highest mean absolute deviation with a value of 12.68