Question

The ages of two groups of karate students are shown in the following dot plots: A dot plot shows Age in years on the horizontal axis. For Group A, there are 2 dots on 4, 5 dots on 5, 3 dots on 7, 4 dots on 8, 2 dots on 9, 2 dots on 11, and 1 dot on 14. For Group B, there is 1 dot on 7, 2 dots on 8, 1 dot on 9, 1 dot on 11, 1 dot on 16, 2 dots on 19, 2 dots on 20, 2 dots on 21, and 1 dot on 26.
The mean absolute deviation (MAD) for group A is 2.07 and the MAD for group B is 5.51. Which of the following observations can be made using these data?

Answer 1

Group A:1 dot at 9:     1 x    9 =     97 dots at 10: 7 x 10 =   708 dots at 15: 8 x 15 = 1208 dots at 17: 8 x 17 = 1366 dots at 19: 6 x 19 = 114
Mean: (9+70+120+136+114) / (1+7+8+8+6) = 449/30 = 14.97
Group B:6 dots at 10: 6 x 10 = 605 dots at 14: 5 x 14 = 706 dots at 18: 6 x 18 = 1085 dots at 25: 5 x 25 = 1254 dots at 28: 4 x 28 = 1124 dots at 29: 4 x 29 = 116
mean: (60+70+108+125+112+116) / (6+5+6+5+4+4) = 591 / 30 = 19.70
The group that has a lower mean age of painting students is Group A. Its mean is 14.97 or 15 years of age.