Question

The dot plots compare the weights of puppies in two different litters.

The dot plot with weights in ounces between 6 to 24 in increments of 2 titled Litter 1 weighs shows one dot at 7, 2 dots at 9, 3 dots at 10, 1 dot at 11, 1 dot at 14.
The dot plot with weights in ounces between 6 to 24 in increments of 2 titled Litter 2 weighs shows one dot at 13, 2 dots at 15, 2 dots at 16, 2 dots at 17, 1 dot at 19.

Which statement correctly compares the difference between the means of the two data sets and the mean absolute deviation of each data set?

A.
The difference between the means is 6.0 times the mean absolute deviation of each data set.

B.
The difference between the means is 4.8 times the mean absolute deviation of each data set.

C.
The difference between the means is 1.6 times the mean absolute deviation of each data set.

D.
The difference between the means is 7.5 times the mean absolute deviation of each data set.

Answer 1

Litter 1: values 7, 9, 9, 10, 10, 10, 11, 14. Mean = 80/8 = 10.
Litter 2: values 13, 15, 15, 16, 16, 17, 17, 19. Mean = 128/8 = 16.
Difference between means = 16 − 10 = 6.

MAD (Litter 1) = (|7−10| + 2|9−10| + 3|10−10| + |11−10| + |14−10|)/8
= (3 + 2 + 0 + 1 + 4)/8 = 10/8 = 1.25.

MAD (Litter 2) = (|13−16| + 2|15−16| + 2|16−16| + 2|17−16| + |19−16|)/8
= (3 + 2 + 0 + 2 + 3)/8 = 10/8 = 1.25.

Difference between means = 6 = 4.8 × 1.25. Answer: B.