Question

A wildlife refuge in South America has howler monkeys and spider monkeys. A biologist working there randomly selected eight adults of each type of monkey, weighed them, and recorded their weights in pounds.
howler monkey: {15, 16, 17, 17, 17, 17, 18, 19}

spider monkey: {12, 13, 13, 14, 14, 14, 16, 16}

1. Calculate the mean and MAD for each type of monkey.
2. Calculate the means-to-MAD ratio for the two types of monkeys.
3. What inference can be made about the weight of both types of monkeys? Explain.

Answer 1

The mean for the howler monkeys is 17 and the MAD is 0.8571.
The mean for the spider monkeys is 14 and the MAD is 1.1429.

The means-to-MAD ratio is 2.6249.

This means that on average, the number of mean absolute deviations that separate the means is 2.6.  This means they are different.

To find the mean of the howler monkeys, add all of the data values and divide by 7:
(15+16+17+17+17+17+18+19)/7 = 119/7 = 17

To find the MAD, subtract each data point from the mean; take the absolute deviation; then average these together:
(|15-17|+|16-17|+|17-17|+|17-17|+|17-17|+|17-17|+|18-17|+|19-17|)/7
=(2+1+0+0+0+0+1+2)/7=6/7 = 0.8571

Repeating these processes for the spider monkeys:
Mean:(12+13+13+14+14+14+16+16)/7 = 98/7 = 14
MAD:
(|12-14|+|13-14|+|13-14|+|14-14|+|14-14|+|14-14|+|16-14|+|16-14|)/7
=(2+1+1+0+0+0+2+2)/7 = 8/7 = 1.1429

To find the means-to-MAD ratio, find the difference in the means and divide it by the larger MAD:
17-14=3; 3/1.1429 = 2.6249