Justify Reasoning

Statistical measures are shown for the ages of middle school and high school teachers in two states.

State A: Mean age of middle school teachers = 38, mean age of high school teachers = 48, mean absolute deviation for both = 6

State B: Mean age of middle school teachers = 42, mean age of high school teachers = 50, mean absolute deviation for both = 4

In which state is the difference in ages between members of the two groups more significant? Support your answer.

Analyze Relationships

The tables show the heights in inches of all the adult grandchildren of two sets of grandparents, the Smiths and the Thompsons. What is the difference in the medians as a multiple of the ranges?

Critical Thinking

Jill took many samples of 10 tosses of a standard number cube. What might she reasonably expect the median of the medians of the samples to be? Why?

Analyze Relationships

Elly and Ramon are both conducting surveys to compare the average numbers of hours per month that men and women spend shopping. Elly plans to take many samples of size 10 from both populations and compare the distributions of both the medians and the means. Ramon will do the same, but will use a sample size of 100. Whose results will probably produce more reliable inferences? Explain.

Counterexamples

Seth believes that it is always possible to compare two populations of numerical values by finding the difference in the means of the populations as a multiple of the mean absolute deviations. Describe a situation that explains why Seth is incorrect.