Question

3. The researchers present the following two figures illustrating the frequency distributions of income for 1) formerly incarcerated respondents (Figure 1) and 2) respondents that had not been previously incarcerated (Figure 2). The figures also provide mean, median and mode for each group’s incomes.      

Should the researchers be concerned about using the mean – rather than the median – for either of these distributions? Why or why not?

Figure 1- Median: 10, Mode: 10, Mean: 22

Figure 2- Median:20, Mode:20, Mean: 22

Answer 1

For Figure 1 the researcher should not use the mean and go for the median.

Because clearly for the 1st group mode and median are the 10 but the mean is 22 which is very far from the median and mode. So this indicates that the data has some outliers for which the mean has increased this much.but the outliers should not be taken in to account for exact measure. So here median or mode should be used.

For Figure 2, here all the 3 measure of central tendencies are almost equal. All of them are indicating same result. That implies there is not much outliers in the data. So here mean is appropriate and best measure of central tendency.