Final answer:
Standard deviation can exceed the average in widely dispersed data sets, and hypothesis testing is used to compare means between groups. As sample size increases, the sample mean tends to be closer to the population mean. Salary distributions shift when all values are increased equally, and gender disparities in salaries are an observed phenomenon.
Step-by-step explanation:
The standard deviation can be greater than the average (mean) if there is a wide dispersion around the mean, particularly if the data includes values that are much lower than the mean.
It is likely that the average salary of a larger population, such as 1,000 residents, will be distributed around the mean with less variability than a smaller sample due to the Central Limit Theorem, which states that as sample size increases, the sample mean of the population distribution is likely to be closer to the actual population mean.
hypothesis test can be conducted to determine if the means are statistically different. For example, if you want to know whether grad school tuitions, the amount spent on texts and supplies, or the average salaries from different companies are different, you would perform a t-test or ANOVA if the assumptions for those tests are met.
When rafting salaries, or increasing them, such as with a $3,000 raise for teachers, the mean of the distribution would shift to the right by the amount of the raise. Gender disparities in salaries are also crucial factors that may be evaluated, as studies have shown differences between what male and female graduates earn.