Question

12. Central tendency and distribution shape Aa Aa E The Bureau of Labor Statistics (BLS) is the main fact-finding agency of the U.S. government in the fields of labor economics and statistics. Data from the Current Population Survey (CPS), conducted by the BLS and the Census Bureau, have been used to indicate a downward trend in retirement age. [Source: Gendell, M. (October 2001). Retirement age declines again in the 1990s. Monthly Labor Review, 124(10), 12-21.] The following DataView tool displays a hypothetical data set consisting of annual income (as measured in thousands of dollars) and age of retirement for 100 retirees. Use the tool to view the histogram of the incomes of the retirees, and answer the questions that follow. (Hint: Click either one of the Variable sliding panels in the bottom left-hand corner of the tool screen. Click the downward-pointing arrow next to Select Variable, and select the variable Income. Click the Histogram button in the middle of the left-hand side of the screen to view a histogram of its distribution.) Retirement Data Set Sample Variables = 2 Observations = 100 Income and Retirement Age for 100 retirees Variables Observations > Observations Values V Missing V Variable Type V Form Income Retirement Age Quantitative Quantitative Numeric Numeric 1000 100 0 Variable Variable Retirement Data Set Retirement Sample Variables = 2 Observations = 100 Retiree Variables > Observations > Income Retirement Age thousands of dollars years o 84.5 61.4 71.1 59.8 104.7 60.5 81.3 63.0 63.2 66.1 73.5 68.9 50.8 71.8 65.9 71.7 47.9 73.5 49.3 60.3 59.1 72.2 56.7 103.5 63.4 63.1 62.6 90.9 63.1 69.1 Variable The right tail of the distribution of the incomes extends farther than the other tail. Therefore, this distribution is positively skewed Use the tool to obtain the mean and median of the retirees' incomes. (Hint: On the Variable sliding panel for the variable Income, click the Statistics button to view computed statistics for the variable.) The mean is $62,900 , and the median is . The mean is than the median. Use the tool to view the histogram of the retirement ages of the retirees. (Hint: Click a Variable sliding panel in the bottom left-hand corner of the tool screen. Click the downward-pointing arrow next to Select Variable, and select the variable Retirement Age. Again, click the Histogram button.) of the distribution of the retirement ages extends farther than the other tail. Therefore, this distribution is Use the tool to obtain the mean and median of the retirement ages. (Hint: Select the Variable sliding panel for the variable Retirement Age, and click the Statistics button.) The mean is , and the median is . The mean is than the median. When the distribution is symmetrical, the mean is the median. When the distribution is positively skewed, the mean is usually the median. When the distribution is negatively skewed, the mean is usually the median. The presence of extremely large or small values in the data affects the mean than the median. Therefore the is the preferred measure of central tendency when the distribution is skewed.