Question

The report "Earnings by Education Level and Gender" (U.S. Census Bureau, 2009) gave the following percentiles for annual earnings of full-time female workers age 25 and older with an associate degree: $$ \begin{array}{l} \text { 25th percentile }=\$ 26,800 \text { 50th percentile }=\$ 36,800 \\ \text { 75th percentile }=\$ 51,100 \end{array} $$ a. For each of these percentiles, write a sentence interpreting the value of the percentile. b. The report also gave percentiles for men age 25 and older with an associate degree: $$ \begin{array}{l} \text { 25th percentile }=\$ 35,700 \text { 50th percentile }=\$ 50,100 \\ \text { 75th percentile }=\$ 68,000 \end{array} $$ Write a few sentences commenting on how these values compare to the percentiles for women.

Short answer

The percentiles present a clear picture of male and female workers' earnings with an associate degree. Comparing the percentiles, it's observed that male workers earn more than female workers - a visible gender pay gap. This can be noted by comparing specific percentiles: The 25th percentile earning for men is higher than the 75th percentile earning for women; also, the 50th percentile or median earning for men is more than the 75th percentile earning for women.

Step-by-step solution

Understanding Percentiles

A percentile is a measure used in statistics indicating the value below which a given percentage of observations in a group falls. For example, the 25th percentile is the value (or score) below which 25% of the observations may be found.

Interpretation of Female Workers' Earnings

For female workers age 25+: \(\newline - The 25th percentile of 26,800 USD means that 25% of female workers earn 26,800 USD or less annually. \newline - The 50th percentile of 36,800 USD means that 50% of female workers earn 36,800 USD or less annually. This is also the median. \newline - The 75th percentile of 51,100 USD means that 75% of female workers earn 51,100 USD or less annually.

Interpretation of Male Workers' Earnings

For male workers age 25+:\(\newline - The 25th percentile of 35,700 USD means that 25% of male workers earn 35,700 USD or less annually. \newline - The 50th percentile of 50,100 USD means that 50% of male workers earn 50,100 USD or less annually. This is also the median. \newline - The 75th percentile of 68,000 USD means that 75% of male workers earn 68,000 USD or less annually.