Earnings by gender According to the 2005 American Community Survey taken by the U.S. Bureau of the Census, the median earnings in the past 12 months was \$32,168 for females and \$41,965 for males, whereas the mean was \$39,890 for females and \$56,724 for males.

a. Does this suggest that the distribution of income for each gender is symmetric, skewed to the right, or skewed to the left? Explain.

b. The results refer to 73.8 million females and 83.4 million males. Find the overall mean income.

#### Solution

(a)

**For Female:**

The median earnings in the past 12 months was \$32,168 for females and the

mean was \$39,890 for females.

Median earning is less than Mean earning for females.

Mean - median $= 39890 -32168=7722$

As the mean earning is greater than median earning for female, the distribution of earning for females is **Positively Skewed** (skewed to the right).

**For Male:**

The median earning in the past 12 months was \$41,965 for males and the mean was \$56,724 for males.

Mean - median $= 59724 -41965 = 17759$

As the mean earning is greater than median earning for male, the distribution of earning for males is **Positively Skewed** (skewed to the right).

Comparing both, distribution of male earnings is more positively skewed than distribution of female earnings.

(b) Overall mean income is

` $$ \begin{aligned} \overline{X} &=\frac{n_1\overline{X}_1+n_1\overline{X}_1}{n_1+n_2}\\ & = \frac{73800000 \times 39890 + 83400000\times 59724}{73800000+83400000}\\ &=50412.618. \end{aligned} $$ `

The overall mean income = \$ 50412.618

#### Further Reading

- Statistics
- Descriptive Statistics
- Probability Theory
- Probability Distribution
- Hypothesis Testing
- Confidence interval
- Sample size determination
- Non-parametric Tests
- Correlation Regression
- Statistics Calculators