Question

ws the yearly earnings, in thousands of dollars, over a for college graduates. -employed wage earners 52 66 101 89 53 64 96 81 60 62 81 84 38 44 51 58 which statement is true about the distributions representing the yearly earnings? the distribution of earnings for wage earners is more symmetric than the distribution of earnings for the self - employed. the standard deviations of the distributions are equal. the mean earnings of the self - employed are higher than the mean earnings of the wage earners.

Explanation:

Step1: Analyze Symmetry

To check symmetry, we can look at the spread and clustering of data. For self - employed earnings (let's list them: 52, 101, 53, 96, 60, 81, 38, 51) and wage earners (66, 89, 64, 81, 62, 84, 44, 58). The self - employed data has a wide range with values like 38, 101 which are more spread out and less clustered around a central point. The wage earners' data seems to be more clustered and has a more balanced spread around a central value. So the distribution of wage earners is more symmetric.

Step2: Analyze Standard Deviation

Standard deviation measures spread. The self - employed data has a larger range (101 - 38 = 63) and more spread out values compared to wage earners (89 - 44 = 45). So their standard deviations are not equal.

Step3: Analyze Mean Earnings

Calculate the mean for self - employed: $\frac{52 + 101+53 + 96+60 + 81+38 + 51}{8}=\frac{532}{8}=66.5$.
Calculate the mean for wage earners: $\frac{66+89 + 64+81+62+84+44+58}{8}=\frac{548}{8}=68.5$. So the mean of wage earners is higher, not self - employed.

Answer:

The distribution of earnings for wage earners is more symmetric than the distribution of earnings for the self - employed.