Suppose you are using a sample from the 2010 GSS data for a research project on

Question

Suppose you are using a sample from the 2010 GSS data for a research project on education in the United States. The GSS includes a question that asks for the number of years of education. Based on 775 individuals, the GSS reports the following frequency distribution for years of education: Years of Education Frequency 0 2 2 2 3 1 4 4 5 2 6 8 7 7 8 15 9 23 10 33 11 38 12 207 13 58 14 102 15 33 16 127 17 30 18 36 19 17 20 30 A) What is the level of measurement of years of education? B) Construct a frequency table, with cumulative percentages, for years of education. C) How many respondents have 8 or fewer years of education? What percentage of the sample does this value represent? D) Suppose that you are really more interested in the general level of education than in the raw number of years of education, so you would like to group the data into four categories that better reflect your interests. Assume that anyone with 12 years of education is a high school graduate, and that anyone with 16 years of education is a college graduate. Construct a cumulative frequency table for education in four categories based on these assumptions. What percentage of the sample has graduated from college? What percentage of the sample has not graduated from high school?

Explanation / Answer

(A) The level of measurement is Interval Scale.

(B) The frequency table is given below.

(C) No. of respondents having 8 or fewer years of education = 41 (from cumulative frequency column).
Percentage of the sample it represents = 5.3% (from cumulative percent column).

(D) The frequency table is given below.

Percentage of sample graduated from college = 24.9% + 6.1% = 31%.
Percentage of sample not graduated from high school = 17.4%

Years of Education Frequency Cumulative Frequency Percent Cumulative Percent 0 2 2 0.3% 0.3% 2 2 4 0.3% 0.5% 3 1 5 0.1% 0.6% 4 4 9 0.5% 1.2% 5 2 11 0.3% 1.4% 6 8 19 1.0% 2.5% 7 7 26 0.9% 3.4% 8 15 41 1.9% 5.3% 9 23 64 3.0% 8.3% 10 33 97 4.3% 12.5% 11 38 135 4.9% 17.4% 12 207 342 26.7% 44.1% 13 58 400 7.5% 51.6% 14 102 502 13.2% 64.8% 15 33 535 4.3% 69.0% 16 127 662 16.4% 85.4% 17 30 692 3.9% 89.3% 18 36 728 4.6% 93.9% 19 17 745 2.2% 96.1% 20 30 775 3.9% 100.0%

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