Mathematics – statistics homework 12

Denishia McCray

October 6, 2023

SOC 2020: Homework Assignment #2

Dr. Maria Paino

Please use excel! And be sure to show your work, type, and label your answers clearly. You can copy/paste your excel work into this document and save in MS Word. You can copy/paste tables and graphs into MS Word.

1. During the 2008 presidential election, health care and health insurance were identified by voters as important issues. Policy analysts have noted that the number of uninsured is increasing in the United States. Data from the National Center for Health Statistics are presented below.

The Uninsured Population Below 65 Years of Age by Selected Characteristics, 2007

Characteristic

Percentage

Age

Below 18 Years

16.2

18-44 Years

61.2

45-64 Years

22.2

Poverty

Below 100% of Poverty Line

25.1

100 to less that 200%

31.6

200 to less than 400%

28.7

400% or more

14.6

Race or Hispanic Origin

Hispanic

31.3

White Only

48.0

Black

13.9

Asian

4.3

Other

2.4

Marital Status

Single

40.2

Married

41.8

Separated/Divorced

16.3

Widowed

1.7

Choose one characteristic from above and graphically display it (use excel!). After the graph, write a brief description of the graph using the format described in class.

Figure 1

A bar graph of Marital status

This bar graph shows that among the Uninsured Population Below 65 Years of Age sampled form 2007, majority of them were either married or single and the least proportion was widowed. Those who were married account for 41.8% while those who are single accounted for 40.2%. The proportion the Uninsured Population Below 65 Years of Age that was separated or divorced was 16.3% while another 1.7% was widowed.

2.
The 2010 General Social Survey (GSS) data on educational level can be further broken down by race as shown on the following page.

a.
Construct two histograms for years of education, one for whites (N=636) and one for blacks (N=136). In constructing them, think how we can best compare two different sample sizes (so that you can answer part b).

Note: You do not have to collapse data into groups, like in homework 1.

b.
Now use the two graphs to describe the differences in educational attainment by race.

 Years of Education Whites Blacks 0 2 0 1 0 0 2 1 1 3 2 0 4 0 0 5 3 1 6 5 0 7 2 0 8 13 1 9 8 6 10 17 8 11 27 6 12 180 36 13 56 18 14 101 33 15 27 5 16 103 13 17 32 1 18 32 2 19 12 1 20 13 4

Figure 2

Histogram for Years of Education for Whites

Figure 3

Histogram for Years of Education for Blacks

From figure 1 and figure 2, the histograms for the years of education between the whites and the Blacks are identical. Most of them have between 0 and 3 years of educaiton. The rest of the categories have fairly equal heights.

3.
Twenty-five students completed an SAT preparation class. Their scores are reported below.

1120 1470 1260 1030 1500 1170 1090 1290 1100 1000

1110 1600 960 1280 1140 1040 1010 1350 1320 910

1030 1070 1190 1200 1030

a.
Display these numbers graphically. (Think about how to do this most clearly – so you can look at the graph and quickly know something about how the scores are distributed/
grouped).

Figure 4

Histogram of SAT Scores

b.
Calculate the mean, mode, and median of the distribution (show your work!).

 Mean =AVERAGE(B2:B26) 1170.8 Mode =MODE(B2:B26) 1030 Median =MEDIAN(B2:B26) 1120

c.
What is the range?

Range=MAX(B2:B26)-MIN(B2:B26)

=1600-910

=690

d.
What is the Interquartile Range (IQR)?

IQR=[MAX(B2:B26)+MIN(B2:B26)]/2

=(1600+910)/2

=1255

Marital Status

Single Married Separated/Divorced Widowed 40.200000000000003 41.8 16.3 1.7

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