Chapter 2, Problem 2.1P

SOC The table that follows reports the marital status of 20 respondents in two different apartment complexes. (HINT: As you solve these problems, make sure that you have the correct numbers in the numerator and the denominator. For example, problem 2.1a asks for “the percentage of respondents in each complex who are married,” and the denominators will be 20 for these two fractions. Problem 2.1d, on the other hand, asks for the “percentage of the single respondents who live in Complex B,” and the denominator for this fraction will be 4 + 6, or 10.)

Status	Complex A	Complex B
Married	5	10
Unmarried (“living together”)	8	2
Single	4	6
Separated	2	1
Widowed	0	1
Divorced	1	0
	20	20

a. What percentage of the respondents in each complex are married?

b. What is the ratio of single to married respondents at each complex?

c. What proportion of the residents of each complex are widowed?

d. What percentage of the single respondents lives in Complex B?

e. What is the ratio of the “unmarried/living together” to the “married” at each complex?

To determine

a)

To find:

The percentages of the respondents in each complex are married.

Answer to Problem 2.1P

Solution:

Complex A: $\frac{5}{20}*100=0.25*100=25.00\%$

Complex B: $\frac{10}{20}*100=0.5*100=50.00\%$

Explanation of Solution

Formula:

Percentage: % = $\left(\frac{f}{N}\right)*100$

Where,

f = frequency, or the number of cases in a specific category.

N = the number of cases in all categories.

For complex A,

The frequency of married respondents is f = 5.

Total number of frequencies is N = 20.

Therefore the percentage of the respondents who are married at,

Complex A: $\frac{5}{20}*100=0.25*100=25.00\%$

For complex B,

The frequency of married respondents is f = 10.

Total number of frequencies is N = 20.

Therefore the percentage of the respondents who are married at,

Complex B: $\frac{10}{20}*100=0.5*100=50.00\%$

To determine

b)

To find:

The ratio of single to married respondents at each complex.

Answer to Problem 2.1P

Solution:

Complex A: 4:5 = 0.80

Complex: B: 6:10 = 0.60

Explanation of Solution

Ratios are computed by dividing the frequency in one category by the frequency in another one. The formula for a ratio is:

Ratio = $\left(\frac{f_1}{f_2}\right)$

Where,

$f_1$ = the number of cases in the first category.

$f_2$= the number of cases in the second category.

For Complex A,

$f_1$ = the number of singles.

$f_2$= the number of married.

Therefore, the ratio of single to married respondents at complex A is $\left(\frac{4}{5}\right)$ = 0.80.

For Complex B,

$f_1$ = the number of singles.

$f_2$= the number of married.

Therefore, the ratio of single to married respondents at complex B is $\left(\frac{6}{10}\right)$ = 0.60.

To determine

c)

To find:

The proportion of the residents of each complex who are widowed.

Answer to Problem 2.1P

Solution:

Complex A: $\left(\frac{0}{20}\right)$ = 0.00.

Complex B: $\left(\frac{1}{20}\right)$ = 0.05.

Explanation of Solution

Formula:

Proportion = $\left(\frac{f}{N}\right)$

Where,

f = frequency, or the number of cases in a specific category.

N = the number of cases in all categories.

For Complex A,

f = the number of widows in Complex A, f = 0.

N = the number of cases in all categories, N = 20.

Therefore, the proportion of the residents of each complex who are widowed is $\left(\frac{0}{20}\right)$ = 0.00.

For Complex B,

f = the number of widows in Complex B, f = 1.

N = the number of cases in all categories, N = 20.

Therefore, the proportion of the residents of each complex who are widowed is $\left(\frac{1}{20}\right)$ = 0.05.

To determine

d)

To find:

The percentage of the single respondents living in Complex B.

Answer to Problem 2.1P

Solution:

$\left(\frac{6}{6+4}\right)*100=\left(\frac{6}{10}\right)*100=0.6*100=60.00\%$

Explanation of Solution

Formula:

Percentage: % = $\left(\frac{f}{N}\right)*100$

Where,

f = frequency, or the number of cases in a specific category.

N = the number of cases in all categories.

For complex B,

The frequency of single respondents from Complex B is f = 6.

Total number of single respondents is N = 6 + 4 = 10.

Therefore the percentage of the single respondents living in Complex B is,

$\left(\frac{6}{6+4}\right)*100=\left(\frac{6}{10}\right)*100=0.6*100=60.00\%$

To determine

e)

To find:

The ratio of the “unmarried/living together” to the “married” at each complex.

Answer to Problem 2.1P

Solution:

Complex A: 8:5 = 1.60.

Complex: B: 2:10 = 0.20.

Explanation of Solution

Ratios are computed by dividing the frequency in one category by the frequency in another one. The formula for a ratio is:

Ratio = $\left(\frac{f_1}{f_2}\right)$

Where,

$f_1$ = the number of cases in the first category.

$f_2$= the number of cases in the second category.

For Complex A,

$f_1$ = the number of singles.

$f_2$= the number of married.

Therefore, the ratio of unmarried/living together to married respondents at complex A is:

$\left(\frac{8}{5}\right)$ = 1.60

For Complex B,

$f_1$ = the number of singles.

$f_2$= the number of married.

Therefore, the ratio of single to married respondents at complex B is $\left(\frac{2}{10}\right)$ = 0.20.