Question

the partially filled contingency table gives the frequencies of the data on age (in years) and sex from the residents of a retirement home.

	60-69	70-79	over 79	total
female	6	5	4
total

what is the relative frequency for males ?
a. $\frac{23}{40}$
b. $\frac{5}{4}$
c. $\frac{5}{8}$
d. $\frac{21}{40}$

Explanation:

Step1: Calculate total number of males

To find the total number of males, we sum the frequencies for males in each age group. So, we add the number of males in 60 - 69, 70 - 79, and Over 79.
The number of males in 60 - 69 is 14, in 70 - 79 is 6, and in Over 79 is 5. So, total males $= 14 + 6 + 5 = 25$? Wait, no, wait. Wait, let's check the female counts too for total population. Wait, first, let's find total number of residents. Wait, no, relative frequency for males is (total males)/(total number of residents). Let's calculate total males first: 14 (male 60 - 69) + 6 (male 70 - 79) + 5 (male over 79) = 25? Wait, no, wait the female counts: 6 (female 60 - 69) + 5 (female 70 - 79) + 4 (female over 79) = 15. So total residents is 25 (males) + 15 (females) = 40. Wait, but let's recalculate total males: 14 + 6 + 5 = 25? Wait, but the options have 23/40 and 21/40. Wait, maybe I made a mistake. Wait, let's check the table again. Male: 60 - 69:14, 70 - 79:6, Over 79:5. So 14 + 6 + 5 = 25? Female: 6 + 5 + 4 = 15. Total: 25 + 15 = 40. But the options have 23/40. Wait, maybe I misread the table. Wait, maybe the male 70 - 79 is 5? No, the table says Male: 60 - 69:14, 70 - 79:6, Over 79:5. Female: 60 - 69:6, 70 - 79:5, Over 79:4. Wait, maybe the total males is 14 + 6 + 5 = 25? But 25/40 is 5/8, but that's option c. Wait, but the options are a. 23/40, b. 5/4, c. 5/8, d. 21/40. Wait, maybe I made a mistake. Wait, let's recalculate total males: 14 (60 - 69 male) + 6 (70 - 79 male) + 5 (over 79 male) = 25. Total residents: 14 + 6 + 5 + 6 + 5 + 4 = 40. So relative frequency for males is 25/40 = 5/8. Wait, but let's check the options. Option c is 5/8. Wait, but maybe the table was misread. Wait, maybe the male 70 - 79 is 5? No, the table says 6. Wait, maybe the female 70 - 79 is 6? No, the table says 5. Wait, let's check again. Male: 60 - 69:14, 70 - 79:6, Over 79:5. Sum: 14 + 6 = 20, 20 + 5 = 25. Female: 6 + 5 + 4 = 15. Total: 25 + 15 = 40. So relative frequency for males is 25/40 = 5/8. So option c.
Wait, but maybe the question is about something else. Wait, the question is "What is the relative frequency for males?" So relative frequency is (number of males)/(total number of observations). So total males: 14 + 6 + 5 = 25. Total observations: 14 + 6 + 5 + 6 + 5 + 4 = 40. So 25/40 simplifies to 5/8. So option c.

Step1: Sum the frequencies for males

Add the number of males in each age group: $14 + 6 + 5 = 25$.

Step2: Calculate total number of residents

Sum all frequencies: $14 + 6 + 5 + 6 + 5 + 4 = 40$.

Step3: Compute relative frequency for males

Divide the total number of males by the total number of residents: $\frac{25}{40} = \frac{5}{8}$.

Answer:

c. $\frac{5}{8}$