Answer :
To determine the relative frequency for males, we need to follow a specific step-by-step process. Let's break down the given information and work our way to the final answer.
First, we are given the frequency counts for both males and females in different age groups:
- Males:
- Age 60-69: 14
- Age 70-79: 6
- Over 79: 5
- Females:
- Age 60-69: 6
- Age 70-79: 5
- Over 79: 4
### Step 1: Calculate the total number of males and females.
Total number of males:
[tex]\[ 14 (60-69) + 6 (70-79) + 5 (Over 79) = 25 \][/tex]
Total number of females:
[tex]\[ 6 (60-69) + 5 (70-79) + 4 (Over 79) = 15 \][/tex]
### Step 2: Calculate the grand total.
Grand total (total people in the retirement home):
[tex]\[ 25 (Total Males) + 15 (Total Females) = 40 \][/tex]
### Step 3: Calculate the relative frequency for males.
Relative frequency for males is calculated by dividing the total number of males by the grand total.
[tex]\[ \text{Relative frequency for males} = \frac{\text{Total Males}}{\text{Grand Total}} = \frac{25}{40} \][/tex]
Simplify the fraction:
[tex]\[ \frac{25}{40} = \frac{5}{8} \][/tex]
### Step 4: Determine the correct option from the given choices.
Given choices:
a. [tex]\(\frac{23}{40}\)[/tex]
b. [tex]\(\frac{5}{4}\)[/tex]
c. [tex]\(\frac{5}{8}\)[/tex]
d. [tex]\(\frac{21}{40}\)[/tex]
The correct option that matches our calculation of the relative frequency for males [tex]\(\frac{5}{8}\)[/tex] is option c.
### Final Answer:
The relative frequency for males is [tex]\(\frac{5}{8}\)[/tex], which corresponds to option c.
First, we are given the frequency counts for both males and females in different age groups:
- Males:
- Age 60-69: 14
- Age 70-79: 6
- Over 79: 5
- Females:
- Age 60-69: 6
- Age 70-79: 5
- Over 79: 4
### Step 1: Calculate the total number of males and females.
Total number of males:
[tex]\[ 14 (60-69) + 6 (70-79) + 5 (Over 79) = 25 \][/tex]
Total number of females:
[tex]\[ 6 (60-69) + 5 (70-79) + 4 (Over 79) = 15 \][/tex]
### Step 2: Calculate the grand total.
Grand total (total people in the retirement home):
[tex]\[ 25 (Total Males) + 15 (Total Females) = 40 \][/tex]
### Step 3: Calculate the relative frequency for males.
Relative frequency for males is calculated by dividing the total number of males by the grand total.
[tex]\[ \text{Relative frequency for males} = \frac{\text{Total Males}}{\text{Grand Total}} = \frac{25}{40} \][/tex]
Simplify the fraction:
[tex]\[ \frac{25}{40} = \frac{5}{8} \][/tex]
### Step 4: Determine the correct option from the given choices.
Given choices:
a. [tex]\(\frac{23}{40}\)[/tex]
b. [tex]\(\frac{5}{4}\)[/tex]
c. [tex]\(\frac{5}{8}\)[/tex]
d. [tex]\(\frac{21}{40}\)[/tex]
The correct option that matches our calculation of the relative frequency for males [tex]\(\frac{5}{8}\)[/tex] is option c.
### Final Answer:
The relative frequency for males is [tex]\(\frac{5}{8}\)[/tex], which corresponds to option c.
