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Sagot :
Sure, let's go through the steps to complete the relative frequency distribution for the surveyed men and women. The relative frequency of each job for men and women is calculated by dividing the count for each job by the total number of men and women, respectively.
### Step 1: Determine the total counts for men and women
First, we need to calculate the total number of men and the total number of women surveyed.
- Total men: [tex]\(43 + 26 + 13 + 13 + 4 = 99\)[/tex]
- Total women: [tex]\(18 + 37 + 13 + 13 + 19 = 100\)[/tex]
### Step 2: Calculate the relative frequencies for men
Next, we calculate the relative frequencies for each job by dividing the count for each job by the total number of men.
1. Job A: [tex]\( \frac{43}{99} \approx 0.434 \)[/tex] (rounded to three decimal places)
2. Job B: [tex]\( \frac{26}{99} \approx 0.263 \)[/tex] (rounded to three decimal places)
3. Job C: [tex]\( \frac{13}{99} \approx 0.131 \)[/tex] (rounded to three decimal places)
4. Job D: [tex]\( \frac{13}{99} \approx 0.131 \)[/tex] (rounded to three decimal places)
5. Not sure: [tex]\( \frac{4}{99} \approx 0.040 \)[/tex] (rounded to three decimal places)
### Step 3: Calculate the relative frequencies for women
Finally, we calculate the relative frequencies for each job by dividing the count for each job by the total number of women.
1. Job A: [tex]\( \frac{18}{100} = 0.180 \)[/tex]
2. Job B: [tex]\( \frac{37}{100} = 0.370 \)[/tex]
3. Job C: [tex]\( \frac{13}{100} = 0.130 \)[/tex]
4. Job D: [tex]\( \frac{13}{100} = 0.130 \)[/tex]
5. Not sure: [tex]\( \frac{19}{100} = 0.190 \)[/tex]
### Step 4: Complete the relative frequency distribution table
| Job | Men | Women |
|--------------|-------|-------|
| A | 0.434 | 0.180 |
| B | 0.263 | 0.370 |
| C | 0.131 | 0.130 |
| D | 0.131 | 0.130 |
| Not sure | 0.040 | 0.190 |
### Step 5: Side-by-side relative frequency bar graph
Although we won’t construct the actual graph here, you would typically represent this data using a bar graph with pairs of bars for each job category, with one bar for men and one for women, labeled accordingly. The height of each bar will correspond to the relative frequencies we calculated.
### Step 6: Analysis of apparent differences in gender
From the relative frequency distribution, we can analyze the differences in job preference between men and women:
- Job A: A higher proportion of men prefer Job A compared to women (43.4% of men vs. 18.0% of women).
- Job B: A higher proportion of women prefer Job B compared to men (37.0% of women vs. 26.3% of men).
- Job C and Job D: Both jobs have similar preferences for both men and women (13.1% of men and 13.0% of women for each job).
- Not sure: A higher proportion of women are unsure compared to men (19.0% of women vs. 4.0% of men).
This detailed comparison highlights some clear differences in job preferences based on gender.
### Step 1: Determine the total counts for men and women
First, we need to calculate the total number of men and the total number of women surveyed.
- Total men: [tex]\(43 + 26 + 13 + 13 + 4 = 99\)[/tex]
- Total women: [tex]\(18 + 37 + 13 + 13 + 19 = 100\)[/tex]
### Step 2: Calculate the relative frequencies for men
Next, we calculate the relative frequencies for each job by dividing the count for each job by the total number of men.
1. Job A: [tex]\( \frac{43}{99} \approx 0.434 \)[/tex] (rounded to three decimal places)
2. Job B: [tex]\( \frac{26}{99} \approx 0.263 \)[/tex] (rounded to three decimal places)
3. Job C: [tex]\( \frac{13}{99} \approx 0.131 \)[/tex] (rounded to three decimal places)
4. Job D: [tex]\( \frac{13}{99} \approx 0.131 \)[/tex] (rounded to three decimal places)
5. Not sure: [tex]\( \frac{4}{99} \approx 0.040 \)[/tex] (rounded to three decimal places)
### Step 3: Calculate the relative frequencies for women
Finally, we calculate the relative frequencies for each job by dividing the count for each job by the total number of women.
1. Job A: [tex]\( \frac{18}{100} = 0.180 \)[/tex]
2. Job B: [tex]\( \frac{37}{100} = 0.370 \)[/tex]
3. Job C: [tex]\( \frac{13}{100} = 0.130 \)[/tex]
4. Job D: [tex]\( \frac{13}{100} = 0.130 \)[/tex]
5. Not sure: [tex]\( \frac{19}{100} = 0.190 \)[/tex]
### Step 4: Complete the relative frequency distribution table
| Job | Men | Women |
|--------------|-------|-------|
| A | 0.434 | 0.180 |
| B | 0.263 | 0.370 |
| C | 0.131 | 0.130 |
| D | 0.131 | 0.130 |
| Not sure | 0.040 | 0.190 |
### Step 5: Side-by-side relative frequency bar graph
Although we won’t construct the actual graph here, you would typically represent this data using a bar graph with pairs of bars for each job category, with one bar for men and one for women, labeled accordingly. The height of each bar will correspond to the relative frequencies we calculated.
### Step 6: Analysis of apparent differences in gender
From the relative frequency distribution, we can analyze the differences in job preference between men and women:
- Job A: A higher proportion of men prefer Job A compared to women (43.4% of men vs. 18.0% of women).
- Job B: A higher proportion of women prefer Job B compared to men (37.0% of women vs. 26.3% of men).
- Job C and Job D: Both jobs have similar preferences for both men and women (13.1% of men and 13.0% of women for each job).
- Not sure: A higher proportion of women are unsure compared to men (19.0% of women vs. 4.0% of men).
This detailed comparison highlights some clear differences in job preferences based on gender.
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