The table shows the frequencies for the data from the previous task about part-time employment for 15 randomly selected high school students. Use the information to complete the relative frequency column of the table. Express answers as percentages rounded to the nearest whole number.
| Employment | Frequency | Relative Frequency |
|---|---|---|
| babysitter | 1 | 7% |
| food service | 6 | 40% |
| lifeguard | 3 | A |
| retail | 5 | B |
[tex]A=\square \%[/tex]
[tex]B=\square \%[/tex]
Answer (2)
Calculate the relative frequency for lifeguard (A): 15 3 × 100 = 20% .
Calculate the relative frequency for retail (B): 15 5 × 100 = 33.33...% .
Round the relative frequency for retail (B) to the nearest whole number: 33% .
The relative frequencies are: A = 20% , B = 33% .
Explanation
Understand the problem and provided data We are given a table showing the frequency of part-time employment for 15 high school students. We need to calculate the relative frequencies for 'lifeguard' and 'retail' employment, expressing the answers as percentages rounded to the nearest whole number.
Calculate the relative frequency for lifeguard (A) To find the relative frequency for 'lifeguard' (A), we divide the frequency of lifeguard employment by the total number of students and multiply by 100. The frequency of lifeguard employment is 3, and the total number of students is 15. Therefore, we have: A = 15 3 × 100
Determine the value of A Calculating the value of A: A = 15 3 × 100 = 0.2 × 100 = 20 So, the relative frequency for lifeguard employment is 20%.
Calculate the relative frequency for retail (B) To find the relative frequency for 'retail' (B), we divide the frequency of retail employment by the total number of students and multiply by 100. The frequency of retail employment is 5, and the total number of students is 15. Therefore, we have: B = 15 5 × 100
Determine the value of B Calculating the value of B: B = 15 5 × 100 = 0.3333... × 100 = 33.33... Rounding this to the nearest whole number, we get 33%. So, the relative frequency for retail employment is 33%.
State the final answer Therefore, the relative frequency for lifeguard employment (A) is 20%, and the relative frequency for retail employment (B) is 33%.
A = 20% B = 33%
Examples
Understanding relative frequencies is useful in many real-world scenarios. For example, if you're conducting a survey about favorite subjects in school, you can use relative frequencies to determine the percentage of students who prefer math, science, or English. This helps in understanding the distribution of preferences within the student population. Similarly, in market research, businesses use relative frequencies to analyze customer preferences and buying patterns, which aids in making informed decisions about product development and marketing strategies.
The relative frequency for lifeguard employment is 20%, and for retail employment, it is 33%. These calculations are derived by dividing the frequency of each employment type by the total number of students surveyed. The results can be expressed as percentages rounded to the nearest whole number.
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