A survey was conducted at a high school to study school sports in different grade levels. The data gathered is in the two-way table below:
| | Football | Baseball | Soccer | Total |
| :-------- | :------- | :------- | :----- | :---- |
| Freshman | 2 | 6 | 0 | 8 |
| Sophomore | 3 | 2 | 1 | 6 |
| Junior | 4 | 0 | 5 | 9 |
| Senior | 1 | 2 | 4 | 7 |
| Total | 10 | 10 | 10 | 30 |
Based on this table, what is the relative frequency that a student is a junior who plays football?
Answer (2)
Find the number of junior students who play football: 4.
Find the total number of students surveyed: 30.
Calculate the relative frequency: 30 4 = 15 2 .
Convert to percentage: 15 2 × 100 = 3 40 ≈ 13.3
The relative frequency is 13.3 % .
Explanation
Understand the problem We are given a two-way table that shows the distribution of students by grade level and the sports they play. We need to find the relative frequency of students who are juniors and play football. This means we need to find the number of junior students who play football and divide it by the total number of students surveyed. Then, we'll convert this fraction to a percentage.
Identify the relevant numbers From the table, we can see that there are 4 junior students who play football. The total number of students surveyed is 30.
Calculate the fraction To find the relative frequency, we divide the number of junior football players by the total number of students: 30 4 We can simplify this fraction by dividing both the numerator and the denominator by 2: 30 4 = 15 2
Convert to percentage Now, we need to convert this fraction to a percentage. To do this, we multiply the fraction by 100: 15 2 × 100 = 15 200 We can simplify this fraction by dividing both the numerator and the denominator by 5: 15 200 = 3 40 Now, we can express this as a mixed number or a decimal. As a decimal, we have: 3 40 = 13.333... Rounding to one decimal place, we get 13.3%.
State the final answer Therefore, the relative frequency that a student is a junior who plays football is approximately 13.3%.
Examples
In market research, relative frequency helps understand customer preferences. For example, if a survey shows that 20 out of 100 customers prefer a certain product, the relative frequency is 20%, indicating the product's popularity among the surveyed group. This helps businesses make informed decisions about product development and marketing strategies.
The relative frequency that a student is a junior who plays football is approximately 13.3%. This is calculated by dividing the number of junior football players (4) by the total number of students surveyed (30) and converting it into a percentage. The calculation results in 13.3% when simplified and rounded appropriately.
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