The eye color for 30 students in a statistics class was recorded. The counts for each color are listed in the table below.
| Blue | Brown | Green | Hazel | Gray |
|---|---|---|---|---|
| 8 | 10 | 6 | 5 | 1 |
Which of the following is the correct relative frequency table for eye color?
| Blue | Brown | Green | Hazel | Gray |
|---|---|---|---|---|
| 0.27 | 0.33 | 0.20 | 0.17 | 0.03 |
| Blue | Brown | Green | Hazel | Gray |
|---|---|---|---|---|
| 0.33 | 0.27 | 0.20 | 0.17 | 0.03 |
| Blue | Brown | Green | Hazel | Gray |
|---|---|---|---|---|
| 8 | 10 | 6 | 5 | 1 |
| Blue | Brown | Green | Hazel | Gray |
|---|---|---|---|---|
| 0.8 | 0.1 | 0.6 | 0.5 | 0.01 |
Answer (2)
Calculate the relative frequency for each eye color by dividing the number of students with that eye color by the total number of students.
The relative frequencies are approximately: Blue (0.27), Brown (0.33), Green (0.20), Hazel (0.17), and Gray (0.03).
Compare the calculated relative frequencies with the given tables.
The correct relative frequency table is:
Blue
Brown
Green
Hazel
Gray
Count
0.27
0.33
0.20
0.17
0.03
Explanation
Calculate relative frequencies We need to calculate the relative frequencies for each eye color. The relative frequency is found by dividing the number of students with a particular eye color by the total number of students.
Calculating each relative frequency The total number of students is 30.
Blue: 30 8 = 0.2666... ≈ 0.27
Brown: 30 10 = 0.3333... ≈ 0.33
Green: 30 6 = 0.20
Hazel: 30 5 = 0.1666... ≈ 0.17
Gray: 30 1 = 0.0333... ≈ 0.03
Finding the correct table Now, we compare the calculated relative frequencies with the given tables to find the correct one. The correct relative frequency table is:
Blue
Brown
Green
Hazel
Gray
Count
0.27
0.33
0.20
0.17
0.03
Examples
Understanding relative frequencies is essential in many real-world scenarios. For instance, in market research, companies use relative frequencies to determine the proportion of customers who prefer a certain product. If a survey of 1000 people shows that 350 prefer Product A, the relative frequency of preference for Product A is 0.35, or 35%. This information helps companies make informed decisions about product development, marketing strategies, and resource allocation. Similarly, in healthcare, relative frequencies can represent the proportion of patients with a specific condition, aiding in resource planning and public health initiatives.
The correct relative frequency table for the eye color data is shown as Blue (0.27), Brown (0.33), Green (0.20), Hazel (0.17), and Gray (0.03). This is calculated by dividing each color count by the total number of students, which is 30. Therefore, the first option is the correct one.
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