The response to a question has three alternatives: A, B, and C. A sample of 120 responses provides 52 A, 29 B, and 39 C responses. Show the frequency and relative frequency distributions (use nearest whole number for the frequency column and 2 decimal for the relative frequency column).
To find the frequency and relative frequency distributions, we need to calculate the number of occurrences of each response and the proportion of each response out of the total number of responses. Here's how you can calculate them:
1. Frequency Distribution:
The frequency distribution shows the number of occurrences of each response.
- Response A: 52 occurrences
- Response B: 29 occurrences
- Response C: 39 occurrences
2. Relative Frequency Distribution:
The relative frequency distribution shows the proportion of each response out of the total number of responses.
To calculate the relative frequency, divide the frequency of each response by the total number of responses (120) and multiply by 100 to express it as a percentage.
- Response A: (52/120) * 100 = 43.33%
- Response B: (29/120) * 100 = 24.17%
- Response C: (39/120) * 100 = 32.50%
Now, rounding the frequency column to the nearest whole number, and the relative frequency column to 2 decimal places, the frequency and relative frequency distributions are as follows:
| Response | Frequency | Relative Frequency (%) |
|----------|-----------|-----------------------|
| A | 52 | 43.33 |
| B | 29 | 24.17 |
| C | 39 | 32.50 |
Please note that in the relative frequency column, only two decimal places are shown for clarity.