the response to a question has three alternative a, b, c, a sample of 120 responses provides 60 a, 24 b, 36 c. show the frequency and relative frequency distributions
To find the frequency distribution, we need to determine the number of occurrences of each alternative (a, b, c) in the sample. In this case, we have the following counts:
- Alternative a: 60 occurrences
- Alternative b: 24 occurrences
- Alternative c: 36 occurrences
To find the relative frequency distribution, we need to calculate the proportion of each alternative relative to the total number of responses. The total number of responses is equal to the sum of the counts for each alternative. In this case, the total number of responses is:
Total responses = 60 + 24 + 36 = 120
Now, we can calculate the relative frequency for each alternative by dividing the count for that alternative by the total number of responses. The relative frequencies are as follows:
- Relative frequency of alternative a = count of a / total responses = 60 / 120 = 0.5 or 50%
- Relative frequency of alternative b = count of b / total responses = 24 / 120 = 0.2 or 20%
- Relative frequency of alternative c = count of c / total responses = 36 / 120 = 0.3 or 30%
So, the frequency and relative frequency distributions for the three alternatives (a, b, c) based on the given sample of 120 responses are as follows:
Alternative | Frequency | Relative Frequency
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a | 60 | 0.5 (50%)
b | 24 | 0.2 (20%)
c | 36 | 0.3 (30%)