Generate a frequency table for the following data: 3, 12, 25, 2, 3, 6, 17, 17, 15, 13, 20, 12, 21, 18, 19.
Use the ranges listed in the table below:
Range Number of Values Relative Frequency
1 – 5
6 – 10
11 – 15
16 – 20
21 – 25
What is the relative frequency for the range 11 – 15?
The Correct Answer and Explanation is:
Here is the frequency table for the given data:
| Range | Number of Values | Relative Frequency |
|---|---|---|
| 1 – 5 | 3 | 0.200 |
| 6 – 10 | 1 | 0.067 |
| 11 – 15 | 4 | 0.267 |
| 16 – 20 | 5 | 0.333 |
| 21 – 25 | 2 | 0.133 |
The relative frequency for the range 11 – 15 is 0.267.
Explanation
A frequency table is a statistical tool that summarizes data by categorizing it into specified intervals or ranges, allowing for easier interpretation and analysis. In this case, the data set contains 15 values ranging from 2 to 25. We divided these values into five distinct ranges: 1–5, 6–10, 11–15, 16–20, and 21–25.
To construct the frequency table, we first counted how many values fell within each range. For the 11–15 range, we found four data points: 12, 12, 13, and 15. This leads to a count of 4 for this range.
Next, we calculate the relative frequency, which is the proportion of values in each range compared to the total number of values. The relative frequency for the 11–15 range is calculated by dividing the number of values in that range (4) by the total number of values (15):
[
\text{Relative Frequency} = \frac{\text{Number of Values in Range}}{\text{Total Number of Values}} = \frac{4}{15} \approx 0.267
]
This relative frequency indicates that approximately 26.67% of the data falls within the 11–15 range. Understanding relative frequency is crucial as it provides insight into how data is distributed across various ranges, helping in making statistical inferences and decisions based on the data set. In practical applications, such as surveys or tests, relative frequency can help in understanding trends or patterns in the responses, guiding further research or analysis.