The relative frequency of a histogram is found by dividing the frequency of each bin (or bar) by the total number of data points.
Here's a more detailed explanation:
Understanding Histograms and Relative Frequency
Histograms visually represent the distribution of a dataset by grouping data into intervals or "bins." Each bar's height corresponds to the frequency of data points falling within that bin. Relative frequency, on the other hand, normalizes these frequencies to show the proportion of the total data that falls within each bin.
Steps to Calculate Relative Frequency
- Determine the Frequency for each bin: This is the count of data points that fall within each bin or category. Typically, this value is read directly from the histogram or can be provided in a table.
- Calculate the Total Number of Data Points: This is the sum of all individual data points or the total frequency of all bins. According to the reference, you count all data points (e.g., 13 in Figure 7).
- Calculate the Relative Frequency for Each Bin: Divide the frequency of each bin by the total number of data points.
- Relative Frequency = (Frequency of the Bin) / (Total Number of Data Points)
Example
Let's say you have a histogram with the following frequencies:
| Bin | Frequency |
|---|---|
| Bin 1 | 2 |
| Bin 2 | 5 |
| Bin 3 | 4 |
| Bin 4 | 2 |
-
Total Number of Data Points: 2 + 5 + 4 + 2 = 13
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Calculate Relative Frequencies:
- Bin 1: 2 / 13 ≈ 0.154
- Bin 2: 5 / 13 ≈ 0.385
- Bin 3: 4 / 13 ≈ 0.308
- Bin 4: 2 / 13 ≈ 0.154
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Results: The relative frequencies are approximately 0.154, 0.385, 0.308, and 0.154. This means about 15.4% of the data falls in bin 1, 38.5% in bin 2, 30.8% in bin 3, and 15.4% in bin 4. These relative frequencies show the proportion of data within each bin relative to the total data.
Practical Insights
- Relative frequencies always add up to 1 (or 100% when expressed as percentages)
- Relative frequencies allow you to compare distributions even if the total number of data points are different across datasets.
- They provide a clearer understanding of the proportion of data within each bin.
Conclusion
Finding the relative frequency of a histogram is straightforward: divide the frequency of each bin by the total count of data points, as suggested by the reference. This process gives a clear picture of the distribution of data across different bins, normalized to the total dataset.
