A relative frequency histogram is a bar chart that shows how data is distributed across intervals, with the height of each bar representing the proportion or percentage of the total data rather than raw counts. Instead of telling you “15 people scored between 70 and 80,” it tells you “30% of people scored between 70 and 80.” The vertical axis is the only difference between a relative frequency histogram and a standard frequency histogram. Everything else, the bars, the intervals, the lack of gaps between bars, stays the same.
How It Differs From a Regular Histogram
A standard histogram uses raw counts on the y-axis. If 40 students scored between 80 and 90 on an exam, the bar for that interval reaches 40. A relative frequency histogram takes that same count and divides it by the total number of observations, so if there were 200 students total, the bar would reach 0.20 (or 20%).
The shape of the two charts is identical. You’re not changing the data or the intervals, just rescaling the vertical axis from “how many” to “what fraction of the whole.” This makes relative frequency histograms more useful in several situations, particularly when you need to compare two datasets that have different sample sizes. Comparing a histogram of 500 observations to one with 10,000 observations is misleading when the y-axis shows raw counts, because the bars in the larger dataset will always be taller. Switching to relative frequencies puts both distributions on the same scale.
The Relative Frequency Formula
The calculation is straightforward:
Relative Frequency = f / n
Here, f is the number of observations in a particular interval (the frequency), and n is the total number of observations across all intervals. The result is a decimal between 0 and 1, which you can multiply by 100 to express as a percentage.
Say a shop sells 66 items in a day, and 20 of those items were priced between $1 and $10. The relative frequency for that price range is 20 / 66 = 0.303, or about 30.3%. If 21 items fell in the $11–$20 range, that interval’s relative frequency is 21 / 66 = 0.318, or 31.8%. One important rule: the relative frequencies across all intervals must add up to 1 (or 100%). In practice, rounding can make the total come out to something like 0.998 or 1.002, but if you keep all the decimal places, the sum is exactly 1.
How to Build One Step by Step
Building a relative frequency histogram takes five steps:
- Choose your class intervals. Decide how to divide your data range into bins. For exam scores from 0 to 100, you might use intervals of 10 (0–9, 10–19, 20–29, and so on). The intervals should be equal in width, with no gaps or overlaps.
- Count the frequencies. Tally how many data points fall into each interval. This gives you a standard frequency distribution table.
- Calculate relative frequencies. Divide each interval’s count by the total number of data points using the f/n formula.
- Draw the bars. Place the class intervals along the x-axis and relative frequencies (as decimals or percentages) on the y-axis. Each bar’s height corresponds to its relative frequency, and bars should touch each other with no gaps, because the data is continuous.
- Label clearly. Mark the y-axis as “Relative Frequency” or “Percentage” so the reader knows they’re looking at proportions, not raw counts.
If you’re comparing two datasets, keep the y-axis scale the same on both histograms. This is the whole point of using relative frequency: it lets you make visual comparisons on equal footing.
Creating One in Spreadsheet Software
Most statistics software, including Minitab, Excel, and Google Sheets, can produce relative frequency histograms. In Minitab, you create a standard histogram and change the y-scale type from “Frequency” to “Percent,” which converts each bar’s height to the percentage of observations in that bin.
In Google Sheets, the process is more manual. After entering your frequency distribution with values in one column and frequencies in another, you add a third column for relative frequency. In that column, you divide each frequency by the sum of all frequencies. For example, if your frequencies run from row 2 to row 12 in column B, you’d enter a formula like =B2/SUM(B$2:B$12) and fill it down. Then you chart the relative frequency column as a bar graph.
Why Relative Frequencies Matter for Probability
Relative frequency histograms do more than describe data. They connect directly to probability. When all the bar heights add up to 1, the histogram starts to resemble a probability density function, which is the smooth curve that statisticians use to model how a variable is distributed in an entire population.
There’s a more precise version called a scaled relative frequency histogram, where the y-axis is adjusted so that the area of each bar (not just its height) equals the relative frequency. This means the total area under all the bars equals 1, just like the total area under a probability density curve. With enough data and narrow enough bins, this type of histogram closely approximates the true underlying distribution of the variable. This is why statistics courses introduce relative frequency histograms early: they’re the visual bridge between “here’s what our sample looks like” and “here’s the probability model for the whole population.”
When to Use One Instead of a Regular Histogram
A standard frequency histogram works fine when you’re exploring a single dataset and care about raw counts. If you’re a teacher looking at how many students scored in each grade range, raw counts are perfectly informative.
Relative frequency histograms become the better choice in a few specific situations:
- Comparing groups of different sizes. If you want to compare exam scores between a class of 30 and a class of 150, relative frequencies let you see whether the distributions have the same shape without the larger class dominating visually.
- Communicating proportions. A shop tracking sales might want to know whether at least 5% of items sold fall in a premium price range. A relative frequency histogram answers that question at a glance.
- Estimating probabilities. If you want to estimate the likelihood that a randomly chosen data point falls in a particular range, the relative frequency of that interval gives you a direct estimate.
The underlying data and the bins are identical in both types of histogram. The only decision is whether your audience (or your analysis) benefits more from seeing counts or proportions. When in doubt, proportions are usually more interpretable, especially for anyone who doesn’t know the total sample size.