Frequency histograms are one of the most basic data analysis tools. I’ve personally used frequency histograms to discover countless insights in industrial equipment performance data. You’ll also use them regularly to visualize data distributions and spot insights. So, how can you use frequency histograms to improve your operations and achieve success?
Frequency Histogram Fundamentals
Frequency histograms are one of the most powerful data distribution visualization tools. I’ve personally leveraged frequency histograms countless times throughout my engineering career to analyze equipment performance trends. In essence, a frequency histogram is simply a set of vertical bars positioned above classes, with the height of each bar being the frequency of that class. By viewing data visually in this way, you can immediately understand the shape and spread of your data.
Therefore, the primary purpose of a frequency histogram is to display a dataset’s distribution. Specifically, you can see how frequently different values fall within predetermined classes or bins. If you’re analyzing data, this is your chance to uncover patterns, trends, or anomalies that are present in your data.
The frequency histogram contains the following key components:
- The vertical axis (y-axis): This axis represents frequency or count.
- The horizontal axis (x-axis): This axis includes the data’s bins or ranges.
- Bars: Each bar’s height represents the frequency of data points within that bin.
- The bin width: This refers to the amount of data each bar covers.
Remember, a frequency histogram is different from other chart types, like a bar chart or line graph. While you might view bar charts to compare discrete categories, a frequency histogram is helpful when you have continuous data distributions. And while you might leverage a line graph to understand trends over time, a histogram is beneficial when you need to understand the data distribution at a specific point in time.
When it comes to data analysis, frequency histograms are incredibly powerful for understanding data properties. They make it easy to identify outliers, skewness, and multimodal distributions. You can also use them to compare datasets, analyze a process’s capability, or make a data-driven decision if you understand the data’s properties. For instance, understanding these data properties can enhance your process optimization efforts.
Plotting Data Distribution
- Gather your data
- Identify the range of your data
- Select the number of bins
- Calculate bin width
- Create a frequency table
- Draw the ‘x’ and ‘y’ axes
- Plot the bars
- Add titles and legends
Selecting the right class intervals and bin width is essential. Too few bins won’t capture enough of the data, while too many will create noise. One quick tip is to use the square root of the data points you have as the number of bins. You can scale this rule of thumb according to your data.
Calculating frequencies involves tallying how many data points fall within each bin. You may also calculate relative frequencies, which represent the proportion of the data in each bin out of the entire dataset.
When you create your histogram, ensure the bars touch if you’re working with continuous data. Make the axes clear and label them. Use equal scales for accuracy.
Tips for a great histogram:
- Use equal bin widths to simplify interpretation
- Align bar heights with the frequency values
- Use a relevant scale to highlight data patterns
- Leverage colors for improved readability
Keep in mind that a histogram designed effectively can expose insights that you would not otherwise find by staring at the raw numbers.
Interpreting Frequency Histograms
Interpreting frequency histograms is really where the magic happens. I’ve used the insights from different histogram shapes throughout my career, and I’ve often found that different histogram shapes tell you something really important about a process or system.
Common frequency curve shapes include symmetrical/bell-shaped, skewed, J-shaped, U-shaped, and multimodal, and each shape tells a different story about your data:
- Symmetrical/bell-shaped: Indicates a normal distribution, which is common in many natural processes
- Skewed: Indicates that the distribution is asymmetric and might suggest process issues or the presence of outliers
- J-shaped: Commonly seen in reliability data (e.g., product lifetimes)
- U-shaped: Often seen when the process might be following two different distributions (or two different processes)
- Multimodal: Indicates that there are multiple peaks in the distribution (and possibly that there are different distributions, and different processes, at work)
Identifying central tendencies is simply a matter of looking at where most of your data occurs. The peak of your histogram likely represents the mode, or the most common value.
Identifying outliers is arguably the most important task of all. These are data points that don’t appear to fit the main distribution of data, and by analyzing histograms, you can easily spot them. Outliers could be measurement errors, truly exceptional events, or something wrong with your process.
Common mistakes to avoid when interpreting histograms:
- Assuming everything should be normally distributed
- Neglecting to check the scale of the axes
- Overanalyzing tiny differences
- Forgetting to consider the big picture of what the data you’re analyzing is actually doing
Best practices to draw conclusions:
- Always keep track of what the data actually is.
- Look for trends and patterns in the data, and don’t just stare at individual bars.
- Compare your conclusions to some kind of relevant benchmark or standard.
- If at all possible, use a statistical test to verify your conclusions.
Remember, histograms are a powerful tool, and they’re also just one step in a comprehensive data analysis process.
Statistical Measures from Frequency Histograms
Calculating statistical measures from frequency histograms allows you to gather quantitative insights in addition to your qualitative visual analysis. The main statistics you can calculate from a frequency distribution are the mean, median, mode, range, and standard deviation.
Calculating the mean from a histogram involves selecting the midpoint of each bin multiplied by the frequency of that bin and dividing by the total number of data points. It’s an approximation because you’re using the midpoint of each bin rather than the exact value.
The median is the middle value of your data set when it’s ordered. In a histogram, you can estimate this by finding the bin that includes the data point in the middle of your data set.
The mode is the bin with the highest frequency. You can easily identify this in your histogram as it will be the tallest bar.
The range is simply the highest bin minus the lowest bin.
Calculating standard deviation from a histogram is a bit trickier. You use the midpoints and frequencies of each bin to estimate the variance and then take the square root of that number.
As you analyze each of these measures, keep in mind:
- The mean is sensitive to outliers.
- The median is a more robust measure of central tendency to extreme values.
- The mode indicates the most common value or range.
- The range gives you a quick sense of how spread out your data is, though it’s also significantly affected by any outliers.
- The standard deviation tells you how much your entire dataset varies from the mean.
These are all excellent statistics to know, but remember that you’re ultimately working with binned data, and these figures aren’t necessarily 100% accurate as a result. Always look at these figures in conjunction with your qualitative visual understanding of the data set.
Software for Graphing Data Distributions
The most common options are:
- Microsoft Excel
- R
- Python (and libraries like Matplotlib)
- SPSS
- Minitab
Here’s a comparison of each software’s features and ease of use:
| Software | Ease of Use | Customization | Statistical Features |
|---|---|---|---|
| Excel | High | Medium | Basic |
| R | Low | High | Advanced |
| Python | Medium | High | Advanced |
| SPSS | Medium | Medium | Advanced |
| Minitab | High | Medium | Advanced |
To make a histogram in Excel:
- Enter your data in a column.
- Select the data.
- Go to Insert > Charts > Histogram.
- Adjust the bin width if you’d like.
Excel is very easy to use, but the statistical features are limited. If I plan to do more complex statistical analysis, I use R or Python. Both offer more flexibility and statistical capabilities.
Dedicated statistical software, like SPSS or Minitab, offers more advanced histogram features. In these tools, you can do things like automatically optimize the bin size, run a normality test, and overlay theoretical distributions.
Select the right software for your needs based on the data you have and the statistics you need to do.
Distribution Plot Uses
Histograms are applicable to a wide range of use cases. I’ve seen them used successfully in manufacturing process improvement and data driven decision making.
In manufacturing, histograms are great for identifying process capabilities and potential quality problems. For example, if the distribution of a product’s dimensions is skewed, this might be a machine calibration problem.
Quality control teams use histograms to keep an eye on defect rates and identify where to make process improvements. If the distribution is multimodal, this likely suggests there are multiple sources of defects and you’ll need a separate intervention for each.
Businesses use histograms to understand customer behavior. For example, a U.S. Census Bureau study found there are 124 million people who work outside of their homes. A histogram of commute times may help businesses understand when people are traveling so you can optimize store hours or delivery times.
In environmental science, histograms are great for analyzing pollution levels or species distributions. If a distribution is skewed, this likely means there’s a local source of pollution or the species has a habitat preference.
In my opinion, histograms are an excellent tool for data driven decision making. They provide a clear, visual view of data, which makes it easy to pick up on a trend or issue. This allows you to make a decision faster and with more confidence, as well as be a more effective problem solver.
While histograms are great, they still are just one tool in your analytical tool belt. Always use histograms in combination with other analyses to build a complete picture of your data.
Final Takeaways
Frequency histograms are one of the most useful data analysis tools. They offer a clear visual of how data is distributed, which is critical to making data-driven decisions. I can’t tell you how many times I’ve watched engineers misinterpret histograms and make costly errors as a result.
Just keep in mind the context of your data and avoid jumping to conclusions too quickly. With experience, you’ll build an intuitive sense of what each histogram shape means. This skill will serve you well in your career as a continuous improvement.
