Using Histograms to Visualize Data Distributions

When you collect numerical data – whether it’s crop yields per hectare, livestock weights, soil pH levels, or market prices – the raw numbers alone don’t tell you much. What you really need to know is how those numbers are distributed: where do most values cluster? Are there extreme outliers? Is the spread symmetrical or lopsided? A histogram answers all of these questions in a single glance. It is one of the most fundamental tools in exploratory data analysis, and for anyone working with agribusiness data, understanding how to read and build one is a non-negotiable skill.

What is a histogram? 🔗

A histogram is a graphical representation that organizes a dataset into a series of adjacent bars, where each bar covers a specific range of values – called a bin or class interval – and the height of each bar shows how many data points fall within that range. The x-axis displays the continuous range of values divided into bins, while the y-axis shows the frequency or count of observations in each bin. Research published in the PM&R journal describes histograms as an indispensable exploratory tool for spotting outliers, skew, bimodality, and other shape features in a dataset.

The word itself traces back to Latin roots meaning “drawn fences,” which is a fitting description: the bars are drawn side by side like fence posts, with no gaps between them, to visually convey that the data is continuous – flowing from one value range directly into the next.

Histogram vs. bar chart: why the difference matters 🔗

These two charts are frequently confused because they both use rectangular bars. However, they serve entirely different purposes and should not be used interchangeably.

According to Storytelling with Data, histograms display quantitative or numerical data, whereas bar charts display categorical variables. In a bar chart, each bar represents a distinct, separate category – for example, sales of corn, wheat, and soybeans. The gaps between the bars visually reinforce that these categories are independent of each other. In a histogram, by contrast, the bars touch because the data is part of a continuous numeric scale: one bin ends exactly where the next begins. Using a bar chart for continuous data like farm income or rainfall measurements would produce a misleading visualization that hides the underlying distribution.

Another key structural difference lies in what each bar actually represents. As Domo explains, in a bar chart each bar represents a single value for a category (such as total sales for a particular month), while in a histogram each bar represents the count of data points within a numerical interval. This makes the histogram uniquely suited to answering the question: how is my data spread across a range of values?

Anatomy of a histogram: bins, frequency, and bin width 🔗

To build or interpret a histogram correctly, you need to understand its core components.

Bins (class intervals) 🔗

Bins are the equal-width intervals into which your data range is divided. If you are analyzing the weights of 200 cattle in a feedlot ranging from 300 kg to 700 kg, you might create bins of 50 kg each: 300-350, 350-400, 400-450, and so on. Each data point is counted into exactly one bin. Venngage notes that a frequency table is often built first – listing each bin alongside the number of data points it contains – before the histogram is plotted.

Bin width and its impact 🔗

The choice of bin width significantly affects what the histogram reveals. Bins that are too narrow produce a jagged, noisy chart that highlights random variation rather than meaningful patterns. Bins that are too wide compress too much information together, potentially hiding important features like a secondary peak or an outlier cluster. The PM&R journal study on histograms demonstrates this effect clearly, showing that only a balanced bin width – guided by rules of thumb such as the Rice Rule – produces a plot that reveals the true shape of the data. There is no single correct bin number, but experimenting with a few options before settling on one is standard practice.

Frequency vs. relative frequency 🔗

The y-axis of a histogram can display raw counts (how many observations fall in each bin) or relative frequency (what percentage of total observations fall in each bin). Relative frequency histograms are particularly useful when comparing two datasets of different sizes – for example, comparing the distribution of soil pH values from two farms with different total numbers of samples. Switching to percentages places both distributions on the same scale, making the comparison fair and meaningful.

Reading histogram shapes: what the distribution tells you 🔗

The most valuable information a histogram provides is the shape of the distribution. Understanding this shape is the single most important step in preliminary data analysis, because it immediately communicates the data’s central tendency, spread, and the presence of outliers or subpopulations. Here are the four main shapes you will encounter in agricultural and agribusiness data.

Normal (bell-shaped) distribution 🔗

A normal distribution produces a symmetrical, bell-shaped histogram where most data points cluster around the central mean, and frequencies taper off equally on both sides. If you measured the daily milk production of a large herd of cows under stable conditions, you would likely see this shape: most animals produce close to the average, with fewer animals at the very low or very high end. The American Society for Quality (ASQ) notes that a normal distribution means data points are roughly as likely to occur on one side of the average as on the other. This shape indicates that standard parametric statistical tests – such as t-tests or analysis of variance – are appropriate for further analysis.

Skewed distributions 🔗

Skewness occurs when the histogram is asymmetrical, with a longer “tail” extending to one side.

In a right-skewed (positively skewed) distribution, the bulk of values are concentrated on the left (lower end), and a long tail stretches to the right. Farm income data often shows right skew: most smallholder farmers earn modest incomes, but a small number of large commercial operations earn substantially more, pulling the tail outward. In this case, the mean is typically greater than the median, because the few extreme high values inflate the average. Reporting only the mean for such data would overstate typical earnings.

In a left-skewed (negatively skewed) distribution, the tail extends to the left. This happens when data has a natural upper boundary – for instance, the percentage of pest-free fruit in a high-performing orchard. Most batches may score close to 95-100%, but a few batches with pest problems pull the tail toward lower values. Here, the mean will typically be less than the median. When skewness is present, analysts are advised to use the median and interquartile range as summary statistics rather than the mean and standard deviation, since those measures are more robust to extreme values.

Bimodal distribution 🔗

A bimodal histogram has two distinct peaks, separated by a visible valley. According to ASQ, this shape typically indicates that the data comes from two different underlying processes or subpopulations that have been combined into one dataset. A classic agribusiness example: if you plot harvest weights from two different crop varieties grown in the same field without labeling them separately, you will likely see two peaks – one for each variety’s typical yield range. As SixSigma.us explains, when bimodality is identified, the correct response is to separate the two subpopulations and analyze them independently, since measures of central tendency like the mean or median become poor descriptors of the combined dataset as a whole.

Histograms as a tool in exploratory data analysis 🔗

Histograms are primarily a tool for exploratory data analysis (EDA) – the initial phase of any quantitative study where you examine your data before applying formal statistical tests. As noted in the PM&R journal, even when no histograms appear in a final published report, they are a quick and indispensable step to help researchers catch potential problems in the data and reveal interesting patterns that would otherwise remain hidden in a table of numbers.

In agribusiness contexts, data visualization tools including histograms are increasingly used to turn raw agricultural data into actionable insights – from crop production to resource allocation and predictive analytics. Some specific applications include:

• Crop yield analysis: Plotting the distribution of yields across different plots or seasons reveals whether performance is consistent or highly variable, and flags underperforming areas for investigation.
• Soil nutrient mapping: A histogram of soil pH values across a farm quickly shows whether most soils fall within the target range for a specific crop, or whether acidic or alkaline outliers need correction.
• Rainfall and irrigation planning: Distribution of monthly rainfall figures helps identify whether the farm typically receives adequate water or faces frequent shortfalls, informing irrigation scheduling.
• Market price monitoring: A histogram of commodity prices over multiple seasons reveals price volatility – whether prices cluster tightly around an average or swing widely, which has direct implications for contract pricing and risk management.
• Comparing treatments: Side-by-side histograms comparing yield distributions from two fertilizer regimes show not just differences in average yield but also differences in variability and risk profiles – information a simple mean comparison would miss entirely.

How to build a histogram: a step-by-step guide 🔗

Creating a histogram is straightforward once you have collected your data. ASQ recommends collecting at least 50 consecutive data points from a process before building a histogram, as smaller samples may not reveal a reliable distribution shape.

Step 1 – Define your range: Identify the minimum and maximum values in your dataset. For example, if you are analyzing fertilizer application rates across 80 fields ranging from 40 kg/ha to 160 kg/ha, your total range is 120 kg/ha.

Step 2 – Choose your number of bins: A commonly used guideline is the Square Root Rule: take the square root of the number of data points to estimate the number of bins. For 80 fields, that is approximately 9 bins. Other rules, such as the Rice Rule (2 × cube root of n), produce similar results. Experiment with a few bin counts to find the one that best reveals the shape of your data.

Step 3 – Set bin boundaries: Divide the total range by the number of bins to get the bin width, then set the boundaries for each interval. Ensure that every data point can fall into exactly one bin, with no overlaps.

Step 4 – Count frequencies: Build a frequency table showing how many data points fall into each bin. This table becomes the direct input for plotting.

Step 5 – Plot and label: Draw adjacent bars with heights corresponding to the frequency of each bin. Label the x-axis with the numeric intervals and include units of measurement. A histogram showing “Number of fields” versus “Fertilizer application rate (kg/ha)” is far more informative than one with unlabeled axes. Adding vertical lines for the mean and median overlaid on the histogram helps viewers understand central tendency at a glance.

Tools commonly used for plotting histograms in agribusiness analysis include Microsoft Excel (using the Data Analysis ToolPak), R, Python (matplotlib or seaborn libraries), and business intelligence platforms like Power BI, which support customizable dashboards for agricultural data.

Common mistakes to avoid 🔗

Even a well-intentioned histogram can mislead if constructed carelessly. The most frequent errors include choosing bins that are too wide (hiding meaningful patterns) or too narrow (introducing visual noise), and failing to label axes with units. Another critical issue is drawing a histogram for categorical data – for instance, plotting crop types on a histogram instead of a bar chart. As Highcharts explains, histograms are specifically designed for continuous numerical variables; applying them to categories produces a chart that is structurally incorrect and difficult to interpret accurately.

It is also worth remembering that a histogram is a snapshot of a sample, not an exact portrait of the population. Small samples in particular may show irregular shapes that smooth out with more data. Treating a histogram as definitive proof of normality or skewness without corroborating statistical tests can lead to flawed analytical decisions downstream.

What do you think? If a histogram of your farm’s crop yields showed a bimodal distribution, what would be your first step in investigating the cause – and how would that finding change your approach to data-driven decision-making in future seasons? Could visualizing your agribusiness data with histograms reveal patterns that a simple average has been hiding from you all along?

References

1. https://www.ers.usda.gov/data-products/data-visualizations
2. https://www.wiley.com/en-us/Histograms%3A+A+Useful+Data+Analysis+Visualization-p-9780470387986
3. https://www.storytellingwithdata.com/blog/2021/1/28/histograms-and-bar-charts
4. https://www.domo.com/learn/charts/histogram-vs-bar-graph
5. https://venngage.com/blog/bar-charts-vs-histograms/
6. https://onlinelibrary.wiley.com/doi/full/10.1002/pmrj.12145
7. https://scales.arabpsychology.com/stats/how-would-you-describe-the-shape-of-histograms-with-examples/
8. https://asq.org/quality-resources/histogram
9. https://www.6sigma.us/six-sigma-in-focus/bimodal-histogram/
10. https://agtech.folio3.com/blogs/data-visualization-in-agriculture/
11. https://www.highcharts.com/blog/best-practices/bar-graph-vs-histogram-how-to-distinguish-and-use-them-correctly/