Histogram

Histogram is a graphical representation of numerical data organized into groups.

A histogram typically displays data intervals (bins) on the X-axis and the frequency of data points within each interval as bars on the Y-axis. Karl Pearson developed a similar type of bar chart in 1891 to describe continuous data distributions and coined the term “histogram” for this new graphic. Pearson derived the term from the idea of presenting data distributions as a “historical diagram.” Over time, histograms became one of the fundamental tools in statistics and quality control. For example, in a quality process, control charts, Pareto diagrams, and histograms are used to analyze the distribution of a data set. Histograms visually reveal the central tendency, spread, and shape of the data such as skewness or multimodal distributions.

Histograms visualize the distribution of data. For instance, the example histogram above contains 100 randomly selected observations from a data set exhibiting a normal distribution. The height of each bar represents the number of values falling within each bin. Whether the histogram shape is symmetric or skewed provides clues about the proximity or distance between measures of central tendency such as the mean, median, and mode. Historically, the type of graph defined by Pearson emphasizes the continuity of numerical data.

Purpose of Histograms in Project Management

In project management, histograms are used to summarize large data sets in an understandable manner. For example, in resource planning, daily or weekly resource requirements derived from man-hour estimates can be displayed using a histogram, making variations in resource demand apparent and providing a basis for schedule revisions. Resource histograms are among the most commonly generated charts in tools like Microsoft Project and enable visualization of fluctuations in resource demand. Additionally, histograms are used to visualize current performance or quality data collected during the project such as volume of completed work, delay durations, or number of defects. These charts support decision-making by providing the project team with an overview of the data. For instance, project management tools like Asana recommend visualizing data using bar charts; a histogram is a numerical adaptation of such bar charts. While bar charts display categorical distributions, histograms present numerical data divided into intervals. Thus, histograms help identify distribution characteristics of numerical project indicators such as duration times or cost distributions.

The primary purposes of histograms in project management are:

• Distribution Analysis: To visualize the spread of values for a measured project variable such as duration or cost. Histograms reveal structures such as normal, skewed, or multimodal distributions.
• Decision Support: The distribution pattern observed in a histogram aids in making decisions regarding project progress. For example, if a histogram of assembly times shows high-frequency deviations within a specific range, this may prompt an investigation and improvement of the process.
• Communication and Reporting: Histograms can summarize situations with high concentration for project stakeholders. For example, the distribution of completed work volume across intervals illustrates the overall performance profile of the project.
• Resource Selection and Planning: Information derived from histograms guides resource allocation and planning. A resource requirement histogram clarifies variations in team or team member workloads and supports recommendations for resource leveling.

Use of Histograms in Quality Management and Risk Analysis

In quality management, histograms are used to visualize the frequency of errors or defects. According to PMI sources, histograms are among the frequently used tools in quality control processes alongside trend charts and control charts. For instance, in a production project, the frequency of different types of defects can be presented in histogram form, with defect categories on the horizontal axis and the number of defects per category on the vertical axis. The resulting histogram clearly identifies the most frequently occurring problems, enabling stakeholders to prioritize areas for improvement. The tallest bars in the histogram indicate the problem sources requiring the most attention.

In risk analysis, distributions obtained from techniques such as Monte Carlo simulation are graphically represented using histograms. For example, when numerous random trials are conducted to estimate a project’s completion time or cost, the results are aggregated into a histogram. This histogram shows the approximate probability distribution of possible outcomes. The mean of the distribution provides the expected value (EMV), while the shape of the histogram reveals the asymmetry and degree of uncertainty. PMI sources note that the shape of simulation output histograms tends to approximate the original probability distribution. Thus, histograms contribute to quantifying risk by serving as a fundamental tool in the uncertainty performance area.

Relationship with PMBOK 7 Performance Areas

The relationship of histograms with the performance areas in the PMBOK Guide Seventh Edition can be summarized as follows:

• Measurement Performance Area: Evaluating and tracking project performance is a core objective of the Measurement area. Histograms contribute to analyzing project performance data by showing the frequency distribution of variances in time or cost. Various indicators and distributions used in performance measurement can be visualized using histograms.
• Planning Performance Area: The Planning area encompasses the organization and coordination required to produce project outputs. In the resource planning process, histograms visualize daily or weekly resource requirements derived from man-hour schedules. Since PMBOK 7 considers planning a continuous and evolving process, histograms provide data support for plan revisions and resource leveling.
• Delivery/Quality Performance Area: The Delivery area focuses on meeting project requirements, scope, and quality expectations. The use of histograms in quality management processes supports quality control steps. For example, a histogram of quality measurements from production processes illustrates the spread of deviations from quality targets. Histograms are regarded in PMBOK as one of the key statistical tools for analyzing quality outputs.
• Uncertainty Performance Area: The Uncertainty area covers activities related to risk and uncertainty. Histograms visualize the distribution of variables under uncertainty, shedding light on risk analysis results. In uncertain projects, such as those using Monte Carlo simulation outputs, histograms display the frequency of possible outcomes, facilitating the understanding of threats and opportunities. Thus, histograms play a significant role in decision-making under uncertainty.

Creation Process

The process of creating a histogram generally follows these steps:

• Data Collection: Gathering relevant measurements for the variable to be displayed in the histogram, typically through control charts or data collection forms.
• Determining Number and Width of Bins: Selecting an appropriate number of bins and defining the width of each interval to cover the data range (for example, choosing between 5 and 15 bins based on the data distribution).
• Defining Bin Limits: Clearly establishing the lower and upper boundaries of each bin, ensuring no overlap between bins.
• Calculating Frequencies: Counting the number of data points falling within each bin interval and recording them in a tally sheet or table.
• Visualization: Representing the calculated frequencies as vertical bars, where the height of each bar corresponds to the bin frequency and the width corresponds to the bin interval. At this stage, axes are labeled and necessary annotations are added.

During this process, care must be taken in selecting the number and width of bins according to the type of numerical data. Excessively wide bins may obscure distribution details, while excessively narrow bins may produce overly fluctuating graphs. It is essential to define meaningful bins and ensure a sufficient sample size for analysis.

Tools and Software Used

Histograms can be created using various general-purpose and specialized software:

• Excel: Histograms can be easily drawn using Microsoft Excel’s statistical chart tools. For example, frequency data entered into Excel can generate an automatic histogram by selecting the histogram chart type from the “Insert” menu.
• Minitab, R, Python: Statistical analysis software provides histogram functions. In Minitab, the Graph > Histogram option allows histogram creation; in R or Python, built-in histogram commands generate histograms based on data.
• Microsoft Project: With its resource management features, MS Project creates resource histograms using resource assignments in the project plan. These histograms show the distribution of resources over time.
• Project Management Tools (e.g., Asana): While tools like Asana do not directly generate histograms, they support reporting and export features that allow project data such as task durations or output counts to be exported to Excel and converted into histograms. PMI sources provide examples of developing histograms in Excel, and project tools facilitate access to similar data.

These tools offer varying levels of flexibility and visualization options according to user needs. For example, Minitab provides options for automatic bin selection and customization of histogram appearance.

Interpretation of Histograms and Decision-Making

Histograms guide the process of extracting and analyzing distribution characteristics of a data set. The height of each bar indicates the number of observations within that bin interval, thereby visually revealing measures of central tendency and spread. For instance, in the above histogram (showing U.S. state areas), tall bars clustered in a specific range indicate concentrations, while skewness or multimodality reveals underlying patterns. Differences between bars or the number of peaks indicate heterogeneity within the underlying process or data set. During interpretation, decision areas are identified by examining which values fall within the highest-frequency bin. In quality management, the peaks in a histogram indicate the most frequently occurring defects and direct preventive or corrective actions to those areas. In risk analysis, the mean of the histogram represents the expected value (EV), while its shape reflects the level of uncertainty, allowing simulation outputs to estimate the probabilities of possible outcomes.

Several details must be considered when interpreting histograms. For example, structures such as skewness or bimodality reveal complex underlying data distributions and may require further investigation. Additionally, data gaps (due to data collection errors) or outliers may appear as isolated tall bars and must be evaluated. Accurate interpretation requires consideration of the data context, assumptions made during histogram creation, and potential data errors.

Considerations to Keep in Mind

Effective use of histograms requires awareness of certain limitations. If inappropriate bin widths are selected (too wide or too narrow), the histogram may be misleading or inaccurate; the starting point of bins also affects the result. As one research finding notes, “the choice of bin number and starting point can significantly influence the visualization and may conceal data characteristics.” Furthermore, histograms only display the frequency distribution of a single variable; they do not reflect relationships between variables or temporal dynamics. For example, while process control charts track changes over time, histograms lack a time axis. Histograms do not present the exact values of data points; they only show the general distribution of frequencies. Therefore, when interpreting histograms, the size of the data set, measurement range, and conditions of data collection must also be taken into account.

In resource usage, it is important to avoid overinterpreting histograms. For example, histograms may not yield reliable results with small data sets. Additionally, too many bins or too few data points can distort the pattern observed in the histogram. When these limitations are considered, histograms should be used in conjunction with other analytical tools such as control charts, distribution plots, and graphical summaries, and interpretations must always be grounded in the detailed characteristics of the available data.