What Is a Histogram? How to Read One

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A histogram is a chart that shows how numerical data is distributed. It sorts values into consecutive ranges, called bins or intervals, and draws a bar for each range whose height shows how many observations fall inside it. Because the ranges cover a continuous scale with no breaks, the bars touch. The result shows at a glance where values cluster, how widely they spread, and whether the distribution is balanced or leans to one side.

How a Histogram Works

Every histogram is built from two decisions: how to divide the range of values into bins, and what to measure on the vertical axis.

The horizontal axis (x-axis) holds the variable being measured, such as ages, minutes or percentage returns, divided into intervals of equal width in the standard form. Each value has to land in exactly one bin, so a boundary rule is needed. A common convention includes the lower edge and excludes the upper edge, so a value of exactly 20 belongs to the 20 to 30 bin, not the 10 to 20 bin.

The vertical axis (y-axis) can show one of three measures:

• Frequency: the raw count of observations in each bin.
• Relative frequency (percentage): each count divided by the total number of observations. This lets you compare datasets of different sizes.
• Density: relative frequency divided by bin width. With density, the area of each bar represents the share of observations, and the total area of all bars equals 1. This is the version statisticians use when comparing a histogram with a theoretical curve such as the normal distribution.

Interpreting a Histogram

Reading a histogram starts with three questions: where is the center, how wide is the spread, and what is the shape?

• Symmetric (bell-shaped): the tallest bars sit in the middle and the sides fall off evenly. The mean and median are close together.
• Right-skewed (positively skewed): most values are on the left with a long tail stretching right. Income and home prices often look like this. The mean is pulled above the median.
• Left-skewed (negatively skewed): the long tail runs to the left, and the mean sits below the median.
• Bimodal: two separate peaks, which often means two different groups have been mixed in one dataset.
• Uniform: bars of roughly equal height, meaning values are spread evenly across the range.

Look also for gaps (empty bins inside the range) and isolated bars far from the rest, which may be outliers or data-entry errors.

Example of a Histogram

Hypothetical example for illustration only. An investor records 40 daily percentage returns for a stock and groups them into 1-percentage-point bins, with each bin including its lower edge:

Plotted as a histogram, the two tallest bars sit on either side of zero, and they hold 28 of the 40 days, or 70%. The distribution is roughly centered near zero with thin tails on both sides, and slightly more days fall in the 1% to 2% bin than in the −2% to −1% bin. If the bins were widened to 2 percentage points, the chart would show only three bars, and the slight lean toward gains would be harder to see.

How to Make a Histogram

1. Collect numerical data. Histograms need quantitative values (measurements or counts), not categories.
2. Find the range. Subtract the minimum from the maximum.
3. Choose the number of bins. There is no single correct number. A traditional starting point is Sturges’ rule, k = 1 + log₂(n), where n is the number of observations. For 40 data points, that gives about 6.3, so six or seven bins.
4. Set the bin width. Divide the range by the number of bins and round to a convenient figure. Keep all intervals the same width.
5. Count observations per bin and record them in a frequency table.
6. Draw the chart: intervals on the x-axis, frequency (or percentage or density) on the y-axis, and one bar per bin with no gaps between bars.

Histogram vs. Bar Chart

Both use rectangular columns, so the terms are often used interchangeably, but they answer different questions.

• Data type: a histogram shows the distribution of one numerical variable. A bar chart compares discrete or categorical items, such as revenue by product line or market share by company.
• Gaps: histogram bars touch because the intervals are continuous. Bar chart bars are usually separated because the categories are distinct.
• Meaning of width: in a histogram, width represents a range of values and is meaningful. If bins have unequal widths, density (area) rather than height must carry the comparison. In a bar chart, width is decorative and only height matters.
• Order: histogram bins must follow numerical order. Bar chart categories can be rearranged, for example from largest to smallest.

A related idea is the frequency polygon, which connects the midpoints of the tops of histogram bars with lines. It shows the same distribution and can make it easier to overlay two datasets.

The MACD Histogram in Trading

Technical traders meet a different “histogram” on price charts. The moving average convergence divergence (MACD) indicator has three parts:

• MACD line = 12-period EMA − 26-period EMA (EMA is the exponential moving average)
• Signal line = 9-period EMA of the MACD line
• MACD histogram = MACD line − signal line

Each bar shows the gap between the two lines for one period. A bar is positive (above zero) when the MACD line is above the signal line and negative when it is below. Growing bars indicate strengthening momentum in that direction, and shrinking bars indicate fading momentum. A bar at zero marks a crossover.

Traders watch the histogram because crossovers of the MACD and signal lines lag price: both lines are built from moving averages. The histogram can warn earlier. When bars start shrinking toward zero, the gap between the lines is narrowing before the crossover occurs. Some traders treat a bar shorter than the one before it as a signal and wait for that bar to complete before entering in the direction of the decline.

This is a momentum tool, not a statistical distribution. Its bars are plotted in time order, not by frequency. It also produces false signals in choppy markets, which is why traders typically confirm it with other indicators and use stop-loss orders in case price does not follow through.

Limitations of a Histogram

• Bin choice shapes the story. Too few bins hide detail, while too many make random noise look like structure. The same data can look smooth or jagged depending on width and starting point, so trying several bin widths before settling on one is common practice.
• Individual values disappear. Once data is binned, you cannot recover exact observations or identify which data points sit in which bar.
• Time order is lost. A histogram of returns shows how often each size of move happened, not when. A cluster of losses in one month and the same losses spread over a year produce identical charts.
• Sample size matters. With few observations, the shape can change sharply when a handful of data points are added.

FAQs

The Bottom Line

Anyone reading return distributions, price data or survey results can use a histogram to see where values cluster, how widely they spread and whether they lean to one side. Because bin width can change the picture, test several widths before drawing conclusions. Traders should also keep the MACD histogram separate in their minds, since it tracks momentum over time and gives false signals in choppy markets.