An interval on a graph is the consistent spacing between values marked along an axis. On a y-axis labeled 0, 10, 20, 30, 40, the interval is 10. On an x-axis showing months, the interval is one month. These evenly spaced steps give a graph its structure and let you read values accurately by creating a predictable scale.
The word “interval” also describes any range between two values on a graph, such as “the interval from 3 to 7 on the x-axis.” Both meanings come up constantly in math and data visualization, so understanding each one will help you read and build graphs with confidence.
Axis Intervals: The Scale of a Graph
Every graph has at least two axes, and each axis needs a scale. The interval is the distance between one labeled tick mark and the next. If you’re plotting test scores that range from 50 to 100, you might set your y-axis interval to 10, creating tick marks at 50, 60, 70, 80, 90, and 100. That choice of interval determines how compressed or stretched the data looks.
Good axis intervals use round, easy-to-read numbers. The UK’s Office for National Statistics recommends gridline intervals like 0, 5, 10, 15, 20 or 0, 250, 500, 750, 1,000 because they’re quick to interpret. Intervals like 0, 7, 14, 21 technically work but force the reader to do unnecessary math. Sticking to multiples of 2, 5, 10, or 25 keeps a graph clean and readable.
The interval you choose should fit your data’s range. If your values span from 0 to 12, an interval of 2 (giving you 0, 2, 4, 6, 8, 10, 12) works well. An interval of 5 would only give you three gridlines, making it hard to estimate values in between.
How Intervals Affect What You See
Axis intervals aren’t just cosmetic. They shape how a viewer interprets the data, and inconsistent or misleading intervals can distort the picture entirely.
The most common distortion is truncating the y-axis, which means starting it at a number higher than zero. A bar chart comparing sales of 98 and 102 looks nearly identical when the y-axis runs from 0 to 200. But if the y-axis starts at 95, that same 4-unit difference suddenly looks enormous. Research published in the Journal of Applied Research in Memory and Cognition found that 83.5% of participants perceived differences as larger on truncated graphs, and this effect persisted even after people were taught about the trick. The intervals themselves were fine, but the starting point made the data misleading.
Unequal intervals cause similar problems. If one section of an axis jumps by 10 and the next jumps by 50, the visual spacing no longer matches the actual data. Always check that the intervals along an axis are consistent.
Intervals as Ranges Between Two Values
Beyond axis spacing, “interval” refers to any bounded range of numbers. When someone says “the function increases on the interval from 2 to 6,” they mean the output values rise for every x-value between 2 and 6. This usage is everywhere in algebra, calculus, and statistics.
Intervals can be written in a few ways. The range “x is between negative 3 and 2, including both endpoints” can be expressed as [-3, 2]. The square brackets mean the endpoints are included, and this is called a closed interval. If the endpoints are excluded, round parentheses are used instead: (-3, 2). This is an open interval. You can also mix them. The notation [2, 7) means 2 is included but 7 is not, creating what’s called a half-open interval.
On a number line or graph, closed endpoints are shown as filled-in dots, while open endpoints are shown as hollow circles. This visual distinction matters when you’re reading a graph of a function’s domain or range, because it tells you whether the boundary values themselves are part of the set.
Intervals in Histograms and Bar Charts
Histograms use intervals in a specific way. The x-axis is divided into adjacent ranges called bins (or classes), and each bar represents how many data points fall within that range. A histogram of exam scores might use bins of 60-69, 70-79, 80-89, and 90-100. Each bin is an interval, and the width of every bin should be equal so the bars are visually comparable.
Choosing how many bins to use involves a tradeoff. Too few bins and you lose detail. Too many and the histogram becomes noisy. A common guideline called Sturges’ rule suggests setting the number of bins close to 1 + 3.3 × log₁₀(N), where N is the number of data points. For a dataset of 100 observations, that works out to about 7 or 8 bins. You don’t need to memorize the formula, but knowing that bin count should scale with dataset size helps you build more useful histograms.
Time Intervals on Graphs
When the x-axis represents time, the interval is the gap between each measurement. A time series graph might plot data every second, every day, every month, or every year, depending on what’s being tracked. Stock prices often use daily intervals. Economic indicators like the Consumer Price Index are typically plotted yearly. Business sales data frequently appears in quarterly intervals, dividing each year into four three-month periods.
The time interval you choose shapes the story the graph tells. Daily stock data reveals short-term volatility, while monthly or yearly intervals smooth out the noise and highlight longer trends. The key rule is consistency: every point on the x-axis should represent the same duration, so the visual slope of a line accurately reflects the rate of change.
Continuous vs. Discrete Intervals
The type of data you’re graphing determines how intervals work in practice. Continuous data, like temperature or weight, can take any value within a range. A thermometer doesn’t jump from 98 to 99 degrees; it passes through every fraction in between. Graphs of continuous data use line graphs or scatter plots, and the intervals on the axes represent a smooth, unbroken scale.
Discrete data, on the other hand, consists of separate, countable values. The number of students in a class is always a whole number. You can’t have 22.7 students. Bar charts and pie charts work better for discrete data because each bar represents a distinct category or count, not a continuous range. When you see a bar chart with gaps between the bars, that visual separation signals discrete intervals. Histograms, by contrast, have bars that touch because they represent continuous ranges with no gaps between them.