Histogram definition
A histogram is a statistical graph used to display grouped numerical data, especially continuous data. Continuous data can take any value within a range, such as height, time, mass, length or temperature. A histogram looks a little like a bar chart, but the bars usually touch because the data is arranged in continuous intervals rather than separate categories.
The most important idea in a histogram is that the area of each bar represents the frequency. This is different from many simple bar charts, where the height of the bar directly shows the frequency. In a histogram, the height may show frequency density, especially when the class intervals have different widths. This means students must look carefully at the scale and the class widths before reading the graph.
Histograms are used in statistics, data handling, grouped frequency tables, probability, science experiments, geography, business data and real-life research. At GCSE level, students may be asked to draw a histogram, complete a missing bar, calculate frequency density, estimate frequency from a bar area, or compare the distribution of data. Histograms help students see patterns such as spread, clusters and skew.
A class interval is a range of values, such as 0 to 10, 10 to 20 or 20 to 30. The class width is the size of the interval. For example, the interval 10 to 20 has width 10. If all class widths are equal, the histogram can look similar to a bar chart. If class widths are unequal, frequency density must be used so that the area of each bar still correctly represents the frequency.
The key formula is frequency density = frequency divided by class width. For example, if a class interval has frequency 30 and class width 5, the frequency density is 30 divided by 5, which equals 6. The bar would have height 6. If another interval has frequency 30 but class width 10, its frequency density would be 3, so the bar would be lower but wider. Both bars can still have the same area and therefore the same frequency.
Histograms are different from bar charts. A bar chart is used for separate categories, such as favourite sports or colours, and the bars normally have gaps. A histogram is used for grouped numerical data and the bars touch. In a histogram, the width of a bar matters because it represents the size of the class interval. This distinction is important in GCSE statistics questions.
A histogram can also be used to estimate information about a data set. The tallest bar shows the interval with the greatest frequency density, but not always the greatest frequency if widths are different. Students should use area, not just height, when comparing frequencies. This is a common source of mistakes in exam questions.
Related ideas include frequency tables, grouped data, class intervals, class width, frequency density, bar charts, averages, range, distributions and probability. A clear definition of histogram helps students understand that it is not simply a bar chart with touching bars. It is a graph where area carries the meaning of frequency, making it powerful for displaying continuous data.