Histograms (Higher Tier)

Understanding Histograms

A histogram is a type of bar chart that graphically displays the frequencies of a given data set.
Unlike bar charts, histograms have bars that are adjacent to one another, without gaps, indicating that the data is continuous rather than discrete.
The horizontal axis of a histogram, also known as the x-axis, represents the variable being measured, while the vertical axis, the y-axis, represents the frequency of the measurements.
Histograms are widely used in statistics to show the distribution of data.

To create a histogram, first organise the data set into a frequency distribution table.
The frequency distribution table classifies the data into classes (also known as bins or intervals), and then counts the number of data points in each class.
Next, draw a bar for each class. The height of each bar corresponds to the frequency of the corresponding class.
The width of the bars corresponds to the range of each class.

To determine the frequency of a class from a histogram, simply look at the height of the bar for that class.
A histogram can be used to ascertain modal class, which is the class with the highest frequency.
Histograms provide insight into the distribution of data, revealing patterns such as symmetry, skewness, and peaks (modes).

Histograms are most effective with larger data sets. Smaller data sets may not display a clear pattern.
The appearance of the histogram can change if the width of each class or the starting point of the first class is varied.
While histograms can provide a general sense of the distribution of data, they don’t provide specific values.

The appearance of a histogram can be altered by changing the number of classes or the class width.
More classes or a smaller class width can give more detail, but might also display noise in the data. Conversely, fewer classes or a larger class width can smooth the data, but also lose details.
A careful balance needs to be struck when adjusting histograms to ensure that a useful representation of the data is achieved.

In some cases, the class intervals in a histogram might not be equal. For these histograms, the height of each bar is modified to ensure it reflects the correct frequency density, rather than the absolute frequency.
Frequency density is calculated by dividing the frequency of each class by the class width.
The area of each bar in these histograms corresponds to the actual frequency of each class, making them suitable for accurately depicting data with unequal classes.