Histograms and Frequency Density

Understanding Histograms

A histogram is a type of graphical representation of data that displays the distribution of data.
Unlike a bar chart, histograms are used for continuous data where the bars represent intervals of data.
The width of each bar represents the class width or interval, while the height represents the frequency density.
Each bar in the histogram does not display the number of data points (frequency), but rather the frequency density - the frequency divided by the class width.
There should be no gaps between bars in a histogram as this indicates that the data is continuous.

Creating a Histogram

When preparing a histogram, the first step is to group the data into class intervals.
The class width must be decided so that each bar spans a particular range of values.
Once the class intervals are defined, the next step is to calculate the frequency density.
The frequency density is calculated by dividing the count for each group (frequency) by the class width.
Plot the histogram with the class intervals on the x-axis and the frequency density on the y-axis.
The area of each bar in the histogram equals the frequency of the data group it represents.

Interpreting Histograms

Histograms provide a visual representation of data distribution. The taller the bar, the greater the frequency density for that interval.
Histograms can show different types of distribution such as normal distribution, where most data falls in the middle with symmetrical spread on either side, and skewed distribution, where the data is not evenly spread.
Peaks in a histogram are known as modes. A histogram may have one peak (unimodal), two peaks (bimodal), or several peaks (multimodal).
A gap in a histogram indicates an absence of data in that particular value range.

Applications of Histograms

Histograms are very useful in statistics and probability for understanding the distribution and density of data.
They are applied in various fields such as finance, health sciences, social sciences, and engineering, to name but a few.
Histograms can help in identifying patterns, trends and outliers in data.
They also make it easier to compare data sets and can be used to make predictions.