Histograms – GCSE Further Mathematics CCEA Revision

Histograms are graphical displays of data which use rectangles to represent the frequency of data items in successive numerical intervals of equal size.
The horizontal axis represents the values of the variables. This is also known as the ‘base’ of the rectangles.
The vertical axis represents the frequency of the variables. The area of each rectangle is proportional to its corresponding frequency.
Height of Rectangle in histogram represents the frequency density. Frequency density is calculated by Frequency ÷ Class Width.
Class widths in a histogram do not always have to be the same.
The ‘bins’ or ‘class intervals’ represent the scale of values on x-axis.
No gaps are left between bars in a histogram as it displays continuous data.

Histograms are useful for interpreting and analyzing data distribution.
Look for symmetry, peaks (modes), skewness and outliers in a histogram to determine distribution type.
The peak of a histogram shows the most common value(s), also known as the mode.
If a histogram is symmetrical, it is likely to show a normal distribution.
The area in a histogram can be used to determine the probability that a variable falls within a specific range.

When constructing histograms, identify the range (max - min) and decide the class interval or width.
Calculate the Frequency Density = Frequency ÷ Class Width for each class interval.
Plot the class interval (or ‘bin’) on the x-axis and the frequency density on the y-axis.
Draw rectangles with width equal to the class interval and height equal to the frequency density.
It’s useful to include a title, labels and a key when drawing histograms.

Histograms can provide a general idea about the distribution of data, but detailed comparisons are difficult.
Outliers may not be visible if the range of data is large.
The appearance of a histogram can be affected greatly by the number of rectangles or class intervals used.