Finding the mean in a histogram (exam question)

A histogram is a graphical display of data using bars to reflect the frequency of occurrences for intervals, or bins, of data.
The mean represents the central value of a set of data, and can be interpreted as the ‘balance point’ of the histogram.
Each bar on the histogram represents a class, the pivot points of these classes are known as the class midpoints.
The frequency refers to the number of data points within each class, represented by the height of the bars.

To calculate the mean from a histogram, you need both the class midpoints and the class frequencies.
The midpoint of each class (class midpoint) can be calculated by finding the average of the lower and upper boundaries of each class.
The product of the class midpoint and the frequency gives the total value for that class, known as the class total.
The summation of all the class totals gives the total of all values in the dataset.
The mean is calculated by dividing the total of all values by the total frequency.

The mean is a measure of central tendency, and informs us about the balance point of the dataset.
The position of the mean on a histogram can provide insight into the symmetry or skewness of the data.
A perfectly symmetrical histogram will have its mean at the centre.
If the histogram is skewed to the right or left, the mean will also shift in that direction.

Get plenty of practice in identifying class midpoints and their corresponding frequencies from a given histogram.
Work on exercises that require calculating the mean. This involves adding up all the class totals and dividing by the total frequency.
Understand what the mean of a dataset tells you about the distribution of the values in a histogram.
Reinforce your learning by interpreting the position of the mean in relation to the skewness or symmetry of the dataset.