How can you calculate an average from a histogram?

To calculate an average from a histogram, it is essential to understand how to utilize the data represented within the histogram effectively. The correct method involves calculating the mid-interval value for each bar (or bin) of the histogram, then multiplying each mid-interval by its corresponding frequency to get a product, known as fx. This process captures the contribution of each interval to the overall average.

Once you have calculated the sum of these products (fx), you can then find the total frequency by adding together all the frequencies from each interval. Finally, the average (mean) is obtained by dividing the total of the fx values by the total frequency. This approach allows you to accurately account for all data points represented in the histogram, weighted by how many times they occur.

Other options do not effectively lead to an accurate calculation of the average. For instance, simply adding frequencies and finding a mean or counting the number of bars does not consider the values represented by those frequencies. Dividing total frequency by the number of intervals would yield a value that does not represent the true average since it doesn’t factor in the actual values of the mid-intervals. Thus, the second option is a comprehensive and rigorous method for calculating the average from the data shown in a histogram