To calculate the mean from a histogram, follow these steps: multiply the midpoints of each class interval by their corresponding frequencies, sum these products, and then divide by the total frequency.

First, determine the midpoints of each class interval in the histogram. The midpoint is calculated as the average of the upper and lower boundaries of each class. For example, for a class interval spanning from $10$ to $20$, the midpoint is computed as:

Next, identify the frequency for each class interval. The frequency corresponds to the height of the bar in the histogram, indicating how many data points fall within that specific interval.

Then, multiply each class midpoint by its corresponding frequency. This calculation yields the total value for each class interval. For instance, if the midpoint is $15$ and the frequency is $4$, the product is:

After calculating these products for all class intervals, sum them to obtain the total of all the products. This sum represents the combined value of all data points, taking into account their frequencies.

Finally, aggregate all frequencies to determine the total number of data points. To find the mean, divide the sum of the products by the total frequency. For example, if the sum of the products is $300$ and the total frequency is $20$, the mean is calculated as follows:

This method enables you to estimate the mean from grouped data displayed in a histogram, providing a valuable summary of the data’s central tendency.