How do you calculate the mean from a histogram?

To calculate the mean from a histogram, multiply midpoints by frequencies, sum these products, then divide by total frequency.

First, identify the midpoints of each class interval in the histogram. The midpoint is the average of the upper and lower boundaries of each class. For example, if a class interval ranges from 10 to 20, the midpoint is (10 + 20) / 2 = 15.

Next, find the frequency for each class interval. The frequency is the height of the bar in the histogram, representing how many data points fall within that interval.

Then, multiply each class midpoint by its corresponding frequency. This gives you the total value for each class interval. For instance, if the midpoint is 15 and the frequency is 4, the product is 15 * 4 = 60.

After calculating these products for all class intervals, sum them up to get the total of all the products. This sum represents the combined value of all data points when considering their frequencies.

Finally, add up all the frequencies to get the total number of data points. Divide the sum of the products by the total frequency to find the mean. For example, if the sum of the products is 300 and the total frequency is 20, the mean is 300 / 20 = 15.

This method allows you to estimate the mean from grouped data presented in a histogram, providing a useful summary of the data's central tendency.