In the mean for grouped data, which does the 'height' term represent?

• A. The data value (class midpoint)
• B. The frequency of the class
• C. The width of the class
• D. The total of all frequencies

Answer: (A)

In grouped data, you estimate the overall average by treating every observation in a class as if it had the class midpoint, and you weight that midpoint by how many observations are in that class. The height of a bar in a frequency distribution reflects the class’s frequency—the number of observations in that class. It’s this frequency that serves as the weight in the mean calculation, not the data value itself. So the data value you use for each class is the midpoint, while the height represents how many observations occupy that class. The mean is then the sum of midpoint times frequency, divided by the total frequency.