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How Do You Read the Mean of a Histogram?

Published in Statistics 2 mins read

The mean of a histogram, representing the average value of the data displayed, is calculated by weighting each bar's value by its frequency. Here's a breakdown of the process:

Steps to Calculate the Mean from a Histogram

  1. Identify the Midpoint of Each Bar (Category): Determine the central value representing each bar on the histogram. If the histogram represents continuous data grouped into ranges (e.g., 10-20, 20-30), use the midpoint of each range (e.g., 15, 25). If the bars represent discrete values (e.g., number of siblings: 0, 1, 2), these values are your "categories".

  2. Determine the Frequency of Each Bar: Read the height of each bar on the y-axis. This represents how many data points fall within that bar's category or range. This is the frequency.

  3. Multiply Midpoint/Category by Frequency: For each bar, multiply the midpoint (or category value) by its frequency. This gives you a weighted value for each bar.

  4. Sum the Weighted Values: Add up all the weighted values calculated in the previous step.

  5. Sum the Frequencies: Add up the frequencies (heights) of all the bars. This is the total number of data points.

  6. Divide the Sum of Weighted Values by the Sum of Frequencies: Divide the sum obtained in step 4 by the sum obtained in step 5. The result is the mean.

Example

Let's say we have a histogram representing the number of books read by students in a class:

Number of Books (Midpoint of Bar) Frequency (Height of Bar)
1 5
2 8
3 10
4 7
  1. Midpoints/Categories and Frequencies: (See table above).
  2. Multiply:
    • 1 * 5 = 5
    • 2 * 8 = 16
    • 3 * 10 = 30
    • 4 * 7 = 28
  3. Sum of Weighted Values: 5 + 16 + 30 + 28 = 79
  4. Sum of Frequencies: 5 + 8 + 10 + 7 = 30
  5. Calculate the Mean: 79 / 30 = 2.63 (approximately)

Therefore, the mean number of books read by students is approximately 2.63.

Summary

Calculating the mean from a histogram involves weighting each bar's value (midpoint or category) by its frequency, summing these weighted values, and then dividing by the total frequency. This provides an estimate of the average value represented by the data in the histogram.