What Is Histogram Mean?
When data are shown in a histogram or grouped frequency table, you cannot recover the exact mean, but you can estimate it by treating every value as if it sat at its class midpoint.
Enter the class boundaries and the frequency of each class. The calculator gives the estimated mean, median, mode and modal class, the standard deviation, the total frequency and a table with midpoints, f × midpoint and cumulative frequencies, plus the histogram.
Below are the formulas, a worked example and answers on how accurate grouped estimates are.
How to Use the Histogram Mean Calculator
- Enter the class boundaries.
- Enter the frequency of each class.
- Read the estimated mean, median and mode.
- Check the grouped table.
Histogram Mean Formula
Estimated mean
Estimated median
Histogram Mean Variables Explained
| Symbol | Meaning | Notes |
|---|---|---|
| m | Class midpoint | |
| f | Class frequency | |
| n | Total frequency | |
| w | Class width |
Histogram Mean Worked Example
Classes 0–10, 10–20, 20–30, 30–40, 40–50 with frequencies 4, 11, 18, 12, 5 have midpoints 5, 15, 25, 35, 45. Σ f·midpoint = 20 + 165 + 450 + 420 + 225 = 1280 and n = 50, so the mean ≈ 25.6.
With the example values loaded in the calculator above, the steps are:
- Class midpoints: 5, 15, 25, 35, 45.
- Mean ≈ Σ(f × midpoint) ÷ n = 1280 ÷ 50 = 25.6.
- Median class is 20–30; median ≈ L + ((n/2 − CF) ÷ f) × w = 25.555556.
- Variance ≈ Σ f (midpoint − mean)² ÷ (n − 1) = 120.04082.
Result: Estimated mean = 25.6; Estimated median = 25.555556.
How to Read a Mean Estimated From a Histogram
When data are grouped, the exact values are lost, so the calculator treats each value as sitting at the midpoint of its class. For classes 0–10 through 40–50 with frequencies 4, 11, 18, 12 and 5, the estimated mean is 1280 ÷ 50 = 25.6.
This is an estimate. The true mean could be a little higher or lower, depending on where the values sit inside each class. Narrower classes give a better estimate.
Where Histogram Mean Is Used
Grouped data
Estimate the mean, median and mode when you only have class boundaries and frequencies.
Exam questions
Check the midpoint working in a grouped frequency problem.
Reading charts
Recover summary statistics from a published histogram.
Spread
Get an estimated standard deviation from the same table.
Common Histogram Mean Mistakes to Avoid
- Class midpoints stand in for the data, so the answer is always an estimate.
- Boundaries must be in order, and there is one more boundary than there are classes.
- Enter frequencies, not frequency densities. If your histogram has unequal class widths, convert density back to frequency first.
- Open-ended classes have no midpoint. Choose a sensible cap before you calculate.
Histogram Mean Terms and Definitions
- Midpoint
- The centre of a class, used to represent all its values.
Histogram Mean FAQs
How do you find the mean from a histogram?
Find the midpoint of each class, multiply it by the class frequency, add the products and divide by the total frequency. In the example, 1280 ÷ 50 = 25.6.
Is the mean from a histogram exact?
No. Only the class a value falls in is known, so the midpoint is an approximation. The estimate improves as the classes get narrower.
How do I find the median from a histogram?
Find the class that holds the middle value and interpolate within it. The calculator gives the estimated median, found by interpolating inside the class that holds the middle value.
What is the modal class?
It is the class with the highest frequency. With equal class widths, it is the tallest bar.