Mean Of Range
Calculator
Results
- Mean
- 50.5
- Number of terms
- 100
- Sum of the range
- 5,050
Statistical results
| Mean | 50.5 |
| Number of terms | 100 |
| Sum of the range | 5,050 |
formula-map diagram
- Mean
- 50.5
- Number of terms
- 100
- Sum of the range
- 5,050
Statistical relationship
Formula
mean = (a + b) / 2, n = b − a + 1, sum = n × (a + b) / 2= 50.5
Note
This is a simplified model: it applies the displayed standard formula to the summary values you entered and assumes their underlying conditions (independence, normality, correct sampling) hold. It does not analyse a real data set. Check the assumptions before relying on the result.
More in Statistics and probability
See all →Frequently asked questions
What does this calculator actually compute?+
It finds the arithmetic mean of every integer between a lower and upper bound, inclusive. For consecutive integers the mean is simply the midpoint: (first + last) / 2, so you don't need to sum every value individually.
Why does the midpoint formula work for a range of integers?+
Consecutive integers are evenly spaced, so they form a symmetric set around the center. Pairing the smallest with the largest, the second-smallest with the second-largest, and so on always gives the same sum, which is why the average collapses to (first + last) / 2.
Does it matter if the range has an even or odd number of integers?+
No. The midpoint formula gives the correct mean either way. With an odd count the mean lands exactly on the middle integer; with an even count it falls halfway between the two middle integers.
What if I enter the bounds in the wrong order?+
The mean of the range from 5 to 10 is the same as from 10 to 5, since averaging doesn't depend on direction. The calculator will still return the correct midpoint regardless of which bound you enter first.
How is this different from the average of a list of specific numbers?+
This tool assumes every integer in the interval is included exactly once. If your actual data skips values, repeats some, or isn't evenly spaced, you need a regular mean calculation on the actual data set instead of the range shortcut.