Range Calculator
Calculate total dataset range ($\text{Max} - \text{Min}$), minimum value, maximum value, midrange, and observation count ($N$).
Calculate Dataset Statistical Range
Enter numbers separated by commas, spaces, or lines.
Calculation Results
Calculated using statistical dispersion range equations: \text{Range} = \text{Max}(X) - \text{Min}(X)
Quick Summary
The Range Calculator evaluates the absolute spread ($\text{Range} = \text{Max} - \text{Min}$), minimum, maximum, and midrange value of a numerical dataset.
Formula Explanation
\text{Range} = \text{Maximum Value} - \text{Minimum Value}
\text{Midrange} = \frac{\text{Maximum Value} + \text{Minimum Value}}{2}How It Works
Range is the simplest measure of statistical dispersion. The Range Calculator identifies the extreme maximum and minimum values in your dataset, computing the total spread span and midpoint midrange.
Step-by-Step Worked Example
Practical Problem: Calculate the range for the dataset: 15, 22, 8, 45, 19, 33 ($N = 6$).
- Step 1: Identify maximum dataset value ($\text{Max}$): $\text{Max} = \mathbf{45}$.
- Step 2: Identify minimum dataset value ($\text{Min}$): $\text{Min} = \mathbf{8}$.
- Step 3: Subtract minimum from maximum: $45 - 8 = \mathbf{37.0000\text{ Range}}$.
- Step 4: Calculate Midrange: $(45 + 8) / 2 = \mathbf{26.5000\text{ Midrange}}$.
- Step 5: Interpretation: The data points span a total range of 37 units.
Real-World Calculation Examples
Scenario 1: Daily Stock Price Range
Parameters: Low $8.00, High $45.00
Result: Range $37.00 (Midrange $26.50).
Scenario 2: Annual Temperature Extremes
Parameters: Min -10°F, Max 95°F
Result: Range 105°F ($95 - (-10) = 105$).
Scenario 3: Manufacturing Tolerance Span
Parameters: Min 9.95mm, Max 10.05mm
Result: Range 0.10mm (Tight process control).
Scenario 4: Exam Score Range (50 to 98)
Parameters: Min 50, Max 98
Result: Range 48 points (48 point score spread).
Key Benefits of Using This Calculator
Instant Spread Measurement
Computes absolute dataset range and extremes in one step.
Midrange Midpoint Output
Calculates the exact average of the maximum and minimum values.
Negative & Positive Numbers
Correctly handles negative minimum values ($95 - (-10) = 105$).
100% Free & Client-Side
Executes locally in your browser with zero latency or web server transmission.
Frequently Asked Questions (FAQ)
What is range in statistics?
Range is the difference between the highest and lowest values in a dataset ($\text{Range} = \text{Max} - \text{Min}$).
Is range sensitive to extreme outliers?
Yes — range depends entirely on the two extreme values in a dataset, making it highly sensitive to outliers.
What is interquartile range (IQR) vs range?
Range measures total spread ($\text{Max} - \text{Min}$), whereas IQR measures middle 50% spread ($Q3 - Q1$), ignoring extreme outliers.
How is range calculated with negative numbers?
Subtract the minimum from the maximum ($\text{Max} - \text{Min}$). For example: $10 - (-5) = 15$.
Can range be a negative number?
No — range is always a non-negative number ($\ge 0$). If all values are identical, range is $0$.
What is midrange?
Midrange is the arithmetic average of the maximum and minimum dataset values ($\text{Midrange} = \frac{\text{Max} + \text{Min}}{2}$).
What is rule of thumb for standard deviation from range?
For a normal distribution, standard deviation is approximately Range divided by 4 ($\sigma \approx \text{Range} / 4$).
Why is range useful in quality control SPC charts?
Statistical Process Control (R-charts) monitor sample range to detect changes in process variability.
What is semi-interquartile range?
Semi-interquartile range is half of the Interquartile Range ($\text{Semi-IQR} = \frac{Q3 - Q1}{2}$).
How do I calculate range in Microsoft Excel?
Use formula =MAX(A1:A10) - MIN(A1:A10).