What Is Relative Average Deviation?
Relative average deviation is the average deviation divided by the mean. It is widely used in chemistry labs to describe the precision of repeated measurements such as titration volumes.
Enter your measurements to get the relative average deviation as a percentage and in parts per thousand, plus the average deviation, the mean and the relative standard deviation for comparison. A chart shows each value’s deviation as a percentage of the mean.
The sections below give the formula, a worked titration example and answers on how this differs from RSD and the coefficient of variation.
How to Use the Relative Average Deviation Calculator
- Enter your repeated measurements.
- Read the relative average deviation as a percentage and in parts per thousand.
- Compare with the RSD.
- Check each value’s contribution in the table.
Relative Average Deviation Formula
Average deviation
Relative average deviation
Relative Average Deviation Variables Explained
| Symbol | Meaning | Notes |
|---|---|---|
| d | Average deviation from the mean | |
| x̄ | Mean of the measurements | |
| RAD | d ÷ x̄ | × 100 for %, × 1000 for ppt |
| n | Number of replicates |
Relative Average Deviation Worked Example
Five titration volumes: 25.12, 25.08, 25.15, 25.10, 25.09 mL. The mean is 25.108. The absolute deviations are 0.012, 0.028, 0.042, 0.008 and 0.018, with a sum of 0.108 and an average of 0.0216. RAD = 0.0216 ÷ 25.108 = 0.00086, or 0.086 %, which is 0.86 parts per thousand.
With the example values loaded in the calculator above, the steps are:
- Mean = 25.108.
- Average deviation = Σ|x − mean| ÷ n = 0.108 ÷ 5 = 0.0216.
- Relative average deviation = average deviation ÷ mean = 0.0216 ÷ 25.108 = 0.00086028357.
- As a percentage: 0.0860284 %. As parts per thousand: 0.860284.
Result: Relative average deviation (%) = 0.0860284 %; Relative average deviation (parts per thousand) = 0.860284 ppt; Mean = 25.108.
How to Read a Relative Average Deviation
The relative average deviation divides the average deviation by the mean, so it expresses precision as a fraction of the measured value. Five titration volumes with mean 25.108 mL and average deviation 0.0216 mL give 0.0216 ÷ 25.108 = 0.086%, or about 0.86 parts per thousand.
A small value means the repeated measurements agree closely. The same number can be shown as a percentage or as parts per thousand. Pick the form your lab report or course uses.
Where Relative Average Deviation Is Used
Titration and lab precision
Summarise how closely repeated volume or mass measurements agree.
Comparing methods
Compare the precision of two methods that measure the same thing on different scales.
Report writing
Quote RAD as a percentage or as parts per thousand, as the course requires.
Checking against RSD
See the relative standard deviation next to RAD for the same data.
Common Relative Average Deviation Mistakes to Avoid
- RAD measures precision, which is closeness of repeated results. It does not say whether they are accurate.
- Use the mean as the divisor. A mean near zero makes the ratio meaningless.
- Report parts per thousand if your lab manual asks for ppt. Multiply the fraction by 1,000.
- With only 3 or 4 measurements, treat RAD as a rough guide.
Relative Average Deviation Terms and Definitions
- Average deviation
- The mean of the absolute deviations from the mean.
- ppt
- Parts per thousand, the relative value multiplied by 1000.
Relative Average Deviation FAQs
What is the relative average deviation?
It is the average deviation from the mean divided by the mean, often written as a percentage or in parts per thousand. It measures how consistent repeated measurements are.
How is it different from RSD?
RSD uses the standard deviation in place of the average deviation. RSD gives more weight to values far from the mean, so it is usually a little larger than RAD.
How do I express RAD in parts per thousand?
Multiply the ratio of average deviation to mean by 1,000. A ratio of 0.00086 is 0.86 parts per thousand.
What is a good RAD?
It depends on the method. A lower value means better precision, and the acceptable limit is set by your lab course or the method you follow, so use the criterion given there.