Laboratory Formula
Arithmetic Mean Formula
Calculates the average of a set of observations.
Formula Summary
Arithmetic Mean
Calculates the average of a set of observations.
- Category
- Laboratory
- Equation
- x̄ = Σx ÷ n
- Calculator
- Use Arithmetic Mean Calculator →
Equation
x̄ = Σx ÷ n
Variables
- x̄ = mean
- Σx = sum of values
- n = number of values
How to Use This Formula
- Identify the known values from the problem statement.
- Convert all values into compatible units.
- Substitute the values into the equation and calculate the result.
- Check that the final answer has the correct unit and meaning.
Explanation
The arithmetic mean calculates the average value of a set of measurements by dividing the total sum of values by the number of observations. It is commonly used to represent a typical result from repeated measurements.
Worked Example
For values 10, 15, and 20, the arithmetic mean is (10 + 15 + 20) ÷ 3 = 15.
Common Mistakes
- Forgetting to include all data values.
- Dividing by the wrong number of observations.
- Adding values incorrectly before calculating the average.
Applications
- Analyzing repeated laboratory measurements.
- Summarizing experimental data.
- Calculating average scientific observations.
Related Formulas
Percent Error
% error = |experimental − accepted| ÷ |accepted| × 100
Compares an experimental result with an accepted reference value.
Learn formula →Percent Difference
% difference = |A − B| ÷ ((|A| + |B|) ÷ 2) × 100
Compares two experimental values when neither is an accepted value.
Learn formula →Sample Standard Deviation
s = √(Σ(xᵢ − x̄)² ÷ (n − 1))
Measures the spread of sample observations around their mean.
Learn formula →