Home 11.1 Uncertainties and errors in measurements and results

# 11.1 Uncertainties and errors in measurements and results

### Qualitative & Quantitative Analysis

- Analysis of data can be classified into two types
- Qualitative Analysis
- Comes from observations and non-numerical methods

- Quantitative Analysis
- Comes from measurements and always associated with uncertainties determined by either the apparatus and human limitations such as reaction times and sight

### Uncertainties

- In science, numerical data is divided into two types
- Data with exact numbers (no uncertainty)
- Data with inexact numbers (Degree of uncertainty involved)

### Precision vs Accuracy

- Precision: Closeness of agreement between interdependent test results
- Accuracy: Closeness of agreement between the result of measurement and the true value

### Significant Figures

- Number of digits reflecting precision of a given measurement
- Sometimes it is useful to write in
**Scientific notation**
- Here are some examples:

- Some rules for significant figures in calculation
**For multiplication or division: **Result should be expressed based on measurement with **smallest number of significant figures.**
**For addition or subtraction: **Result should be expressed based on measurement with **smallest number of decimal places**
- (A simple rule on the side is that your
__final answer__ should be expressed in the number of significant figures of the measurement with the __lowest number of significant figures__)

### Experimental Error

- Every measurement has a degree of uncertainty with it called
__experimental error__
- There are two types of experimental error
__Systematic error__: A flaw in experimental design or methodology. This affects the **accuracy** of the results.
__Random error__: Occur because of uncontrolled variables. **Cannot be eliminated**. This affects the **precision** of the results.

### Absolute and Relative Uncertainty

**Absolute Uncertainty** is the margin of uncertainty associated with the result from a measurement.
- Its symbol is given by ΔA

**Relative Uncertainty **is the ratio comparing the size of the absolute uncertainty.
- Relative uncertainty = ΔA / A

- All experimental results should be reported in form:
**Experimental result = (A ****± ****Δ****A) units**

### Percentage Error