Презентация на тему Introduction to laboratory-treatment of uncertainties

and Systematic Errors

Estimating Random Experimental Errors

Combining Experimental Errors

end of the lab session.
Your report must be structured
Introduction

/ Aim of the experiment
Apparatus
Experimental results (including tables and graphs)
Answers to the questions in the lab instructions
Uncertainty analysis
Conclusion

a measurement, calculation conforms to the correct value or

a standard
=> accuracy is the measure of exactness

Precision: Refinement in a measurement, calculation, as represented by the number of digits given
=> precision is the measure of reproducibility or consistency

quantity
Is equally likely to be positive or negative
Can be

reduced by measuring the same quantity several times and taking the average (or the mean)

it is relatively free from systematic errors
A result is

said to be precise if the random error is small

V =

(3.36± 0.01) V

Linear / Vernier Scale: reading error is usually taken as the smallest scale division

L = (16.7 ± 0.1) cm

quantity, the best estimate is the average (mean)

The random

error can be estimated from the minimum and maximum value

(visually or using Excel) the random error of the

gradient of the best-fit line as follows:

1) Draw a best-fit line and calculate the gradient G
2) Draw two lines of minimum (Gmin) and maximum (Gmax) gradients
3) Estimate the uncertainty in the gradient ΔG as:



Note that gradients usually have a dimension (hence a unit)

are added








is called the fractional

uncertainty in A
It has no dimension

are added








is called

the absolute uncertainty in A
It has the same dimension as A

to gravity, g, using a simple pendulum and we

estimated:
- the period T = (1.848 ± 0.015) s from multiple readings
- the length L = (0.95 ± 0.05) m

Calculate the value of g and its estimated absolute random uncertainty

Earth’s surface, what can you conclude about random and

systematic errors?