Random and systematic
errors
Try to guess and explain why
Errors (uncertainties)
Random errors
Systematic errors
 Unpredictable (mistakes that
experimenter makes) ->
unavoidable
 Predictable (mistakes that
experimenter makes or a fault in
apparatus) -> can be avoided
 Unbiased in a direction
 Biases measurement in ONE
direction - result is either too large
or too small
Comparison
Random
Systematic
 Systematic error (also called systematic bias)
 Random error (also called
is consistent, repeatable error associated with
unsystematic error, system noise or
faulty equipment or a flawed experiment
design. These errors are usually caused by
random variation) has no pattern.
measuring instruments that are incorrectly
One minute your readings might
calibrated or are used incorrectly. However,
they can creep into your experiment from
be too small. The next they might
many sources, including:
be too large. You can’t predict
 A worn out instrument. For example, a plastic
random error and these errors are
tape measure becomes slightly stretched over
the years, resulting in measurements that are
usually unavoidable.
slightly too high.
 An incorrectly calibrated or tared
instrument, like a scale that doesn’t read zero
when nothing is on it.
 A person consistently takes an incorrect
measurement. For example, they might think
the 3/4″ mark on a ruler is the 2/3″ mark.
Pictured errors
Random
Measurements
Systematic
Correct value of a
physical quantity
Ampermeter showing 0.1 A when it is
not connected to power
Systematic
If you do not look at an analogue
meter directly from above
Systematic
More people measure the duration of
period of mathematical pendulum and get
different results
Random
The ball is not centered between the jaws of
the caliper and that gives different results
for the circumference of the ball
Both
The jaws of the caliper are tightened too
much so we get a smaller circumference
Systematic
The ball may not be perfectly round
Random
The temperature of the ball may
change during the measurement
Random
If your eyes are not aligned with the liquid
level in the cylinder you get different
readings
Systematic
Calculating acceleration from Newton’s 2nd
law without taking in account friction force
Systematic
When we use a metal ruler on a very
hot day
Systematic
Result with systematic error
represented on a graph
Result with random errors represented
on a graph
Prevention
Random
 Random error can be reduced
by:
 Using an average measurement
from a set of measurements, or
 Increasing sample size.
Systematic
 It’s difficult to detect — and
therefore prevent — systematic
error. In order to avoid these types
of error, know the limitations of
your equipment and understand
how the experiment works. This
can help you identify areas that
may be prone to systematic
errors.
Accuracy and precision
In relation to random and systematic errors
4 cases
Case (a)
Random error – small
Systematic error - small
Case (b)
Random error – small
Systematic error - large
Case (c)
Random error – large
Systematic error - small
Case (d)
Random error – large
Systematic error - large
INFLUENCES
Random error
Systematic error
Precision
Accuracy
Averages; absolute, fractional and
percentage uncertainty
Average or mean value of physical quantity
Is the best estimate of the real quantity
Uncertainties
Propagation of uncertainties
Addition and substraction
Multiplication and division