Measurements & Uncertainty

Textbook page 560

Systematic Errors

Measurement errors in which the measurements differ from the true values by a consistent amount each time a measurement is made.

Random errors

Measurement errors in which measurements vary unpredictably and can happen when any measurement is being made.

Zero Error

The reading is not zero on a measuring device when the quantity being measured is zero (the device is faulty). This is a type of systematic error.

2 potential reasons for random errors

• factors that are not controlled in the experiment

• difficulty in deciding on the reading given by a measuring device.

2 potential reasons for systematic errors

• the way in which measurements are taken

• faulty measuring devices.

True Value

The value that would be obtained in an ideal measurement.

Measurement Error

The difference between a measured value and the true value for the quantity being measured.

Precision

How close repeated measurements are to each other - the closer they are to each other, the more ____ the measurement is.

Accuracy

How close a measurement result is to the true value - the closer it is, the more ____ it is.

Uncertainty in a measurement

The interval within which the true value can be expected to lie.

Absolute uncertainty in the mean of a measurement

Approximated as half the range. This is often expressed as ± value.

Percentage uncertainty in the mean of a measurement

calculated from its absolute uncertainty and mean value as follows: ____ = (absolute uncertainty) / (mean value) × 100

Absolute uncertainty

Uncertainty in a measurement expressed as a numerical value.

Percentage Uncertainty

Uncertainty of a measurement expressed as a percentage of the recorded value.

How can we tell if an experimental result is accurate, and why does this work?

An accurate result has an uncertainty which is larger than the difference between the experimental result and the true value, because this means that the true value lies within the uncertainty range.

How can we tell if an experimental result is inaccurate?

Inaccurate result (difference > uncertainty). True value lies outside uncertainty range