## Errors and Statistics## Instrument Uncertainty and Least Count |

Each instrument has an inherent amount of

Here are some typical uncertainties of various laboratory instruments:

- Metre stick: 50% of the least count; usually ± 0.05 cm
- Vernier caliper: ± 0.01 cm
- Triple-beam balance: 50% of the least count; usually ± 0.05 g
- Graduated cylinder: 50% of the least count

**Here's an example.** The uncertainty of all measurements
made with a metre stick whose smallest division (or least count) is one
millimetre is 50% of 1mm or 0.05cm. Say you use that metre stick to measure a
metal rod and find that the rod is between 10.2 cm and 10.3cm. You may think
that the rod is closer to 10.2cm than it is to 10.3cm, so you make your **best
guess** that the rod is, say, 10.23cm in length. Since the uncertainty in the
measurement is 0.05cm, you would report the length of the metal rod to be 10.23
± 0.05cm (0.1023 ± 0.0005 m).

With any experiment it is important to properly display the precision with which each measurement is made. No measurement is absolutely precise. For example, it is impossible to measure the exact length of an object. We might measure the length as 1.23cm, but this does not mean that the actual measurement is 1.23000000...cm! We must carefully describe how precise our measurement is. A experimental value of 1.23 ± 0.10 cm is less precise than a measurement of 1.23 ± 0.01cm. The ± term gives the measure of the precision of the measurement. The accuracy of the value is given either by percentage error or percentage difference.

When a quantity is graphed, it is common for the uncertainty
of that quantity to be represented by **error bars**. For more information
about error bars, see the Excel tutorial on using error bars.

<< Back |

[ Close window | Accuracy and Precision | Measurement Tools | Percentage Error and Percentage Difference | Error Propagation | An Introduction to Statistics on the TI-83 ]