The result of every measurement by any measuring instrument contains some uncertainty. This uncertainty is called error. Every calculated quantity which is based on measured values also has an error.
The accuracy of a measurement is a measure of how close the measured value is to the true value of the quantity.
Precision tells us to what resolution or limits the quantity is measured.
The accuracy in measurement may depend on several factors, including the limit or the resolution of the measuring instrument. For example, suppose the true value of a certain length is near 3.678 cm. In one experiment, using a measuring instrument of resolution 0.1 cm, the measured value is found to be 3.5 cm, while in another experiment using a measuring device of greater resolution, say 0.01 cm, the length is determined to be 3.38 cm. The first measurement has more accuracy (because it is closer to the true value) but less precision (its resolution is only 0.1 cm), while the second measurement is less accurate but more precise.
Types of Errors:
In general, the errors in measurement can be broadly classified as
- Systematic errors
- Random errors.
The systematic errors are those errors that tend to be in one direction, either positive or negative.Some of the sources of systematic errors are :
- Instrumental errors: that arise from the errors due to imperfect design or calibration of the measuring instrument, zero error in the instrument, etc.
Example: The temperature graduations of a thermometer may be inadequately calibrated (it may read 104 °C at the boiling point of water at STP whereas it should read 100 °C).
- Imperfection in experimental technique or procedure: To determine the temperature of a human body, a thermometer placed under the armpit will always give a temperature lower than the actual value of the body temperature. Other external conditions (such as changes in temperature, humidity, wind velocity, etc.) during the experiment may systematically affect the measurement.
- Personal Errors: that arise due to an individual’s bias, lack of proper setting of the apparatus or individual’s carelessness in taking observations without observing proper precautions, etc.
The random errors are those errors, which occur irregularly and hence are random with respect to sign and size.
For example, when the same person repeats the same observation, it is very likely that he may get different readings every time.
Least Count Error:
The smallest value that can be measured by the measuring instrument is called its least count.
The least count error is the error associated with the resolution of the instrument. Using instruments of higher precision, improving experimental techniques, etc., we can reduce the least count error.