Units and Dimensions - Accuracy, Precision & Error
Description:
Accuracy and Precision
Accuracy of a measurement describes how close a measured value is to the actual value.
Precision of a measurement describes the limit of resolution of a measurement.
Example −
Let’s say the length of a pencil is 5 cm.
- Instrument 1 measures it to be 4.9 cm.
- Instrument 2 measures it to be 5.345 cm.
Instrument 1 is more accurate and Instrument 2 is more precise.
Instrument 3 measures it to be 5.0034 cm. Instrument 3 is both accurate and precise!
Errors in Measurement
No measuring instrument is perfectly accurate or precise. Also, mistakes can happen while taking measurements. This leads to errors in measurement.
Errors can be either positive or negative.
Positive error (Example): Actual mass of a box is 5kg but, reported mass is 5.1 kg.
Negative Error (Example): Length of a rod is 4 cm but, reported length in 3.8 cm.
Systematic Errors
Systematic Errors tend to be only in one direction (either positive or negative). For Example −
- A speedometer always shows 10km/hour more speed than actual.
- A clock is always slow by 5 minutes behind the actual time.
Sources of systematic errors −
Instrumental Errors − Arises because of imperfectly designed instruments. E.g. a meter scale which is not calibrated properly.
Imperfect experimental technique − Arises because experimental techniques are not properly followed.
Personal Errors − Arises because personal biases like taking improper readings from the instrument.
Systematic errors can be minimized by improving experimental techniques, choosing better instruments and removing personal biases.
Random Errors
Random errors occur irregularly and can be both positive and negative. There can be known or unknown sources for Random errors. Random errors cannot be minimized/controlled.
Sources of random errors can be −
unpredictable fluctuations in temperature, voltage, mechanical vibrations, etc.
unbiased personal errors.
Least count and Least Count Error
Least Count − The smallest value that can be measured by the measuring instrument is called its least count.
Least Count Error − It is the error associated with the resolution (least count) of the instrument.
Illustration −
The red scale measures the rod as 3 cm. This introduces an error in measurement due to least count. (It can’t measure the part of the rod crossed off in red)
The blue scale measures the rod as 3.5 cm. This, once again, introduces an error in measurement due to least count. (It can’t measure the part of the rod crossed off in blue)