Error Analysis

Error Analysis Least count The minimum measurement that can be taken using a device is called its least count. Accuracy of a measurement It refers to the closeness of a measurement to the true value of the physical quantity. Precision of measurement It refers to the resolution of the limit to which the quantity id measured. It is determined by the least count of the measuring instrument. Example Suppose we try to measure the length of a rod, whose actual length is 5.26 m using two different scales. With the first scale we get the reading as 5.2 m whereas with the second one we get it as 5.18 m. the first reading 5.2 m is more accurate as it is closer to the actual value. But the second reading 5.18 m is more precise as its resolution is up to two digits after decimals. Error It is the difference between the true value and the measured value of a quantity. Thus, Error = true value – measured value. Types of error Systematic errors The errors that tend to occur in one direction, either positive or negative are called systematic errors. They may be due to the following reasons. Instrumental errors Imperfection in experimental technique Personal error Errors due to external causes. These errors may be minimized by using quality instruments, better experimental techniques without any bias and controlling the external conditions at the time of experiment. Random errors The errors which occur irregularly and at random, in magnitude or direction are called random errors. These errors have an equal chance of being negative or positive; hence they are minimized by arithmetic mean of large number of observations as the true value.