Accuracy: – and instrument is said to be accurate if the measured value of a physical quantity resembles very closely to its true value.
Precision: – an instrument is said to have a high degree of precision of the measured value remains unchanged, howsoever, large number of times it may have been repeated.
Difference between actual and measured value of a physical quantity is called error. If am is measured value and at is actual value of a physical quantity then the error is
E = ∆a = |am – at|
Types of error
Errors may broadly be divided into two types: systematic errors and random errors.
Systematic error: – errors arising due to the system of measurement or the errors made due to the parts involved in the system of measurement are called systematic errors.
Instrumental error: – these may occur (a) due to faulty calibration (b) due to wear and tear (for instance, zero error in venire caliper or screw gauge) (c) because of faulty fitting and so on.
Personal errors: – or errors caused by the observer each observer has a peculiar behaviour. Some may be quite carless while the others get bore when they have to of repeated jobs and still others cannot read correct due to eyesight problem or due to other personal problems. Such errors are eliminated if the observations are taken by different observers.
Environmental error: – change in temperature (due to weather conditions), pressure, wind direction, humidity and so on play a vital role while recording the reading. For example, if we measure the length of a rod in summer and in winter it would be different as rod and measuring scale may have different expansion coefficients, however, these errors can be avoided b artificially creating the same environment in the laboratory.
Random errors: – (or statistical errors) consider an example. The probability of tossing a coin is 1/2. If a coin is tossed 1000 times then the chance that we get exactly 500 times head and 500 time tail is negligible. If 1 m A current is passing through a wire, can we be
Sure that always [n = 10-3 / 1.6 x 10-19 – 6.25 x 1015]
Constant numbers of electrons equal to 6.25 x 1015 are flowing per second through it. These examples illustrate how random errors creep in. even this error cannot be removed.
Methods of expressing error
Absolute error: – the deviation from true value of measured value or deviation of the value from its mean value (of all observations).
Thus, ∆Xi = | xi – xm|
Is absolute error where xm is mean value and Xi is the component of the observation?
Relative error: – the ratio of mean absolute error to the true value of physical quantity is called relative error.,
∆x /x or ∆x / xm is called relative error.
Percentage error = relative error x 100 = ∆x / x 100
Propagation or combination of errors
Case (i) when x = a +b
Then maximum possible % error = ∆x/x x 100 = ∆a + ∆b / a + b x 100
Case (ii) when x = a – b
Then maximum possible % error = ∆x / x x100 = ∆a + ∆B / a – b x 100
Case (iii) when x =a. b
Then maximum possible % error = ∆x/x x 100 = [∆a / a =+ ∆b / b] x 100
Case (IV) when x = a/b
Then maximum possible % error = ∆x/x x 100 = (∆a /a + ∆b / b) x 100
Case (v) when x = a1 bm / yp zk
Then maximum possible % error
= ∆x/x x 100 = (I∆a/a + m∆b/b + p∆y/y + k∆z/z) x 100