Accuracy & Precision
Accuracy & Precision
Difference between accuracy and precision
3) Least count error - Every instrument has a least count; below which the
measuring instrument unable to read. The error rise due to this problem is known
as least count error.
Significant figure/digit- The digit in a measurement which is trustworthy; are called significant figures
Accuracy - Accuracy refers to the closeness of a reading from true value; taken by a measuring instrument.
Precision - Precision refers to the closeness of two or more readings taken by a measuring instrument.
The above two statement will get a clear view from the following example-
The above two statement will get a clear view from the following example-
let the true value of
tea in a cup is 20 ml.
Difference between accuracy and precision
Accuracy
|
Precision
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Accuracy is the agreement of
the result of measurement with true value. It is an ability to approach
correct result.
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Repeatability of measuring
process is called Precision
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Your measurement will be close
to the standard measurement.
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Your measurement will be
similar every time you measure.
|
Accuracy can be improved.
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Precision cannot be improved.
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Accuracy depends upon simple
techniques of analysis.
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Precision depends upon many
factors like temperature etc.
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Accuracy is necessary but not a
sufficient condition for precision.
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Precision is necessary but not
a sufficient condition for accuracy.
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Error
Every measured value
contains some uncertainty this uncertainty is called error.
Error = reading value - True value.
Note - It may be positive or
negative; but both has equal importance
Classification of error
→On the basis of nature of error
1. Systematic error - Systematic
error are those error that tend to be in one direction, either positive or
negative.
Some of causes
of systematic error are
a)
Instrumental error - Those errors which arise due to
imperfect designing of measuring instruments. E.g- After regular use of spring weighing scale; the spring get elongates permanently and shows readings more than the accurate value.This kind of error is called instrumental error.
b)
Imperfect technique - Imperfection in experimental
technique or processor leads to systematic error. E.g- Thermometer should be placed in the mouth to get accurate temperature of the body but if we place it any where else in the body we get the reading which has some error.
c)
Personal error - These errors arise due to inexperience
of the observer. E.g- when we stand on the weighing scale; the reading goes
change when we tilt in any direction.
2. Random Error - These error
cause due to change in experimental condition which are out of control. E.g. - measurement
which are temperature dependent.
→ On the basis of mathematical calculations of measurement
1. Absolute Error - The difference between current reading
and average reading is called absolute error.
Note: In this case positive or negative sign is not considered.
2. Mean absolute error - Average of absolute error is called
mean absolute error.
3. Relative error /Fractional error - It is the ratio of
mean absolute error to average value or true value.
4. Percentage error - If the relative error is multiplied
with 100 then it is called percentage error.
You can easily understand these
four errors through this example. Suppose the time period of a S.H.M is 2.4s, 2.5s, 2.7s &
2.4s. Now see the table below
Significant figure/digit- The digit in a measurement which is trustworthy; are called significant figures
→ Rules for finding significant figure
(i)
Leading o's - insignificant
E.g.
0.054 km = 54 m
Here 0.0 is Insignificant.
(ii)
O’s bet two non-zero digit - significant
E.g. 1.012
Here all digits are significant.
(iii)
trailing o's
a)
Decimal point – significant
E.g. 0.230
Here last 0 is significant
b)
No decimal point – insignificant
E.g. 34000
Here last three 0 is insignificant (since we assumed as rounded off)
(iv)
All non 0’s digit is significant.