What is purity and its need:
Suppose I have to lay rugs on the floor in my room, I measured the length and width of my room and brought a rug of its size, but when I laid it in the room, I saw that it does not fit. It has come big. why did this happen ? This happened because maybe I did not measure properly or in other words, there was some error in my measurement. If my measurement was accurate, it would fit in the room and my time and money would not be wasted.
Definition of accuracy: In the measurement of any object, it is called accuracy to get a value almost equal to or exactly equal to its actual value.
For example, if the length of a wire is 5 meters and when we measure it, then 4.98 or 4.99 or 5 comes in our measurement, then we can call it a pure value but there is some error in it too.
Definition of error: The difference between the actual and measured value of something is called error.
As the actual length of the wire is 5 meters and the measured length is 4.98 meters, then by definition
Error = 5 – 4.98 = 0.02 m
% Error = (Actual Value – Measured Value) / Actual Value
Percentage error = (5 – 4.98)(100)/5 = (0.02 x 100 )/5 = 0.4%
Types of errors :
There are mainly three types of error –
1. Systematic errors
2. Random errors
3. gross errors
Now let us read about all these errors in detail.
1. Systematic errors
This type of error can be easily discovered or can be easily reduced by finding out its cause.
These errors occur due to various reasons, their main reasons or types are as follows –
Error due to the device: This type of error arises due to the machines used, such as the error in the design of the device, etc. If a yantra is fitted with more than one scale, then it is necessary to match their zeros, otherwise zero error occurs in this yantra. To remove this error, we should use good quality equipment.
Personal error: When a person does not have experience in operating or using any machine, then this type of error can arise due to his lack of experience. For example, if one does not know how to use Vernier calipers scale, then he makes an error in measurement which we will call personal error. To remove this type of error, first of all the person must have the right knowledge of the equipment.
Error due to lack of completeness: The reason for such errors is in front of us, that is, it is known, yet they cannot be removed. For example, if the measurement of heat is done after radiation loss, then the measurement is obtained with error.
Fixed error: When the same thing is measured repeatedly and if the value of error is the same in all the measurements, then this type of error is called fixed error.
Error due to external factors (Error due to environment): This type of error arises due to external factors i.e. environment like change in temperature and pressure etc. To remove this type of error, the observations should be done in such a place which is less affected by the external environment.
2. Random errors
When the same thing is measured repeatedly and each time some error occurs in the observation, in this situation it is difficult to say which reading is correct.
In this case the mean of all the readings is taken and this mean is considered as the true measure of the object.
3. gross errors
When carelessness is taken by a person in the measurement of an object, then the error that arises due to this carelessness is called gross error.
The reason for causing a gross error is as follows –
( a). wrong measurement by person
(b).measurement error
(C). write some values wrong while calculating
(d). Take readings without adjusting equipment.
Absolute error, Relative error and Percentage error
1. Absolute error: The difference between the actual value and the measured value of any quantity is called absolute error. Let the actual value of a quantity be x and its observed value (measured value) is x0 , then according to the definition of absolute error, their difference is called absolute error.
absolute error = Δx = x0 – x
Suppose the actual weight of an object (sugar) is 1 kg and when we weigh it, for some reason we do not have a weight of 1 kg, there is a weight of 100 g, so we weigh sugar by 100 g, then in the end we get Realize that in this way we get 950 gm in weight, this may be because when we were weighing 100 gm we were adding a little more pulses, well whatever the reason but we got the error.
Param Error = Actual Value – Received Value
Absolute error = 1000 – 950 = 50 gm
2. Relative error : The value of relative error is obtained by comparing the absolute error like suppose the length of something is 5 cm and we are getting an error of 1 cm then here the value of relative error is more But when an error of 1 cm is found in measuring a length of 100 cm, then this relative error is considered very small, this small error can be considered in the category of ultimate error.
So we can say that the absolute error depends on the size of the object, it is called relative error.
3. Percentage error: The percentage error in the measurement of any thing from its actual measurement is called percentage error.
Percentage error =
( Measured Value – Actual Value) x 100 / actual value
