# Errors in Measurements

## Main Question or Discussion Point

Here's what I understand....

Types of errors

1.Systematic errors
• Zero Error
• errors due to slow stopwatches
• errors due to incorrectly graduated scales
2.Random errors
• error due to unevenness of the measuring item
• parallax error

Ways of comparing errors
1. Absolute error$\rightarrow$error when reading scales=least count
2. fractional error
3. percent error
Is this grouping correct ?

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Khashishi
Random error is wrong. I have no idea what "unevenness of the measuring item" means. Random errors are errors that will not reproduce themselves with repeated measurements using the same methodology. I guess parallax error could be due to either random or systematic causes. Shot noise is a very good example of random error.

Fractional error and percent error should be combined into "relative error" since they are the same thing.

I have no idea what "unevenness of the measuring item" means
let's take that we're going to measure the thickness of a hard board..well if the surface is uneven then we get a wrong value..but we can minimize the error by getting measure from more than one place and calculating the mean..

Random error is wrong.
Why?..Isn't it a type of error..can't we divide errors into these two types...systematic and random...?

I guess parallax error could be due to either random or systematic causes.
How it can be systematic ?..I think it's not coming from the instrument...We can avoid parallax by positioning the eye in the correct way..

Can you suggest me a correct grouping please ?..Because many websites giving many many different groupings...
here's the words in my mind....
Systematic error,Zero Error,Random error,parallax error,Absolute error,fractional error,percent error,least count,error when reading scales..
can u pls group these for me ...help is much appreciated...thanks !

From Squires' "Practical Physics" (which I highly recommend):

"A systematic error is one which is constant throughout a set of readings. A random error is one which varies and which is equally likely to be positive or negative."

These are the only two groupings you need.

A parallax error is systematic because if you keep measuring the same length and your head is in the same place, you're going to keep getting the same error. This is different to a random, for example when you can't justify quoting a value to any higher precision than about half the smallest division width on a ruler. Every measurement has that error, in addition to any systematic error.

edited....
Types of errors

1.Systematic errors
• Zero Error
• errors due to slow stopwatches
• errors due to incorrectly graduated scales
• parallax error
2.Random errors
• error due to unevenness of the measuring item

Ways of comparing errors
1. Absolute error$\rightarrow$error when reading scales=least count
2. Relative error$\rightarrow$percent error,fractional error

From Squires' "Practical Physics" (which I highly recommend):

"A systematic error is one which is constant throughout a set of readings. A random error is one which varies and which is equally likely to be positive or negative."
Can you give me some instances for random error rather than unevenness of the surface when we using MR,VC,MMSG,TM,SM instruments?

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Khashishi
Unevenness of the measuring item will cause a systematic error if the unevenness doesn't change. Your warped ruler is going to still be warped the same amount from one measurement to the next, unless you have some uncontrolled humidity or something weird like that. In that case, it could be a random error, but it's a very bad example of one.

Unevenness of the measuring item will cause a systematic error if the unevenness doesn't change.
How can that be ?...we can have some mean value for that...when we take the hard board..there are +error and -errors...so the mean value will reduce the quantity of error

How can that be ?...we can have some mean value for that...when we take the hard board..there are +error and -errors...so the mean value will reduce the quantity of error
Khashishi seems to be correct. And what do you mean by - and + errors ? If the instruments are assumed to be perfect and all other errors are assumed to be eliminated , then maximum error can be due to least count of that measuring instrument. Thus observed value can be written within the limit as "True Value ± Least Count".

Khashishi seems to be correct. And what do you mean by - and + errors ? If the instruments are assumed to be perfect and all other errors are assumed to be eliminated , then maximum error can be due to least count of that measuring instrument. Thus observed value can be written within the limit as "True Value ± Least Count".
You know the surface of the hard board is not regular(even)..

You know the surface of the hard board is not regular(even)..
Now you're taking in account - "error due to imperfection" which comes under "systematic error". If you take this into account , then again observed value will be having more limit. Thus in your case :

Observed value : x (say.)

Then ,

true value - least count≥x≥true value + least value