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What is Absolute Error, Relative Error and Percentage Error?

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Absolute Error Formula
Absolute error is defined as the magnitude of difference between the actual and the individual values of any quantity in question.

Say we measure any given quantity for n number of times and a1, a2 , a3 …..an are the individual values then

Arithmetic mean am = [a1+a2+a3+ …..an]/n

am= [Σi=1i=n ai]/n

Now absolute error formula as per definition =
Δa1= am – a1
Δa2= am – a2
………………….
Δan= am – an

Mean Absolute Error= Δamean= [Σi=1i=n |Δai|]/n
Note: While calculating absolute mean value, we dont consider the +- sign in its value.

Relative Error or fractional error
It is defined as the ration of mean absolute error to the mean value of the measured quantity
δa =mean absolute value/mean value = Δamean/am

Percentage Error
It is the relative error measured in percentage. So
Percentage Error =mean absolute value/mean value X 100= Δamean/amX100

An example showing how to calculate all these errors is solved below
The density of a material during a lab test is 1.29, 1.33, 1.34, 1.35, 1.32, 1.36 1.30 and 1.33

So we have 8 different values here so n=8

Mean value of density u= [1.29+1.33+1.34+1.35+1.32+1.36+1.30+1.33] / 8 = 1.3275 = 1.33 (rounded off)

Now we have to calculate absolute error for each of these 8 values
Δu1 = 1.33 – 1.29 = 0.04
Δu2 = 1.33 – 1.33= 0.00
Δu3 = 1.33 – 1.34= -0.01
Δu4 = 1.33 – 1.35= -0.02
Δu5 = 1.33 – 1.32= 0.01
Δu6 = 1.33 – 1.36= -0.03
Δu7 = 1.33 – 1.30= 0.3
Δu8 = 1.33 – 1.33= 0.00

Now remember we don’t take +- signs in calculating Mean absolute value
So mean absolute value = [0.04+0.00+0.01+0.02+0.01+0.03+0.03+0.00]/8 = 0.0175 = 0.02 (rounded off)

Relative error = +- 0.02/1.33 =+- 0.015 = +- 0.02

Percentage error = +- 0.015*100 = +- 1.5%

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Comments
  • anjana July 17, 2012 at 11:16 am

    thanks a ton! 🙂

  • Peerzada Towfeeq May 26, 2013 at 12:40 am

    Thanks alot!!! Very much easy and understandable!!!

  • deepa June 5, 2013 at 8:00 pm

    good explanation

  • sai June 8, 2013 at 2:54 am

    hey can the realtive error be in positive or negetive plz explain??

  • krishna August 4, 2013 at 1:06 am

    super fine

  • Harjedayour January 6, 2014 at 1:59 pm

    Thanks a lot

  • sreenivas reddy June 24, 2014 at 9:07 am

    very helpful………..
    thanks a lot

  • john manzo August 5, 2014 at 3:59 am

    nice explanation….. thanx man

  • hirok March 20, 2015 at 9:04 pm

    Nice explanation…. thanx a lot

  • David Mwendwa May 19, 2015 at 3:57 am

    Good supports for studies. be blessed

  • Jade smith May 25, 2015 at 9:46 am

    What is an example for absolute error

  • Huma June 25, 2015 at 8:44 am

    Thanks a lot…its very easy to understand now…

  • Astina joice July 18, 2015 at 7:30 pm

    Good explanation with example. Thank you

  • Subham August 6, 2015 at 12:10 pm

    thanks a lot…..it clears all my doubt

  • bhoomika August 20, 2015 at 8:25 am

    It’s very understandable…… Thanks a looot

  • Rupesh August 23, 2015 at 3:50 am

    Thanks a lot:-) good explanation

  • hanu September 5, 2015 at 1:11 am

    Super explanation

  • Marvelous October 25, 2015 at 10:39 am

    Thank u

  • kirti patil December 24, 2015 at 12:28 am

    simple & nice explanation

  • ghalib khaliq January 24, 2016 at 1:22 am

    thanks a ton! good explanation

  • Muthukumar January 24, 2016 at 11:13 pm

    Thank you very much.This is usefull for my viva

  • ayushka July 26, 2016 at 12:14 pm

    very good and easy explanation!
    too much helpful!

  • Anzila July 27, 2016 at 4:17 am

    simple & perfect explanation

  • hrithikgt2312@gmail.com August 21, 2016 at 5:52 am

    thanks

  • Sarthak Saraswat December 24, 2016 at 7:05 am

    Really nyc explanation..
    It will be more grtful if u can give more examples abt dis..

  • Aman May 13, 2017 at 6:42 pm

    This is the best explanation method and very easy to understand

  • Aysha June 11, 2017 at 10:11 am

    Tnx a lot

  • Nandani Sarraf June 25, 2017 at 2:24 am

    Thanxxx a lot. It helps me very much

  • amirtharaj July 26, 2017 at 5:55 am

    very nice, more than thanks I couldn’t do any thing, it is helpful for me.

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