Explain why a percent error describes a range of possible values instead of just one value.

Question

Please make the answer understandable, and not really really confusing. Thank You!

Answer 1

Percent error is:   "The difference between Approximate and Exact Values,
as a percentage of the Exact Value" -- http://www.mathsisfun.com/numbers/percentage-error.html

 Note that the exact value must be known in order to calculate percent error.

 

Usually, the percent error is rounded for simplicity.  For example, an exact percent error of 4.8429% would be rounded to 5%.  But -- so would 5.3665%.  The point is:  the percent error has been rounded, so multiple values could have produced it.

 

Suppose the percent error was 5% and the actual value was 764.  What range of values could have produced 5%?

 

ANS:  Any of the following:
  approximation    error         percent of 764

    729 or 799        35               4.5812
    730 or 798        36               4.712
    731 or 797        37               4.8429
    732 or 796        38               4.9738
    733 or 795        39               5.1047
    734 or 794        40               5.2356
    735 or 793        41               5.3665
    736 or 792        42               5.4974

 

Practice:  If there are exactly 892 graduates of the local university this year and 20% of them received advanced degrees, how many of them could have received advanced degrees?  (give all possibilities)

Answer 2

Emma,

 

Suppose your measuring tape can measure distance to an accuracy of 1%.  When you measure the distance you're interested in, you find a value of 100 meters.  But, your measuring tape is only accurate to within 1%.

 

That means that the actual distance is 100 meters ± 1% or 100 meters ± 1 meter (since 1 meter is 1% of 100 meters).

 

As a result, the real distance is anywhere in between 99 and 101 meters.

 

Does this make sense?