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30 - Absolute and Relative Errors

 1. If the correct answer is 100 and it is stored as 100.9, that is not too far off. However, 1.9 is a long way from an answer of 1.0. The latter presents a greater error.

  TRUE

  FALSE

 2. If we denote the correct answer as 'x' and the stored value as 'x0', then the absolute error is simply ______________

  x - x0

  x - x/x0

  x + x0

  x/x0+x0/x

 3. In the following example, what is the absolute error in both cases?
Example 1:
==========
Stored number: 1.9
Correct answer: 1

Example 2:
==========
Stored number: 100.9
Correct answer: 100 

  None of the above

  In example one the error is 0.9 and in example two the error is 100.

  In both examples the error is 0.9

  In both examples the error is a factor of 1 i.e 1.

 4. It is critical to see what the error is in relation to _______________________

  how large the number is

  how many bits are in the number

  the value of the number (especially if it is very small)

  None of the above

 5. The actual number difference beween the desired value and the rounded value is called the ___________________________

  absolute error

  marginal error

  relative error

  floating error

 6. The percentage difference between the desired value and the rounded value is called the ___________________

  relative error

  absolute error

  floating error

  marginal error

 7. In the following example, fill in the blanks for 1. and 2.
absoluteandrelativeerrors.png

  1. relative error 2. absolute error

  1. absolute error 2. relative error

  None of these options apply

  Both 1 and 2 are different ways of representing the absolute error

 8. For example, if p = 0.4 and p? = 0.404, the absolute error in the approximation is:

  Answer: 0.4

  Answer: 0.004

  Answer: 0.01

  Answer: 0.404

 9. If p = 0.4 and p? = 0.404, the relative error in the approximation is:

  Answer: 0.404

  Answer: 0.4

  Answer: 0.004

  Answer: 0.01

 10. Using 8 bit fixed point unsigned fraction with 4 bits for the decimal points: Is the calculation shown to find the absolute error trying to represent 8.8 correct? (True or False?)
1000.1101
8.8 - 8.8125 = 0.0125
(0.0125/8.8) * 100 = 0.14%

  FALSE

  

  TRUE

  

 11. Errors, especially rounding errors, can have deadly consequences. e.g. the 1991 patriot missile misses scud and 1996 - Ariane rocket explodes!

  FALSE

  TRUE

 12. An absolute error could also be be described as the approximate value - true value.

  FALSE

  TRUE

 13. The relative error is the absolute error/absolute error +1 1 * 100

  TRUE

  FALSE

 14. Some people tend to use the term accuracy when speaking of absolute errors and the term precision when speaking of relative errors

  FALSE

  TRUE

 15. What is the absolute error? Refer to the image below.
finaltestdatarepabsoluteerror.png

  Answer: 11111110000 000101 (–5 – 234 = –33)

  Answer: 0.025 / -0.025 / 6.9-6.875 / 1/40

  None of the above

  Answer: 0.00362319 / 0.025/6.9 / 1/276 = 0.362319%