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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.

  FALSE

  TRUE

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

  x + x0

  x - x0

  x/x0+x0/x

  x - x/x0

 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 

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

  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

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

  how many bits are in the number

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

  how large the number is

  None of the above

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

  floating error

  relative error

  absolute error

  marginal error

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

  floating error

  marginal error

  absolute error

  relative error

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

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

  None of these options apply

  1. absolute error 2. relative error

  1. relative error 2. absolute error

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

  Answer: 0.01

  Answer: 0.4

  Answer: 0.404

  Answer: 0.004

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

  Answer: 0.01

  Answer: 0.4

  Answer: 0.004

  Answer: 0.404

 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%

  TRUE

  

  FALSE

  

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

  TRUE

  FALSE

 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

  FALSE

  TRUE

 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: 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%

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