Error

1
Error
2
Error

• Error is the difference between a measured or
  calculated (reported) value and the true value.
• Engineers recognize that errors are present in
  their professional lives and must be able to
• 1. Identify types of errors
• 2. Numerically express the magnitude of errors
• 3. Recognize the confidence that may be
  placed in a printed number

3
Simple Error Analysis

• Suppose a rod of unknown length is measured with
  a standard meter stick.
• Spend 5 minutes as a team completing this
  exercise
• What can be said about the length of the rod is
  reported as
• 7 to 8 cm
• 7.5 to 7.6 cm
• 7.57 to 7.59 cm?

4
Systematic Errors

• Systematic Errors - errors that can be attributed
  to some regular outside occurrence.
• Engineers must be aware of the presence of
  systematic errors and eliminate those possible
  and try to quantify and correct for those
  remaining.

5
Systematic Errors

• The error associated with systematic errors can
  be corrected if the source and magnitude are
  known.
• Repeating measurements will not eliminate or
  reduce systematic errors.

6
Random Errors

• Accidental (Random) Errors - errors that occur in
  a random nature.
• The presence of accidental errors is evident by
  the scatter in measured data.

7
Random Errors

• It is impossible to predict the magnitude and
  sign of the accidental error present in any one
  measurement.
• Repeating measurements and averaging the results
  will reduce the random error in the average.

8
What type of error is

• The produce scale at the grocery store has water
  on it. (The water runs off the produce)
• The timekeeper sneezes at he moment the runners
  cross the finish line.
• Gasoline sloshed from your tank prior to the pump
  shutting off (mpg calculation).
• Measuring with a 100 ft tape that is actually
  99.01 ft.
• Press the wrong key(s) on a calculator during a
  long calculation.

9
Definitions

• There are three ways to numerically describe
  error
• 1) True error Reported value - True Value
• 2) Fractional error True error / True value
• 3) Percent error Fractional error 100

10
An example

• Can you calculate the true error, fractional
  error and percent error for

Reported Value Distance feet
Correct Value Distance feet
109
100
1050
1000
45
50
17
20