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Tuesday, 15 January 2013

CHAPTER 1 : ACCURACY & CONSISTENCY

Accuracy and Consistency in Measurements
1.4.1  Accuracy
1.     ___________  of a measurement is how close the value of a measurement
        to the ____________ value.

2.     The level of accuracy is related to the relative error.
                                               
3.     An error is a                      between the measured value and the actual
        value  .

4.     Accuracy can be improved by  : -

            (a)   repeated readings are taken and the average value is calculated 
            (b)   avoid parallax errors
            (c)   avoid zero errors
            (d)   use measuring instruments with a higher accuracy.
    
       For example, a vernier  callipers is more accurate than a ruler 
1.4.2  Consistency
1.                           / Precision of an instrument is the ability of the instrument
        to measure a quantity with little or no deviation among measurements.
                               
2..    A measurement is considered consistent  will have a              relative
        deviation or no deviation from the  average value .

3.    A deviation is a difference between a  _______________value and its
       average value .

                                                     
4.     average deviation   =          Total deviation 
                                            __________________
                                            number of value taken
                                               
5.     relative deviation   =   average deviation    x  100  %
                                           ______________
                                              average value

6.     Consistency can be improved by
            (a)  eliminating parallax errors
           (b)  exercising greater care and effort when taking readings.
            (c)  using an instrument which is not defective.

7.          Comparisons between  consistency and  accuracy by considering a  target.


Example:
A student used vernier callipers to measure diameter of a glass rod. The table below shows the readings.
Measurement
Diameter rod (cm)
Deviation
1
2.23
0.012
2
2.26
0.018
3
2.24
0.002
4
2.23
0.012
5
2.25
0.008
Average
2.242
0.01

Relative deviation        = ( 0.01 / 2.242) x 100%

                                    = 0.45 %

1.4.3  Sensitivity in Measurements
1. Sensitivity of an instrument is its ability to detect a small change in the
    quantity to be measured.

2. A measuring instrument that has a scale with a smaller  divisions is more
   sensitive .

3. Measuring  instruments.
           

Measuring instruments
Smallest magnitude of quantity (cm)

Sensitivity / Accuracy
Metre rule
0.1
0.1 cm (low)
Vernier callipers
0.01
0.01 cm (moderate)
Micrometre screw gauge
0.001
0.001 cm (high)



1.4.4
Errors in Measurements

1. An error is the difference between the measured value and the actual
    value.

2. There are two main types of errors in measurements,
    A.    systematic errors
    B.    random errors.

A. Systematic  errors

    i.      The error in calibration of instrument which makes the instrument
            defective. (We must examine the instrument carefully before using
            them)
                 
ii.                   ________ error which means the pointer of the instrument does not
        return to zero when not in use. ( Zero error can be corrected by   
        compensating the readings)
                                   
    iii.    A problem which persists throughout  the experiment such as
            repeated error in reaction time and wrong assumption.
    
    Systematic errors will lead to decrease in                                    


B. Random errors

    i.     Arise from unknown and unpredictable variations in condition, and
           will produce a different error every time you repeat the experiment.

    ii.    May be due  to:
           (a)  personal  error  (human limitations of  sight and touch)
           (b)  lack of sensitivity  ( instrument does not respond  / indicate
                 insignificant or small change )
           (c)  natural errors  ( wind , temperature, humidity, refraction, magnetic
                 Field or gravity )
           (d)  wrong  technique  ( applying excessive pressure when
                 turning a micrometer screw gauge )

     iii.   Can be minimized by repeating the measurement several times  
           and taking the average (mean) of the reading .

    iv.   Parallax error
          An error in reading a measurement because an observer’s eye and
          the pointer are not in a line perpendicular to the plane of the scale .
          (the eyes of the observer must be align and perpendicular to the scale of
           measuring instrument)

                   

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