presentation - random errors

8/12/2019 Presentation - Random Errors

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Group 2

1. Thaatchayani Muralle

2. Nurul Hazwani Idrus3. Ong Hui Hui

4. Tan Guo Liang

5. Ayisy Hariz Bin Sukiman


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TITLE:

RANDOM ERRORS


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Definition of

RANDOM ERRORS


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1. Discrepancy or uncontrolled variation

between an observed (measured) value and

the value predicted by a specification,standard, or model.

2. Where numbers are sufficiently large (as inrepeated measurements or mass production),

random errors tend to cancel each other out,

and their sum approaches zero.

3. Also called chance error or statistical error.


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Random error is caused by any factors that

randomly affect measurement of the variable

across the sample.For instance, each person's mood can inflate or

deflate their performance on any occasion. If

mood affects their performance on the

measure, it may artificially inflate the observed

scores for some people and artificially deflate

them for others.

The important thing about random error isthat it does not have any consistent effects

across the entire sample. Instead, it pushes

observed scores up or down randomly.


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This means that if we could see all of

the random errors in a distribution

they would have to sum to 0 -- there

would be as many negative errors as

positive ones.

The important property of random

error is that it adds variability to thedata but does not affect average

performance for the group.


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Errors that can be reliably estimated by

repeating measurements are called random.

In all our examples in this tutorial, when we

mentioned error we meant random error.

Remember the measuring of the oscillation

period of a pendulum with a stopwatch? Some ofour measurements were above the mean, while

some of them were below.

That's why we call this kind of error random.

Our error estimate is obtained from the random

distribution of our measurements around the

mean value.


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As we have shown in this tutorial,

random error can be easily

quantified using the standard

deviation formula. Most of theerror analysis in your lab will

involve the estimation of random

errors.


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Characteristics

ofRANDOM error:


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Corrected reading=direct reading random

error


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The main source of randomerror is the observer. Thesurroundings and theinstruments used are alsosources of random errors.


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Example ofRANDOM error:


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The uncertainty of the instrument is shown inthe table belowInstruments Uncertainty Example of readings

Millimeter rule 0.1 cm (50.1 0.1)cm

Vernier caliper 0.01 cm (3.23 0.01)cm

Micrometer screw gauge 0.01 mm (2.63 0.01)mm

Stopwatch (analogue) 0.1 s (1.4 0. I )s

Thermometer 0.5 C (28.0 0.5)C

Ammeter (03A) 0.05 A (1.70 0.05)A

Voltmeter (05V) 0.05 V (0.65 0.05)V


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A random error is one that has anequal chance of giving a readingwhich is either greater or smallerthan the value it ought to be.It can be caused by:


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The random error can be revealed by taking various reading fora particular quantity: this proced ure coup led w ith averag inghelps to attenuate its effect. Ho we ver random e rrors cann ot becompletely eliminated.

Set of measurements w ith (a) random errors on ly and (b) with

systematic plus random errors


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What areSYSTEMATIC & RANDOM

errors?


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Are systematic errors, ones where you useequipment which is not 100 accurate. Forexample using a ruler which is accurate to+/- 0.1mm?Are random errors ones where theexperiment is done slightly different forexample instead of taking readings every30 seconds you take one at 31 seconds andanother at 29 seconds?


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EXAMPLE


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1. Random: e.g different roomtemperature / atmosphericpressure might cause a suddenincrease in results.

2. Systematic: e.g a thermometerwhich allways reads 1oC higher thanwhat the actual temperature is buthappens all the time and so will notaffect the results.


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Addition and subtractionWhen two or more measured values areadded or subtracted, the final calculatedvalue must have the same number ofdecimal places as that measured valuewhich has the least number , of decimalplaces.


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1. a = 1.35 cm + 1.325 cm

= 2.675 cm

= 2.68 cm

2. b = 3.2 cm

0.3545 cm=2.8465 cm

=2.8 cm

3. c == 1.142 cm

= 1.14 cm

Example
http://keterehsky.files.wordpress.com/2010/02/clip_image040.gif


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Multiplication and divisionWhen two or more measured values aremultiplied and/or divided, the final calculatedvalue must have as many significant figures asthat measured value which has the leastnumber of significant figures.


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Example :1. Volume of a wooden block

= 9.5 cm x 2.36 cm x 0.515 cm

= 11.5463 cm

3

= 12 cm3

2. If the time for 50 oscillations of a simplependulum is 43.7 s, then the period of

oscillation = 43.7 50 = 0.874 s


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Example 1

The diameter of a cone is (98 I)mm and the height is

(224 I )mm. What is:

(a) The absolute error of the diameter.

(b) The percentage error of the diameter.

(c) The volume of the cone. Give your answer to the correct number

of significant number.

Example 2

The period of a spring is determined by measuring the time for10 oscillations using a stopwatch. State a source of:

(a) Systematic error

(b) Random error


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..THE END

presentation - random errors

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