measuremt errorbar

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DATA HANDLING AND

MEASUREMENT


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With every measurement,no matter how carefully it ismade, there is an

associated error anduncertainty inherent withthe measurement


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The magnitude of the erroris due to the precision ofthe measuring device, the

proper calibration of thedevice, and the competentapplication of the device


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Random ErrorIf you measure a quantity many times

and get lots of slightly different

readings then this called a random

error.For example, when measuring the

bounce of a ball it is very difficult to

get the same value every time even if

the ball is doing the same thing.


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Sources of random errors include:The readability of the instrument

The observer being less thanperfectThe effects of change in the

surroundings


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Systematic Error

This is when there is somethingwrong with the measuringdevice or method.

Using a ruler with a broken endcan lead to a zero error. Evenwith no random error in theresults, youd still get the wronganswer.


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Sources of systematic errors

include:

An instrument with zero error. To

correct for zero error, the valueshould be subtracted from every

reading

An instrument being wronglycalibrated


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Reducing Errors

To reduce random errors youcan repeat your measurements.

If the uncertainty is truly random,

they will lay either side of the true

reading and the mean of these

values will be close to the actual

value.


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To reduce a systematic error you

need to find out what is causing

it and correct yourmeasurements accordingly

Sometimes when you look at the

graph of your results

An accurate experiment is one

that has a small systematic error,

whereas a precise experiment is

one that has a small random

error.


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Estimate The Uncertainty Range

An uncertainty range applies toany experimental value.

The idea is that, instead of just

giving one value that implies

perfection, we give the likely range

of measurement.


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Uncertainties Representation.

Uncertainty can be written in 3

formats. If a value of a measurementis 6.25 m and the uncertainty is 0.05

cm, this uncertainty can be

represented in the forms below :

Absolute uncertainty : 6.25 0.05cm

Relative uncertainty : 6.25 (1.000.008) cm

Fractional (percentage) uncertainty: 6.25 (1.00 0.008) cm = 6.25

0.8%


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State uncertainties as absoluteuncertainties.

Add 1 of the smallest significantfigure.

13.21 m 0.010.002 g 0.001

1.2 s 0.1

12 V 1


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Determine the uncertainties in results.

The uncertainty in data is not enough, we

need to include it in any calculations we dowith the data.

Addition and subtraction

When performing additions and subtractions

we simply need to add together the absoluteuncertainties.

Example:

Add the values 1.2 0.1, 12.01 0.01, 7.21

0.011.2 + 12.01 + 7.21 = 20.42

0.1 + 0.01 + 0.01 = 0.12

20.42 0.12


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Graphical Representation of

Uncertainty

In many situations the best method of

presenting and analysing data is to use graph.

If this is the case, a neat way of representing

the uncertainties is to use error bars. The

graphs below explain their use.


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Error bars are a graphical representationof the variability of data and are used

on graphs to indicate the error, or

uncertainty in a reported measurement.

They give a general idea of how

accurate a measurement is.
http://en.wikipedia.org/wiki/Error%23Experimental_sciencehttp://en.wikipedia.org/wiki/Error%23Experimental_science


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To add error bars to a point on a

graph, we simply take the

uncertainty range (expressed as" value" in the data) and drawlines of a corresponding size

above and below the point

depending on the axis the valuecorresponds to.

.


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Since the error bar represents the uncertainty

range,

the best-fit line of the graph should pass

through ALL of the error rectangles created by

the error bars

(ie. vertical error bar & horizontal error bar for

a graph point).


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Best-Fit" Line

The "best-fit" line is the straight line which

passes as near to as many of the pointsas possible.

By drawing such a line, we are

attempting to minimise the effects ofrandom errors in the measurements.


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Time 0.2 s Distance 2 m

3.4 135.1 36

7 64


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Determine the uncertainties in the

gradient Gradient

To calculate the uncertainty in the

gradient, we simply add error bars to the

first and last point, and then draw a

straight line passing through the lowest

error bar of the one points and the

highest in the other and vice versa.


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Date post:	14-Apr-2018
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