TOPIC 11 : TOPIC 11 : Measurement and data Measurement and data

processingprocessing

1.1.1Describe and give examples of random uncertainties and systematic errors

1.1.2Distinguish between precision and accuracy

Learning Outcomes:At the end of the lesson the students should be able to:

1.1.4State random uncertainty as an uncertainty range (±)

1.1.5State the results of calculation to the appropriate number of significant figures

1.1.3Describe how the effects of random uncertainties may be reduced

Why do we need to learn this topic

1. Systematic and Random Errors

Systematic errors can result Systematic errors can result fromfrom

Systematic errors can be eliminated or corrected Systematic errors can be eliminated or corrected before the investigations is carried out on most before the investigations is carried out on most

occasionsoccasions

Examples of systematic Examples of systematic Errors:Errors:

Random uncertaintiesRandom uncertainties

Caused by:Caused by:

What happened when a number of What happened when a number of readings/samples are takenreadings/samples are taken

2. Precision and accuracy2. Precision and accuracy

3. 3. UncertaintyUncertainty range (±) range (±)

ExampleExample

Consider the given data Consider the given data belowbelowTime ± 0.5 s 0.0 30.0 60.0 90.0 120.0

pH ± 0.05 1.00 1.20 12.00 12.00 13.00

+0.05

-0.05

-0.5 s -0.5 s

According to scale

4. Absolute and % 4. Absolute and % uncertaintiesuncertainties

% % UUncertainties=abs. ncertainties=abs. uncer/measurement x 100%uncer/measurement x 100%

E.g. Mass of salt = 9.8 ± 0.2 g

% uncer. =0.2g/9.8g x 100% =2.0%

Treatment of Treatment of uncertainties in uncertainties in

calculationcalculation

e.g. If the values of two e.g. If the values of two temperature are 36.3 ± 0.1 temperature are 36.3 ± 0.1

00C and 56.3 ± 0.1 C and 56.3 ± 0.1 ooCC

When multiplying and dividing, add the When multiplying and dividing, add the % uncer. of the measurements being % uncer. of the measurements being

multiplied/divided multiplied/divided

=(1.0g/100.0g + 1.0K/12.0K) x 100%=1.0% +8.3 %=9.3%

If one uncer. is much larger than others, the approximate uncer. in the result calculated can be taken as due to that quantity aloneE.g. ∆E =mc ∆T% uncer =(∆m/m + ∆T/T) x 100% =(1.0g/100.0g +1.0K/2.0K) x 100% = 1% + 50% = 50%

Others RuleOthers Rule

5. Plotting graphs5. Plotting graphsChoice of axesIndependent Variable: x-axis

(altered)Dependent Variable :y-axis

(measured)Y-axis

X-axis

Note: Time always be the independent variable

Scales & LabelsScales & Labels

Volume of gas, V (cm3)

Time,t (s)

Volume of gas, V (cm3)

Time,t (s)

Good graph Bad graph

Line of best fitLine of best fit

Straight line and Curve Straight line and Curve GraphGraph

Include obvious data errors on the graph but Omit them when drawing the line. Such an omitted point is

called an “outlier”

Volume of gas, V (cm3)

Volume of gas, V (cm3)

Time,t (s)

Time,t (s)