Measurements and Errors

Question 1

Name all quantities and their fundamental base units

Answer 1

Time - seconds 
Mass - kilograms 
Length - metres 
Current - amperes
Temperature - kelvin 
Intensity - candela
Amount of substance - mole

Question 2

Dimension

Answer 2

type of quantity independent of its units or value, e.g. time, length, mass etc.

Question 3

Name all prefixes in standard form

Answer 3

tera (T) = x10^12
giga (G) = x10^9
mega (M) = x10^6
kilo (k) = x10^3
centi (c) = x10^2
milli (m) = x10^-3
micro (μ) = x10^-6
nano (n) = x10^-9
pico (p) = x10^-12
femto (f) = x10^15

Question 4

Random Errors

Answer 4

• unpredictable (out of your control)
• present when any measurement is taken
• cannot be corrected

Question 5

Suggest how to reduce the effect of random error on an investigation

Answer 5

• taking repeat measurements

- calculating a mean

Question 6

Systematic Error

Answer 6

• readings differ from true value by consistent amount each time a measurement is taken
• arise from environment, methods of observation + uncalibrated measuring instruments

Question 7

Suggest how to reduce the effect of systematic error on an investigation

Answer 7

• CANNOT carry out simple repeats

- must change technique or measuring instruments based on error suspected then repeat

Question 8

How do random and systematic errors affect accuracy and precision

Answer 8

• random errors produce imprecise data

- systematic errors produce inaccurate data which may still be precise

Question 9

Anomalies

Answer 9

• outliers (considerably outside of range)
• judged as not part of variation caused by random uncertainty
• excluded from data since results in invalid conclusion

Question 10

Calibration

Answer 10

• establishing relationship between values recorded by measuring instruments and standard reference values
• calibration curve plotted

Question 11

Repeatable

Answer 11

measurement is repeatable if investigation is repeated using same method and equipment to obtain same results

Question 12

Reproducible

Answer 12

measurement is reproducible if investigation is repeated using different equipment and techniques to obtain same result

Question 13

Accuracy

Answer 13

close to true value

Question 14

Precision

Answer 14

little spread around mean dependent only on random errors

Question 15

Suggest how to quote uncertainty of measurement

Answer 15

• uncertainty of a reading (one judgment) is half resolution of instrument
• uncertainty of measurement (two judgments) is resolution of instrument
• round uncertainty to same number of decimal places as measurement itself

Question 16

Suggest how to find uncertainty of repeat measurements

Answer 16

mean value has uncertainty of half the range of measured values

Question 17

Describe how to draw error bars on a graph

Answer 17

• plot mean values
• calculate range from repeats (ignoring anomalies)
• add error bars with lengths half the range on either side of data point

Question 18

Describe how to determine uncertainties for gradients and y intercepts

Answer 18

• draw ‘best’ line of best fit
• draw dashed steepest/shallowest gradient possible
• % uncertainty = (best gradient - worst gradient)/best gradient x 100
• y intercept uncertainty found with same method

Question 19

Suggest how to combine percentage uncertainties when adding or subtracting values

Answer 19

add absolute uncertainties

Question 20

Suggest how to combine percentage uncertainties when multiplying or dividing values

Answer 20

add percentage uncertainties

Question 21

Suggest how to calculate percentage uncertainty when raising a value to a power

Answer 21

multiply percentage uncertainty by the power

Question 22

Suggest how data and graphs can be manipulated to determine the relationship between two variables

Answer 22

• plot graph of y against x
• if graph is not linear then square, cube or square root y and plot graphs
• the straightest line graph suggests the relationship between x and y

Question 23

Zero Error

Answer 23

• measuring system gives false reading when true value of measured quantity is zero
• may result in systematic error