Uncertainties

Question 1

Systematic uncertainty

Answer 1

occurs when readings taken are either all too small or all too large. This can arise due to faulty measurement techniques or experimental design.

Question 2

Scale reading uncertainty

Answer 2

is an indication of how precisely an instrument scale can be read.

Question 3

Random uncertainty

Answer 3

arises when measurements are repeated and slight variations occur. Random uncertainty may be reduced by increasing the number of repeated measurements.

Question 4

Calibration uncertainty

Answer 4

arises when there is a difference between a manufacturer’s claim for the accuracy of an instrument when compared with an approved standard.

Question 5

Absolute uncertainty should normally be rounded to

Answer 5

one significant figure

Question 6

when uncertainties in a single measurement are combined, an uncertainty can be ignored if

Answer 6

it is less than one third of one of the other uncertainties in the measurement.

Question 7

ΔW = √ΔX^2 + ΔY^2 + ΔZ^2

to determine the uncertainty in 1 reading

Answer 7

3 different uncertainties known for 1 reading i.e. the measurement of the wavelength.

calibration uncertain + scale reading uncertainty + random uncertainty

Question 8

ΔW/W = √(ΔX/X)^2 + (ΔY/Y)^2 + (ΔZ/Z)^2

to determine the absolute uncertainty in a different reading.

Answer 8

3 different uncertainties for 3 different readings to find the uncertainty/value in another reading.

ΔX/Y/Z = are the absolute uncertainties i.e. ± 0.02
W/X/Y/Z = the calculated value
ΔW = combined absolute uncertainty

Question 9

(ΔWⁿ/Wⁿ) = n(ΔW/W)

to determine the uncertainty in a value raised to a
power.

Answer 9

when working with a percentage uncertainty

Question 10

The accuracy of a measurement

Answer 10

compares how close the measurement is to the ‘true’ or accepted value.

Accuracy refers to the closeness of a measured value to a standard or known value.

Question 11

The uncertainty in a measurement

Answer 11

gives an indication of the precision of the measurement.

Question 12

the precision of a measurement

Answer 12

compares how close the measurements are to each other.

Precision refers to the closeness of two or more measurements to each other.

Question 13

calculate the percentage uncertainty before the main calculation this can be achieved by

Answer 13

if it is 3% uncertainty i.e.
271 ± 3%
then

271 x (3/100)