1.1e Measurement and Uncertainty

Question 1

All numbers in science can be broken down into 2 types:

Answer 1

measurements (continuous)

integers (discrete)

Question 2

All measurements must contain…

Answer 2

uncertainty

Question 3

Uncertainty is expressed as a

Answer 3

+/-

Question 4

Reading error (defn)

Answer 4

is the amount of error expected from taking a measurement. It is intrinsic to the measuring device

Question 5

Reading error on an analog device is …

Answer 5

half the smallest increment of the device

Question 6

Reading error on a digital device is …

Answer 6

the smallest decimal place shown

Question 7

Estimated error (defn)

Answer 7

the amount of error expected due to what is being measured and the limitations of the situation. It is usually much larger than the reading error. It comes from thinking about the measurement being taken.

Question 8

Random Error (defn)

Answer 8

is the error that comes from taking trials. The random variation in reading or estimating the uncertain digit of the measurement.

Question 9

Random Error is expected to follow what kind of distribution?

Answer 9

Bell Curve a.k.a Normal or Gaussian distribution

Question 10

Standard deviation (defn)

Answer 10

the average difference between each measurement and the mean. It is a measure of the spread in the data.

Question 11

Data error (defn)

Answer 11

equal to twice the standard deviation. It includes 95% of the data and excludes the 5% that are outliers.

Question 12

Upper Limit (defn)

Answer 12

the mean + the data error

Question 13

Lower limit

Answer 13

the mean - the data error

Question 14

Absolute Uncertainty (defn)

Answer 14

half the range in the data ((max-min)/2)

Question 15

absolute uncertainty

Answer 15

any uncertainty expressed in units like cm, kg, etc. (as opposed to %).

Question 16

% Uncertainty

Answer 16

any uncertainty expressed as a % of the mean value

Question 17

% uncertainty (defn)

Answer 17

the ratio of the absolute uncertainty to the mean value

Question 18

Why do we take trials?

Answer 18

to know the mean better

Question 19

Why do we want to know the mean?

Answer 19

the mean is the best estimate of the true value

Question 20

How many trials is enough?

Answer 20

• a minimum of 5 is required to calculate the standard deviation
• when taking more trials will no longer change the mean given the precision of the measurements
• when we are convinced that the running mean will no longer change by taking more trials

Question 21

Can we say two values are different from each other when the means are different?

Answer 21

No. The overlap of the uncertainties must be taken into account.

Question 22

What is the name of the test to tell if two sets of data overlap?

Answer 22

t-test (unpaired)

Question 23

A t-test tells us…

Answer 23

the probability that the amount of overlap occurred by chance, given the mean values and the data error

Question 24

accuracy (defn)

Answer 24

the correctness of a value

Question 25

accuracy (example)

Answer 25

a student determined pi to be 3.15, when the actual value is 3.14. Their results were fairly accurate.

Question 26

precision (defn)

Answer 26

• how specifically and narrowly a value is known
• tied to decimal place
• tied to data error

Question 27

accurate, but not precise (example)

Answer 27

a student got a value of pi of 3.1 +/-2.6. Although the mean was close, the range of possible answers was very wide, including anything from 0.5 to 5.7!

Question 28

accurate and precise (example)

Answer 28

a student achieved 3.14+/-0.01. The value is correct and 95% certain to be between 3.13 and 3.15.

Question 29

not accurate and not precise (example)

Answer 29

a student got a value of 6.5 +/-2.4 for the value of pi. The value is far off the accepted value of 3.14. The range of values, 4.1 to 8.9 is very broad and also doesn’t include the actual value.

Question 30

Not accurate but precise

Answer 30

A student got a value of 5.62+/-0.02 for pi. The value is off the accepted value by a lot, although it is know to be between 5.60 and 5.64.

Question 31

Systematic error (defn)

Answer 31

when all the values (trials or cases) are incorrect by the same amount.

• associated with a y-intercept shift

Question 32

systematic error (examples)

Answer 32

• zero errors on a balance (reads 0.12g before something is placed on it - all masses will be large by 0.12g)
• calibration errors (thermometer reads 1.2°C when placed in an ice bath - all temperatures will read 1.2°C higher than they actually are)