PHY 01 Lesson 1.2: Uncertainty of Measurement

Accuracy

indicates how close a measurement is to the true value.

Precision

refers to the consistency of repeated measurements

Random Errors

result from unpredictable or inevitable changes

Systematic Errors

usually come from the measuring instrument or in the design of the experiment itself

Percent Error

when there is an expected or true value of quantity.

usually considered in judging the accuracy of a measurement

Percent Difference

measures how far apart the different measured values are from each other

usually an indication of precision

Variance

used to describe the consistency (precision) of measurements This measures how far or close the measurements are from the mean (average).

Variance (𝝈 𝟐 )

defined as the average of the squared difference of the measurements (𝑥) from the mean (𝑋ത)

defined as the average of the squared difference of the measurements (𝑥) from the mean (𝑋ത)

standard deviation

Where N is the number of measurements done. The square root of the variance

close to zero (0)

A standard deviation ______________ indicates that the data points are close to the mean.

High standard deviation

indicates that the measurements are spread out over a wide range of values.

Certain or Exact digits

are the ones that measuring instruments can give you.

Least count

the smallest marked division in the measuring instrument

Uncertain digits

are the ones that you estimate

Uncertainty

shows the range of values where the measurement lies with a level of confidence

(1)a measured value with the proper unit that best estimates the quantity, and

(2)the degree of uncertainty in the measurement.

A measurement must be represented by two components

Absolute uncertainty

same unit as the quantity

For example: the resistance of a wire is (𝟐𝟓. 𝟎𝟎 ± 𝟎. 𝟎𝟓)𝛀 Absolute uncertainty is 𝟎. 𝟎𝟓𝛀. Therefore, (𝟐𝟓. 𝟎𝟎 − 𝟎. 𝟎𝟓)𝛀 to (𝟐𝟓. 𝟎𝟎 + 𝟎. 𝟎𝟓)𝛀 or from 𝟐𝟒. 𝟗𝟓 𝛀 to 𝟐𝟓. 𝟎𝟓 𝛀.

Relative uncertainty

dimensionless and is obtained dividing the absolute uncertainty by the numerical or measured value.

For example: the resistance of a wire is 𝟐𝟓. 𝟎𝟎 ± 𝟎. 𝟎𝟓 𝛀 Relative uncertainty is 𝟎.𝟎𝟓𝛀 𝟐𝟓.𝟎𝟎𝛀 𝒙𝟏𝟎𝟎 = 𝟎. 𝟐%. Thus, same resistance may be expressed as 𝟐𝟓. 𝟎𝟎 ± 𝟎. 𝟐%.

Independent variable

changed by an experimenter

GRAPH

It is a pictorial representation of the relationship between variable. It shows how a quantity changes with other variables.

Dependent variable

affected by the change of independent variable

best-fit line or curve

is drawn close to all data points.

Equation of a line

y=mx+b

Formula for slope (m)

m = (y2 - y1) / (x2 - x1)