Assignment 1 - Error Analysis

7/23/2019 Assignment 1 - Error Analysis

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Waqar Azeem

NUST-SNS

Error Analysis

Waqar Azeem

NUST-SNS

September 21, 2014

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Introduction

Some numerical statements are exact: Mary has 3 brothers,

and 2 + 2 = 4. However, all measurements have some de-gree of uncertainty that may come from a variety of sources.The process of evaluating this uncertainty associated witha measurement result is often called uncertainty analysis orerror analysis.

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Difference Between Accuracy and Precision

Accuracy is the closeness of agreement between a measuredvalue and a true or accepted value. Measurement error is

the amount of inaccuracy.Precision is a measure of how well a result can be deter-mined (without reference to a theoretical or true value). Itis the degree of consistency and agreement among indepen-dent measurements of the same quantity; also the reliabilityor reproducibility of the result.

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Difference Between Accuracy and Precision

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Relative Uncertainty and Relative Error

Precision is often reported quantitatively by using relativeor fractional uncertainty

RelativeUncertainty = uncertainty measuredquantity

(1)

Accuracy is often reported quantitatively by using relativeerror

RelativeError = measured value − expected value expected value

(2)

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Measuring the Length and Width of a Table

Length (cm) Width (cm)140 93

140.2 93.1

140.1 92.8139.8 92.8139.9 92.9140 93.1

140.1 92.9

139.6 93.2139.5 92.7

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NUST-SNS For single measurement:

Length = 140 ± 0.2 (3)

Width = 93 ± 0.2 (4)

Mean Length = 139.9 cm

Mean Width= 92.9 cm

Standard Deviation (S L) = 0.026 cm

Standard Deviation (S W ) = 0.17 cm

Error in Each Measurement = Measurement ± SD

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Histogram and Normal Distribution

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Error in Mean

Standard Error (σ) = S √ N

σL = 0.0087 cm

σW = 0.057 cm

Area of Table = 12996.71 cm2

Perimeter of Table = 465.6 cm

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Propagation of Error

σf =

∂ f

∂ x

2

σ2x +

∂ f

∂ y

2

σ2y (5)

σP = 2

(σ2l + σ2

w ) (6)

σA = lw

σl

l

2

+

σw

w

2

(7)

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Perimeter of Table = 465.6±

0.307 cm

Area of Table = 12996.71 ± 11.12 cm2

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Assignment 1 - Error Analysis

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