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Hearing Exam 1 > Measurement and Uncertainty > Flashcards

Measurement and Uncertainty Flashcards

1
Q

what is measurment

A

act of quantifying a characteristic element or object

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2
Q

the units used to quantify depend on what

A

the type of measurement being made

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3
Q

if it is a fundamental quantity, then the label is simply

A

meters or kilograms or seconds

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4
Q

if it is a derived quantity, then the label represents

A

the elements from which the measure is derived
-square meters or Pascal

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5
Q

if it is a derived quantity, then the label represents

A

the elements from which the measure is derived
- square meters or Pascal

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6
Q

every measurement has a degree of uncertainty, how is it determined?

A

by the scale used to make the measurement
- finer markings have less uncertainty

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7
Q

what is precision?

A

being able to make repeated measurements and get the same outcome each time

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8
Q

what is accuracy?

A

degree of closeness of the measurement to the actual measurement value

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9
Q

what is error and what is it used to do?

A
  • the difference between the average value and the true value
  • summarize all the flaws in the measurement
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10
Q

what is random error referred to as?

A

variability or random variation

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11
Q

what is random error?

A

error due to chance

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12
Q

random error does not have what?

A

direction
- average of all deviations from average value will be ~0

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13
Q

what happens to random error when more samples are taken and what is affected?

A

the reduction in error will be greater
- impacts precision

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14
Q

systematic error is referred to as what?

A

bias

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15
Q

what is systematic error?

A

error not due to chance alone

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16
Q

what does systematic error have?

A

net direction
- averaging over a large number of samples does not remove the error

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17
Q

how do you fix systematic errors and what is impacted?

A

by recognizing the source of the error
- recalibrating the equipment
- impacts accuracy and precision

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18
Q

which set is more precise?
A) 18.2 , 18.4 , 18.35
B) 17.9 , 18.3 , 18.85
C) 16.8 , 17.2 , 19.44

A

A

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19
Q

who is more accurate when measuring a book that has a true length of 17.0 cm?
Susan: 17.0 cm, 16.0 cm, 18.0 cm, 15.0 cm
Amy: 15.5 cm, 15.0 cm, 15.2 cm, 15.3 cm

A

Susan

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20
Q

who is more precise when measuring the same 17.0 cm book?
Susan: 17.0 cm, 16.0 cm, 18.0 cm, 15.0 cm
Amy: 15.5 cm, 15.0 cm, 15.2 cm, 15.3 cm

A

Amy

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21
Q

how do you decide what is accurate or precise?

A

Accuracy- consider the mean value and compare that to the expected (nominal value)

Precision- consider the standard deviation among the measurement (spread in the data)

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22
Q

summary for accuracy and precision

A

Accurate/Precise= on target #

Accurate/Not precise= near target #

Not accurate/precise= near e/o, not near target #

Not accurate/Not precise= random, not near e/o or target #

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23
Q

what to remember about accuracy/precision

A
  • A measurement can be precise but not accurate
  • A measurement can be neither accurate or precise
  • A measurement can be accurate but not precise (increased variability)
  • A measurement can be precise and accurate
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24
Q

if I measure a length of string and record that is it 10 cm long and my colleague measures the same string and finds that it is 3.93 inches, who is right?

A

Both are

  • difference is the measurement system
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25
Q

how can we describe errors in measurement?

A
  • random
  • systemic (bias)
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26
Q

how is systemic bias split/what type of errors are systematic?

A
  • offset errors
  • scale factor errors
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27
Q

what is the difference between offset errors and scale factor errors?

A

offset- calibration error or no offset made

scale factor- errors proportional to “true” measurement

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28
Q

example of offset error-
imagine you have a home scale, and you want to measure 1 lb of hamburger to freeze from a large amount of hamburger you brought from the store. you haul out the scale and it is set to zero and you put the bowl that will hold the meat on the scale. what will be the offset error?

A

Any measurement you make will be off by the same amount- the weight of the bowl that holds the meat

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29
Q

consider that you are using a tape measure to measure some fabric and the tape measure has been stretched to 101% of its original size. what will be the scale factor error?

A

Any measurements that are made with this tape measure will be 101% of the actual measurement.

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30
Q

how do you calculate percent error?

A

% error= (observed result-expected result)/expected results x 100%

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31
Q

SI Prefixes

A

10^1 deca da
10^‐1 deci d
10^2 hecto h
10^‐2 centi c
10^3 kilo k
10^‐3 milli m
10^6 mega M
10^‐6 micro μ
10^9 giga G
10^‐9 nano n
10^12 tera T
10^‐12 pico p

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32
Q

non-SI units

A

time (minute (m), hour (h). day (d))
volume (liter (L or l))
mass (ton (t))
energy (electronvolt (eV))

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33
Q

non-SI unit relation to Si

A

time:
- 1 min= 60 s
- 1 h= 3600s
- 1 d= 86400s

volume:
- 1 L= 1 cm^3

mass:
- 1 t = 1000 kg

energy:
- 1 eV= 1.602 x 10^-19 J

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34
Q

base units

A

time (seconds- s)
length (meter- m)
mass (kilogram- kg)

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35
Q

what are derived units?

A

units that combine two base units

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36
Q

events that repeat

A

If there are events that occur repeatedly then it makes it easier to talk about the time it takes before the event starts again.
- This time between events is the period and is measured in units of time (s)
- Can also consider how many times an event happens in a unit of time (frequency)

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37
Q

Relation between period and frequency

A

Frequency (Hz)= 1/ Period (s)

  • have inverse relationship
    As freq increases, period decreases
    As period decreases, freq increases
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38
Q

velocity

A

measure of distance over time (v (m/s)= d (m)/t (s))

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39
Q

acceleration and velocity relationship

A

if the velocity of an object changes then it is accelerating

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40
Q

how to calculate acceleration

A

acceleration (m/s^2)= change in velocity (m/s)/time (s)

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41
Q

change in velocity

A

velocity at the end of the measurement interval- velocity at the beginning of the measurement interval

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42
Q

what two measurements are needed to calculate area?

A

length and width
reported as m^2

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43
Q

what three measurements are needed to calculate volume?

A

length, width and height
reported as m^3

  • need to count # of cubes if object is irregular shape
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44
Q

what is density and how do you calculate it?

A

measurement of mass and volume

d (kg/m^3) = mass (kg)/ volume (m^3)

45
Q

density of water

A

1000 kg/m^3

46
Q

density of air

A

1 kg/m^3

47
Q

Accuracy in the lab/clinic

A
  • measurement are expected to be no greater than 0.1%
48
Q

Sig Fig reporting

A

3 sig figs
- # of leading 0 does not count!!
ex. 1.23, 0.340, 0.00000000631 are all 3 sig figs

49
Q

how to get 3 sig figs

A

Round the values by looking at the 4th digit (ignore leading zeroes)
- If the 4th value is < 5 then truncate the number
- If the 4th value is > 4 then add 1 (round up) the third digit and truncate after the third digit

50
Q

what are the two parts of a number when the calculator breaks the answer?

A

mantissa and exponent

51
Q

what is the mantissa?

A

between 1 and 10

52
Q

what is the exponent?

A

number 10 is raised to (10^-8, the exponent is -8)

53
Q

what is scientific notation

A

a mean to express very large or small numbers in an efficient way

54
Q

how to add/subtract exponents

A

if the exponent is the same, then add or subtract the mantissa and use the exponent

55
Q

adding exponent example

A

2.0 x 10^3 + 1.2 x 10^2
- Convert 1.2 x 10^2 to 0.12 x 10^3 to make the exponent the same (larger exponent #)
- add the mantissas (2.0 and 0.12) = 2.12
- The final sum is 2.12 x 10^3 or 2120

56
Q

subtracting exponent example

A

1.5 x 10^3 - 6.5 x 10^2
- Convert 1.5 x 10^3 to 15.0 x 10^2 to make the exponent the same (smaller exponent #)
- subtract the mantissas (15 and 6.5) = 8.5
- The final sum is 8.5 x 10^2 or 850

57
Q

how to multiply/divide exponents

A

multiplication: mantissas are multiplied and exponents are added

division: mantissas are divided and exponents are subtracted

58
Q

converting from standard notation to scientific notation

A
  • Place a decimal after the first non‐zero digit
  • Place the rest of the non‐zero digits after the decimal
  • Add x 10^n
  • Count the number of places the decimal was moved to get n
  • If the standard # value is > 0 exponent is positive, if not exponent is negative
  • Scientific notation: #(mantissa) x 10^n
59
Q

what is an exponent

A

number of times a base is multiplied by itself

60
Q

if the exponent is 0, the value is ALWAYS

A

1

61
Q

what do exponents tell you about the number

A

10^0=1
10^positive #= # of zeros in result after mantissa
10^negative #= # of decimal places in result

62
Q

Logs

A

logs are always base 10 unless told otherwise and is a rewrite of an exponent

63
Q

log examples

A

log(1000)=4 is 10^4=1000

log base 2 of 16 = 4 is 2^4=16

64
Q

exponent and log relation

A

log base b of a= c
b^c=a

ex. log base 5 of 25= 2
5^2=25

65
Q

antilog

A

opposite of log

66
Q

antilog equation

A

antilog base b of a= c
b^a=c

ex. antiog base 10 of 4 = 10,000
10^4=10,000

67
Q

what is geometry

A

study of points, lines, angles, surfaces, and shapes

68
Q

what are the two divisions of geometry

A

plane
solid

69
Q

why does geometry matter

A

helps describe and understand how sound waves travel and how sound is afected as it encounts objects in space

70
Q

angle

A

the space between the sides of a figure or the displacement of one side relative to the other

71
Q

acute angle

A

displacement is <90 degrees

72
Q

right angle

A

displacement is 90 degrees

73
Q

obtuse angle

A

displacement is >90 degrees and <180 degrees

74
Q

circle

A

every point along circumference is equidistant from the center

75
Q

circumference

A

equivalent to the perimeter (C)

76
Q

radius

A

line from the center of the circle to any point of the circle (R)

77
Q

diameter

A

line from one side of the circle to the other side and passes through the center of the circle (D)

78
Q

how to calculate circumference

A

c=2pi x Radius
c=pi x Diameter

79
Q

what is the angle referred to as and in what

A

theta θ
degrees

80
Q

Degrees

A
  • Angles in the upper half of the circle are between 0 degrees and 180 degrees
  • Angles in the lower half of the circle are between 0 degrees and 180 degrees
  • These are conventions so it is possible to start anywhere.
    The figure MUST be labelled
81
Q

Radians

A

1 radian is equal to the angle that is created when the radius moves such that the arc on the circle is the same length as the radius

82
Q

how many radians are in one complete circle?

A

6+

83
Q

how to convert radians to degrees and vice versa

A

x(rad)= y(degree) x pi/180 degrees

x(degrees)= y(rad) x 180 degrees/pi

84
Q

right triangle

A

one 90 degree angle
opposite side to right angle is hypotenuse

85
Q

pythagorean theorem

A

a^2 +b^2 = c^2
where c is hypotenuse, b is adjacent, and a is opposite

86
Q

trig functions

A

sinθ= opposite/hypotenuse
cosθ= adjacent/hypotenuse
tanθ= opposite/adjacent

cosecantθ= hypotenuse/oppositve=1/sinθ

87
Q

Cartesian or rectangular coordinates

A

mapping system to identify point in 2D space

88
Q

how do we identify a point in 2D space

A

provide an x‐ coordinate and y‐coordinate relative to some (0,0) location or center location or origin

89
Q

what do the x and y coordinates do

A

capture how far to the right or left (x) the point is from the origin and how far up or down the point is from the origin

90
Q

polar coordinates

A

each point in space is defined by the radius and the
angle (r, θ)

91
Q

what is θ referred to as in polar coordinates

A

phase angle

92
Q

trig in polar coordinates

A

sinθ= opposite/hypotenuse
sinθ= y/radius (r) or y= rsinθ

cosθ= adjacent/hypotenuse
cosθ= x/radius (r) or x= rcosθ

93
Q

Cartesian and polar plots

A

same point in space can be labelled in (x,y) values and in (r, θ)

94
Q

what two things can we do to describe a series of points in space over a time window

A
  • draw a graph
  • create a function that describes a value as a function of time
95
Q

what is a function?

A

an equation that shows a relationship between values on one axis when the other axis is known; or the relationship between two sets of number

96
Q

what is a graph?

A

a visual representation between two variables

97
Q

what is interpolation?

A

determining the value of f(x) when x is not one of the numbers we used

98
Q

what is extrapolation?

A

determining the value beyond what is graphed

99
Q

straight line equation

A

y=mx+b

100
Q

slope of line

A

m
change in y/change in x
rise/run

101
Q

y-intercept

A

b
where the function crosses y-axis

102
Q

linear function

A

no bends- straight lines only
no variables raised to a power >1

103
Q

ordinal scale

A
  • order is important
  • no numerical quality assigned
104
Q

ratio scale

A
  • quantitative/numerical value
  • absolute 0 (0-calorie condition)
  • measurable distance
105
Q

nominal scale

A
  • nothing important about order
  • # is typically assigned based on the order of registration
106
Q

interval scale

A
  • no true 0
  • represents values below 0
  • measures difference between values
107
Q

Which of the following scales of measurement best describes values used to determine the number of shoe sizes for a specific footwear brand?

A

Interval

108
Q

Which of the following represents an ordinal scale of measurement?

A

Rank of test scores

Hearing Exam 1 (5 decks)

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