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Hearing Exam 1 > Measurement and Uncertainty > Flashcards

Measurement and Uncertainty Flashcards

(108 cards)

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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
how can we describe errors in measurement?
- random - systemic (bias)
26
how is systemic bias split/what type of errors are systematic?
- offset errors - scale factor errors
27
what is the difference between offset errors and scale factor errors?
offset- calibration error or no offset made scale factor- errors proportional to "true" measurement
28
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?
Any measurement you make will be off by the same amount- the weight of the bowl that holds the meat
29
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?
Any measurements that are made with this tape measure will be 101% of the actual measurement.
30
how do you calculate percent error?
% error= (observed result-expected result)/expected results x 100%
31
SI Prefixes
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
32
non-SI units
time (minute (m), hour (h). day (d)) volume (liter (L or l)) mass (ton (t)) energy (electronvolt (eV))
33
non-SI unit relation to Si
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
34
base units
time (seconds- s) length (meter- m) mass (kilogram- kg)
35
what are derived units?
units that combine two base units
36
events that repeat
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)
37
Relation between period and frequency
Frequency (Hz)= 1/ Period (s) - have inverse relationship As freq increases, period decreases As period decreases, freq increases
38
velocity
measure of distance over time (v (m/s)= d (m)/t (s))
39
acceleration and velocity relationship
if the velocity of an object changes then it is accelerating
40
how to calculate acceleration
acceleration (m/s^2)= change in velocity (m/s)/time (s)
41
change in velocity
velocity at the end of the measurement interval- velocity at the beginning of the measurement interval
42
what two measurements are needed to calculate area?
length and width reported as m^2
43
what three measurements are needed to calculate volume?
length, width and height reported as m^3 - need to count # of cubes if object is irregular shape
44
what is density and how do you calculate it?
measurement of mass and volume d (kg/m^3) = mass (kg)/ volume (m^3)
45
density of water
1000 kg/m^3
46
density of air
1 kg/m^3
47
Accuracy in the lab/clinic
- measurement are expected to be no greater than 0.1%
48
Sig Fig reporting
3 sig figs - # of leading 0 does not count!! ex. 1.23, 0.340, 0.00000000631 are all 3 sig figs
49
how to get 3 sig figs
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
what are the two parts of a number when the calculator breaks the answer?
mantissa and exponent
51
what is the mantissa?
between 1 and 10
52
what is the exponent?
number 10 is raised to (10^-8, the exponent is -8)
53
what is scientific notation
a mean to express very large or small numbers in an efficient way
54
how to add/subtract exponents
if the exponent is the same, then add or subtract the mantissa and use the exponent
55
adding exponent example
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
subtracting exponent example
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
how to multiply/divide exponents
multiplication: mantissas are multiplied and exponents are added division: mantissas are divided and exponents are subtracted
58
converting from standard notation to scientific notation
- 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
what is an exponent
number of times a base is multiplied by itself
60
if the exponent is 0, the value is ALWAYS
1
61
what do exponents tell you about the number
10^0=1 10^positive #= # of zeros in result after mantissa 10^negative #= # of decimal places in result
62
Logs
logs are always base 10 unless told otherwise and is a rewrite of an exponent
63
log examples
log(1000)=4 is 10^4=1000 log base 2 of 16 = 4 is 2^4=16
64
exponent and log relation
log base b of a= c b^c=a ex. log base 5 of 25= 2 5^2=25
65
antilog
opposite of log
66
antilog equation
antilog base b of a= c b^a=c ex. antiog base 10 of 4 = 10,000 10^4=10,000
67
what is geometry
study of points, lines, angles, surfaces, and shapes
68
what are the two divisions of geometry
plane solid
69
why does geometry matter
helps describe and understand how sound waves travel and how sound is afected as it encounts objects in space
70
angle
the space between the sides of a figure or the displacement of one side relative to the other
71
acute angle
displacement is <90 degrees
72
right angle
displacement is 90 degrees
73
obtuse angle
displacement is >90 degrees and <180 degrees
74
circle
every point along circumference is equidistant from the center
75
circumference
equivalent to the perimeter (C)
76
radius
line from the center of the circle to any point of the circle (R)
77
diameter
line from one side of the circle to the other side and passes through the center of the circle (D)
78
how to calculate circumference
c=2pi x Radius c=pi x Diameter
79
what is the angle referred to as and in what
theta θ degrees
80
Degrees
- 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
Radians
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
how many radians are in one complete circle?
6+
83
how to convert radians to degrees and vice versa
x(rad)= y(degree) x pi/180 degrees x(degrees)= y(rad) x 180 degrees/pi
84
right triangle
one 90 degree angle opposite side to right angle is hypotenuse
85
pythagorean theorem
a^2 +b^2 = c^2 where c is hypotenuse, b is adjacent, and a is opposite
86
trig functions
sinθ= opposite/hypotenuse cosθ= adjacent/hypotenuse tanθ= opposite/adjacent cosecantθ= hypotenuse/oppositve=1/sinθ
87
Cartesian or rectangular coordinates
mapping system to identify point in 2D space
88
how do we identify a point in 2D space
provide an x‐ coordinate and y‐coordinate relative to some (0,0) location or center location or origin
89
what do the x and y coordinates do
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
polar coordinates
each point in space is defined by the radius and the angle (r, θ)
91
what is θ referred to as in polar coordinates
phase angle
92
trig in polar coordinates
sinθ= opposite/hypotenuse sinθ= y/radius (r) or y= rsinθ cosθ= adjacent/hypotenuse cosθ= x/radius (r) or x= rcosθ
93
Cartesian and polar plots
same point in space can be labelled in (x,y) values and in (r, θ)
94
what two things can we do to describe a series of points in space over a time window
- draw a graph - create a function that describes a value as a function of time
95
what is a function?
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
what is a graph?
a visual representation between two variables
97
what is interpolation?
determining the value of f(x) when x is not one of the numbers we used
98
what is extrapolation?
determining the value beyond what is graphed
99
straight line equation
y=mx+b
100
slope of line
m change in y/change in x rise/run
101
y-intercept
b where the function crosses y-axis
102
linear function
no bends- straight lines only no variables raised to a power >1
103
ordinal scale
- order is important - no numerical quality assigned
104
ratio scale
- quantitative/numerical value - absolute 0 (0-calorie condition) - measurable distance
105
nominal scale
- nothing important about order - # is typically assigned based on the order of registration
106
interval scale
- no true 0 - represents values below 0 - measures difference between values
107
Which of the following scales of measurement best describes values used to determine the number of shoe sizes for a specific footwear brand?
Interval
108
Which of the following represents an ordinal scale of measurement?
Rank of test scores

Hearing Exam 1 (5 decks)

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