Checklist
Notes
For Unit 1C, we only focus on pages 162 - 167. This is
titled Undertanding Errors
Describe two types of errors.
Connect 3B with the current unit with absolute and
relative errors.
Describe the differences of accuracy and precision.
We omit significant digits and combining errors.
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Assignment
Notes
Assignment:
1. p 169 Quick Quiz
2. p 170 - 171 Excercises 40, 45, 49, 50, 51, 54, 55
3. Exam 1 on Thursday, February 13. 1C, 1D, 2A, 2B,
3A, 3B, 3C
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Key Words
Notes
Random errors Error caused by random and inherient
unpredictable events in the measurement process.
Systematic errors A problem in the measurement
system that affects all measurements in the same way.
Absolute error How far a measured or claimed value
lies from the true value as a difference.
Relative error The ratio of the size of the error
(absolute difference) to its true value.
Accuracy How close a measurement is to the true
value.
Precision The amount of detail in the measurement.
For instance, 2.3 miles is less detailed than 2.32 miles.
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Reliable estimates
Notes
Should an estimate you make be far or close to the actual
value, it is important to know how the uncertainty may
appear. Error type roughly falls in two categories:
Random errors. Example: Trying to weigh a wiggling
baby maybe will have readouts that jump around,
ranging from value to value for the same baby.
Systematic errors. Example: You find the baby scale
records a weight of 1.2 lbs when no baby is being
weighed!
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Example - Global Temperature Data
Notes
Trying to measure the average global temperature has
several difficulties. Two are: (1) Temperatures were
measured with simple thermometers and recorded by
hand, during the 20th century. (2) Most recordings are
near urban areas that are warmer due to heat output by
human activity.
Discuss whether each of this two difficulties produces
random or systematic errors, and consider how to correct
them.
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Example - Census Data
Notes
Every ten years, the government mandates a census of the
population. This is conducted by distributing household
surveys by mail or through personal visits.
Suggest sources of of both random and systematic errors
in the census.
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Sizes of Errors
Notes
Besides types of errors, it is desired to know the overall
size of the error. Will a large error be of concern, and
equally will a small error be unimportant? More
technically,
Absolute error describes how far a measured or
claimed value is from the true value. Example: We
ask for 6 pounds of hamburger but only get 4 pounds.
The absolute error is 2 lbs.
Relative error compares the size of the absolute error
to the actual value. Example: 2 lbs is half the weight
of the actual 4 lbs. Then 2/4 is the relative error.
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Example - Calculations
Notes
Find the absolute and relative error in each case.
Example The label on a bag of dog food says, ”30 lbs,”
but the true weight is only 29 pounds.
Example A weather report claims today’s high
temperature will reach 42◦ , but it reaches 48◦ .
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Accuracy and Precision
Notes
Next, consider if any reported errors are accurate or
precise. Minimizing error is prefered, so more accurate
results are closer to true values. Then, the amount of
detail given to the measurement is how precise it is.
Accuracy - How close a measured or claimed value is
to the true value.
Precision - How much detail in measurement is taken.
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Example - Describing the Results of Calculations
Notes
Consider the dog food bag weight example. The true
weight is 29 lbs. Consider the scale at time of
manufacture reads 29.5 lbs and reads out to the nearest
0.1 lbs. A scale used at a pet supply store reads only to
the nearest 0.2 lbs and says it weighs 29.4 lbs.
Which is more accurate, and which is more precise?
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Study Tips!
Notes
Here are some tips for studying for Exam 1.
1. Try the homework problems. Recall the units on Exam
1 are 1C, 1D, 2A, 2B, 3A, 3B, 3C.
2. Join a study group. By now you may have already
worked with some other students in class. Try
studying together!
3. Prepare early, study early.
4. The T. Benny Rushing Math tutoring center is free
and open 8 AM - 8 PM Monday to Friday, but closes
at 6 PM Friday.
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Study Tips!
Notes
During the exam,
1. Read through the exam to know what is expected
from you. This will also help you prioritize questions.
2. Clearly write out each step. Check that you start at
the beginning a provided enough detailed work.
3. Double check your work, especially when you use a
calculator.
4. Recall Tip 8 from 2C: Don’t work yourself to hard on
one problem. Come back to hard problems later.
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