1. The document discusses sources of error in experimental measurements and how to minimize errors. It defines two main types of error - random and systematic error. Random errors can be reduced by taking multiple measurements and finding the average. Systematic errors produce consistent biases and are harder to identify and reduce. 2. Several specific sources of error are described, including instrumental errors, environmental errors, procedural errors, and human errors like transcription mistakes. Taking repeated measurements and calibrating instruments can help minimize different error sources. 3. Formulas for mean, standard deviation, and standard error are provided to quantify errors from multiple measurements of a single quantity. The standard deviation measures variation in individual measurements while the standard error estimates uncertainty in the mean

1. Hello everyone!
I’m Judylyn Tam
General Physics 1 Class

2. Prayer
Dear Lord and Father of all
Thank you for today
For your protection and love we thank you
Help us to focus our hearts and minds now on what
we are about to learn
Inspire us by Your Holy Spirit as we listen and write.
Guide us by your eternal light as we discover more
about the world around us.
We ask all this in the name of Jesus.
Amen.

3. MODULE 2
Sources and Types
of Error
General Physics 1

4. Let’s Review!
CONVERSION OF UNITS
1. 8 km =_________ m
2. 6 ft =_________ in
SCIENTIFIC NOTATION
1. 0.00518 =_________
2. 452 X10-4 =_________
8000
72
5.18 X10-3
0.0452
Differentiate accuracy from precision

5. Most Essential Learning Competency
1.Differentiate random errors from
systematic errors (STEM_GP12EU-Ia-3)
2.Estimate errors from multiple
measurements of physical quantity
using variance (STEM_GP12EU-Ia-5)

6. Engage:
Fill in the graphic organizer below.
TYPES OF ERROR SOURCES OF
ERROR
Preventable Natural Variation

7. EXPLORE: MINIMIZING ERRORS
Objective
• Demonstrate the sources of experimental error and the
effect of replicate measurements in reducing the size of the
error.
Materials: ruler
Task:
• Using a ruler, measure the largest span of your left or right
hand in centimeters (cm) – this is the largest distance you
can reach between the tip of your smallest finger and end of
your thumb (see figure on the right). Write down your
measurement, relax your hand, then measure it again. Do
this again until you have a total of ten measurement.

8. Trials 1 2 3 4 5 6 7 8 9 10
Measure
ment
(cm)

9. Q1. Are the results exactly the same for all ten measurements? If
not, what is the largest difference between the values?
Q2. Why do you think measurements are different?
Q3. What is the importance of taking repeated measurements of
a single quantity?
Q4. Do you think you will have a different result if you used a
different measuring tool? Why or why not?
Q5. Suggest ways to minimize the differences in measurements

11. Error
the difference
between your results
and the expected or
theoretical results.
1. RANDOM ERROR
 occurs due to chance
 caused by slight fluctuations in an
instrument, the environment, or
the way a measurement is read.
How to address random error ?
 By replication(repeating a
measurement many times and
taking the average).

12. Error
the difference
between your results
and the expected or
theoretical results.
2.SYSTEMATIC ERROR
 gives measurements that are
consistently different from the
true value in nature
 one form of bias
 Bias is often caused by
instruments that consistently
offset the measured value from
the true value

13. Error cannot be
completely
eliminated, but it
can be reduced
1. Instrumental error
2. Environmental error
3. Procedural error
4. Human error

14. Error cannot be
completely
eliminated, but it
can be reduced
1. Instrumental error
 happens when the
instruments being used
are inaccurate, broken or
not properly calibrated.

15. Error cannot be
completely
eliminated, but it
can be reduced
2. Environmental error
 happens when some
factor in the environment,
such as temperature,
leads to error.

16. Error cannot be
completely
eliminated, but it
can be reduced
3. Procedural error
 occurs when different
procedures are used to
answer the same question
and provide slightly
different answers.

17. Error cannot be
completely
eliminated, but it
can be reduced
4. Human error
 due to carelessness or to
the limitations of human
ability. Two types of
human error are
transcriptional error and
estimation error.

18. Error cannot be
completely
eliminated, but it
can be reduced Transcriptional error occurs
when data is recorded or
written down incorrectly.
Estimation error can occur
when reading measurements
on some instruments.
HUMAN ERROR

19. Situational Analysis
Suppose you are
trying to determine
which will reach the
ground first a crumpled
piece of paper or a rock
when released from the
same height at the same
time
1. What type of error
might you make and
what sources might
have caused it?
2. Can you do anything to
reduce the amount of
error that might occur?

21. Suppose you want to
know just how high the okra
you planted at the beginning
of your summer vacation
have grown. You take several
measurements just to be
sure. Here are the
measurements you came up
with.

22. Mean (𝑋)
𝑋 =
𝑋
𝑛
Where:
x is each value in a data
set
𝑋 is the mean of all
values in the data set
n is the number of
measurements
 the expected central
value for a set of data.

23. Mean (𝑋)
𝑋 =
𝑋
𝑛
=
22.8+23.1+22.7+22.6+23.0
5
=
114.2
5
= 22.8
 the expected central
value for a set of data.

24. (X - 𝑋)
 the expected central
value for a set of data.
Trial 1 22.8-22.8 = 0
Trial 2 23.1-22.8 = 0.3
Trial 3 22.7-22.8 = -0.1
Trial 4 22.6-22.8 = -0.2
Trial 5 22.8-22.8 = 0.2

25. (X - 𝑋)𝟐
Trial 1 02
= 0
Trial 2 0.32
= 0.09
Trial 3 - 0.12
= 0.01
Trial 4 - 0.22
= 0.04
Trial 5 0.22
= 0.04
 the difference between
a measured quantity and
its true value.
0.18
JUST
ADD

26. STANDARD DEVIATION
SD =
(x − 𝑋)𝟐
𝑛
SD =
0.18
5
SD = 0.036
SD = 0.189 OR 0.19
 the expected spread from
the mean for a set of data.

27. STANDARD ERROR of the MEAN
SEM =
𝑺𝑫
𝒏
=
𝟎.𝟏𝟗
𝟓
=
0.19
2.24
= 0.08
 estimates how repeated measurements taken on the
same instrument are estimated around the true score.
The SD is a measure of the
amount of variation due to
differences among individuals.
It is not due to errors in
measurement and differs from
the SEM, which is caused by
errors in replicate
measurements.

28. HOME-BASED ACTIVITY
Two students determined the concentration of a
hydrogen peroxide solution by the same volumetric
technique. They each carried out the analysis in
triplicate and obtained the results you see in the
data table. The true concentration of the hydrogen
peroxide solution is 0.893 mol L-1 .Determine the
error in measurements of students A and B by solving
for the SD and SEM. Show your complete solution.

29. Student A B
Hydrogen peroxide
concentration/mol
L-1
0.893 0.884
0.897 0.882
0.889 0.883

30. Trial
Concentrati
on, x
(mol L-1 )
x- x̄ (x- x̄)2
1 0.893
2 0.897
3 0.889
x̄= ∑(x- x̄)2 =
SD= SEM=
A.

31. SD= SEM=
B.
Trial
Concentration, x
(mol L-1 )
x- x̄ (x- x̄)2
1 0.884
2 0.882
3 0.883
x̄= ∑(x- x̄)2 =