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    Module 1 Lesson 2

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    Rainiel Montalba
    1. An error is the difference between a measured quantity and its true value. There are three main causes of errors: instrumental errors, personal errors, and natural causes. 2. There are two main types of errors: systematic errors, which are constant and can accumulate, and accidental or random errors, which are small and unavoidable. Mistakes are inaccuracies caused by carelessness while blunders are significant mistakes caused by human error. 3. Accuracy indicates how close a measurement is to the true value, while precision refers to the consistency and refinement of measurements. The most probable value is the quantity that is most likely to be correct based on the available data.

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    Module 1 Lesson 2

    Uploaded by

    Rainiel Montalba
    46 views17 pages
    1. An error is the difference between a measured quantity and its true value. There are three main causes of errors: instrumental errors, personal errors, and natural causes. 2. There are two main types of errors: systematic errors, which are constant and can accumulate, and accidental or random errors, which are small and unavoidable. Mistakes are inaccuracies caused by carelessness while blunders are significant mistakes caused by human error. 3. Accuracy indicates how close a measurement is to the true value, while precision refers to the consistency and refinement of measurements. The most probable value is the quantity that is most likely to be correct based on the available data.

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    1. An error is the difference between a measured quantity and its true value. There are three main causes of errors: instrumental errors, personal errors, and natural causes. 2. There are two main types of errors: systematic errors, which are constant and can accumulate, and accidental or random errors, which are small and unavoidable. Mistakes are inaccuracies caused by carelessness while blunders are significant mistakes caused by human error. 3. Accuracy indicates how close a measurement is to the true value, while precision refers to the consistency and refinement of measurements. The most probable value is the quantity that is most likely to be correct based on the available data.

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    © All Rights Reserved
    Download as PPTX, PDF, TXT or read online from Scribd
    Download as pptx, pdf, or txt
    46 views17 pages

    Module 1 Lesson 2

    Uploaded by

    Rainiel Montalba
    1. An error is the difference between a measured quantity and its true value. There are three main causes of errors: instrumental errors, personal errors, and natural causes. 2. There are two main types of errors: systematic errors, which are constant and can accumulate, and accidental or random errors, which are small and unavoidable. Mistakes are inaccuracies caused by carelessness while blunders are significant mistakes caused by human error. 3. Accuracy indicates how close a measurement is to the true value, while precision refers to the consistency and refinement of measurements. The most probable value is the quantity that is most likely to be correct based on the available data.

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    © All Rights Reserved
    Download as PPTX, PDF, TXT or read online from Scribd
    Download as pptx, pdf, or txt
    of 17

    MISTAKES AND

    ERRORS
    LESSON 2
    ERROR is the difference between a measured quantity and its true value.

    Causes of Errors:
    1. Instrumental error
    2. Personal error
    3. Natural causes.

    Types of Error

    1. Systematic Error
    Also referred to as mechanical errors or cumulative errors. Repetitive errors that are
    caused by imperfections in the surveying equipment, by the specific method of observation, or
    by certain environmental factors. These errors are constant in magnitude and direction or sign
    (either plus or minus). They usually have no tendency to cancel, and if corrections are not
    made, they can accumulate to cause significant difference between the measured and actual
    or true quantities.
    2. Accidental Error or Random Error
    the difference between a true quantity and the measurement of that quantity that is
    free from blunders or systematic error. It always occurs in every measurement. They
    are the relatively small, unavoidable errors in observation that are generally beyond
    the control of the surveyor. These errors are not constant in magnitude or direction.

    MISTAKES

    are inaccuracies in measurements which occur because some aspect of a surveying


    operation is performed by the surveyor with carelessness, inattention, poor
    judgment, and improper execution.
    Frequently committed mistakes:

    1. Reading wrong graduation on the tape

    2. Omitting a whole length of tape

    3. Transposition of figures

    4. Reading a scale backward


    5. Misplacing a decimal point

    6. Incorrect recording of field notes

    7. Adding a row or column of numbers

    BLUNDERS - a significant mistake caused by human error. It may also be called gross error.
    ACCURACY indicates how close a given measurement is to the absolute or true value of
    the quantity measured.
    PRECESION refers to the degree of refinement and consistency with which any physical
    measurement is made.
    MOST PROBABLE VALUE refers to a quantity which based on available data has more
    chances of being correct than has any other.

    mpv or X = X/n = (X1 + X2 + X3 +…….. + Xn)/n


    RESIDUAL sometimes referred to as the deviation is the difference between any measured
    value of a quantity and its most probable value
    v=x–x
    where: v – the residual in any measurement
    x – measurement made of a particular quantity
    x – most probable value of the quantity measured
    Probable Error – a quantity which when added to and subtracted from the most probable value
    defines a range within which there is a 50 percent chance that the true value of the measured
    quantity lies inside (or outside) the limits thus set.

    The 9O PERCENT ERROR or E90 is a usual criterion for rating survey methods. It is
    sometimes called the maximum anticipated error.
    PEs = ± 0.6745

    PEm = ± 0.6745

    where: PEs = probable error of any single measurement of a series


    PEm = probable error of the mean
    v2 = summation of the squares of the residuals
    n = number of observations
    E90 = 1.645

    Sample Problem 1

    A Civil Engineer measures the distance of points A and B and the following values were
    recorded in a series of measurement.
    Trials Number of Measurements
    1 200.58
    2 200.40
    3 200.38
    4 200.46

    1. Determine the average value (mean)


    2. Determine the probable error of mean
    3. Determine the precision of the measurements
    Solution

    1. Average Mean Value = = 200.455

    2. Probable Error of the Mean


    Length V V2
    200.58 200.58 - 200.455 = +0.125 0.015625
    200.40 200.40 - 200.455 = -0.055 0.003025
    200.38 200.38 - 200.455 = -0.075 0.005625
    200.46 200.46 - 200.455 = +0.005 0.000025
    ∑V2 = 0.0243

    PEm = 0.6745 = 0.6745 = ± 0.03


    3. Precision of the measurement = 0.03/200.455 = 1/6681.83
    Sample Problem 2

    From the measured values of distance AB, the following trials were recorded
    TRIALS DISTANCE
    1 120.68
    2 120.84
    3 120.76
    4 120.64

    1. Find the probable error


    2. Find the standard deviation
    3. Find the standard error
    Solution
    1. Mean Value = = 120.73

    Residual V V2
    120.68 - 120.73 = -0.05 0.0025
    120.84 - 120.73 = +0.11 0.0121
    120.76 - 120.73 = +0.03 0.0009
    120.64 - 120.73 = - 0.09 0.0081
    ∑V2 = 0.0236

    PEm = 0.6745 = 0.6745 = ± 0.0299


    2. Standard Deviation

    SD = = = ± 0.0887

    3. Standard Error

    SE = = = ± 0.0443
    Sample Problem 3

    The following shows the difference in elevation between A and B.

    Trial Difference in Elevation No, of Measurements


    1 520.14 m 1
    2 520.20 m 3
    3 520.18 m 6
    4 520.24 m 8

    1. Compute the probable weight of trial 3


    2. Determine the most probable diff. in elevation
    3. Compute the elevation of B if elevation of A is 1000 with B higher than A
    Solution
    1. Weight of trial 3 = 6

    2. Probable diff in elev.


    Total weight = 18
    Weighted Values
    520.14(1) = 520.14
    520.20(3) = 1560.60
    520.18(6) = 3121.08
    520.24(8) = 4161.92
    Sum = 9363.74

    Probable value of diff. in elev. = = 520.21

    3. Elevation of B = 1000 + 520.21 = 1520.21


    Sample Problem 4

    A distance was measured five times as follows: 75.3, 76.2, 75.7, 75.5 and 75.8 m.
    Compute the most probable distance and the 90% error of that procedure.
    Mean = 75.7 m

    (75.3 - 75.7)2 = 0.16


    (76.2 - 75.7)2 = 0.25
    (75.7 - 75.7)2 = 0
    (75.5 - 75.7)2 = 0.04
    (75.8 - 75.7)2 = 0.01
    ∑V2 = 0.46
    Solution

    E90 = = = ± 0.15 m
    RESIDUAL sometimes referred to as the deviation is the
    difference between any measured value of a quantity and
    its most probable value

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