This document discusses different types of surveys based on accuracy, purpose, equipment used, and position of instruments. It also covers concepts like error in measurement, accuracy vs precision, most probable vs residual errors, theory of least squares, and measures of precision like standard deviation and modulus of precision. Surveys can be classified based on whether they account for earth's curvature, intended map use like control, topographic, or cadastral surveys, and the equipment employed like chain, theodolite, plane table, or photogrammetric methods. Random errors follow probability laws and can be minimized using least squares to find the most probable value.

1. SURVEY
ERROR ACCURACY AND MEASUREMENT

2. CLASSIFICATION OF SURVEY :-
• BASED ON ACCURACY OF WORKS
GEODECTIC SURVEY …..
CURVATURE OF EARTH IS TAKEN INTO ACCOUNT
HIGH ACCURACY
PLAIN SURVEY
 CURVATURE OF EARTH IS NOT TAKEN INTO ACCOUNT
SUITABLE FOR AREA WITHIN 250 SQKM

3. CLASSIFICATION OF SURVEY CONTINUE :-
• BASED ON USE OR PUPOSE OF RESULTING MAP
• CONTROL SURVEY ………. Use set up vertical and horizontal point for other
survey
• TOPOGRAPHIC SURVEY…. Show the natural feature of country like river
mountain hill
• CADASTRAL SURVEY……. To established property line, boundary, corners
• HYDROGRAPHIC SURVEY … for shore line and water depth
• Route survey
• Mine survey

4. CLASSIFICATION OF SURVEY CONTINUE :-
• BASED ON EQUIPMENT USE
• CHAIN SURVEY
• THEODOLITE
• PLANE TABLE
• TACHEOMETRIC
• PHOTOGOMATRIC
• BASED ON POSITION OF INSTRUMENT
• GROUND SURVEY
• ARIEAL SURVEY

5. SHAPE AND SIZE OF EARTH
• GEOD = The surface which is normal to the direction of gravity
• Geoid
• to help in mathematical computation a spheroid (which is obtained
by rotating an ellipse about its minor axis) is assumed which nearly
fits the shape of the earth.is very irregular
• The angle between normal to geoid and normal to the spheroid is
known as deflection of lite vertical or station error

7. • A Horizontal Plane is perpendicular to the plumb line at a point
• a Level Surface is at all points perpendicular to the Local Plumb Line.
• The two surfaces are coincident at the instrument station but diverge
with increasing distance from it due to the earth's curvature. Hence
there is a technical difference' between a Horizontal Distance (HD)
and a Level Distance (LD).

8. Let’s visualize it
FOR SMALLER HD (1)
if precision of a long and/or steep
distance measurement

9. ERROR IN MEASUREMENT
• ERROR OCCURS DUE TO
NATURAL CAUSE (Wind, temperature, humidity. refraction, gravity and magnetic.
Declination)
PERSONAL CAUSE
INSTRUMENTAL IMPERFECTION
 ERROR TYPES
 Systematic or cumulative
 Its magnitude and sign always measurable so always be corrected
 Accidental or compensating or random error
 Corrected by the law of probability

10. ACCURACY AND PRECISION IN MEASUREMENT
• ACCURACY = is the closeness or nearness of the measurements to
the "true" or "actual" value of the quantity being
measured.
• PRECISION = amount by which a measurement deviate from its
mean

11. • Random errors or accidental errors are unpredictable both as regard
to size and algebraic signs
• BUT THEY SHOW SOME CHARACTERISTICS
• SMALL ERROR ARE FORE FREQUENT
THAN LARGER
• VERY LARGE ERROR DO NOT OCCUR
AT ALL
• +VE AND –VE ERORRS OF SAME SIZE
OCCURE WITH SAME FREQUENCY
Y is the relative frequency of occurrence of an error of a
given size, x Is the size of the error, k and h are
constants that determine the shape of the curve,
And e is the base of the natural logarithms

12. MOST PROBABLE VS RESIDUAL ERROR
• MOST PROBABLE = error with maximum probability of occurrence
• RESIDUAL ERROR = OBSERVED VALUE – MOST PROBABLE VALUE
• A residual error is treated as a random error in every respect. It
follows the laws of probability and can be expressed in the form
𝒚 = 𝒌𝒆−𝒉 𝟐 𝒗 𝟐
here v =residual error
𝒑𝒗 𝒏 = 𝒚 𝒏∆𝒗 = 𝒌𝒆−𝒉 𝟐 𝒗 𝒏
𝟐
According to the laws
of probability; the
probability that a set
of events will occur
simultaneously is the
productof
theirseparate
probabilities
𝒑(𝒗 𝟏, 𝒗 𝟐,…, 𝒗 𝒏) = 𝒌 𝒏
∆𝒗 𝒏
𝒆−𝒉 𝟐(𝒗 𝟏
𝟐+⋯…+𝒗 𝒏
𝟐)
MAXIMUM
MINIMUM

13. Theory of least square
• the most probable value or the value of a quantity which has the
maximum probability of occurrence is obtained when sum of the
squares of the residuals is minimum.
• Let a quantity is measured n times, we get values like 𝑴 𝟏, 𝑴 𝟐, …….
𝑴 𝒏. If M be the most probable value.
so residual 𝒗 𝒏 = 𝑴 𝒏 − 𝑴
According to the theory of least square 𝒗 𝒏
𝟐
should be minimum
so
𝒅
𝒅𝑴
𝒗 𝒏
𝟐
= 𝟎
𝒅
𝒅𝑴 𝟐 𝒗 𝒏
𝟐 < 𝟎 𝒂𝒏𝒅 𝒘𝒆 𝒈𝒆𝒕 ,
𝑀 =
𝑀1+𝑀2+⋯……….+𝑀 𝑛
𝑛
WE GET THE MOST PROBABLE
VALUE BY TAKING MEAN OF THE
OBSERVED VALUES AND INSTEAD OF
TRUE ERRORS WE GET
RESIDUALS BY OBTAINING DEVIATION
FROM THE MEAN.

14. Measure of precision
DATA ARE
MORE PRECISE
DATA ARE NOT
PRECISE
• Statistically, precision can be measured by means of quantity a known as
Standard Deviation or Standard Error and is given by
𝝈 =
𝒗 𝟐
𝒏−𝟏
; 𝒚 =
𝟏
𝝈 𝟐𝝅
𝒆
−𝟏
𝟐𝝈 𝟐 𝒗 𝟐
Smaller the value of 𝝈
greater is the precision
( n -1) is called degrees of
freedom
k =
𝟏
𝝈 𝟐𝝅
h=
−𝟏
𝟐𝝈 𝟐
Modulus of
precision
PRECISION INCREASES WITH h and k

15. 𝐸50, 𝐸90, 𝐸95 ERRORS
• we can find out the limit within which 50, 90 and 95% of the errors
will lie.
𝑬 𝟓𝟎 =. 𝟔𝟕𝟒𝟓𝝈
𝑬 𝟗𝟎 = 𝟏. 𝟔𝟒𝟒𝟗𝝈
𝑬 𝟗𝟓 = 𝟏. 𝟗𝟓𝟗𝟗𝝈
• PROPOGATION OF RANDOM ERROR
𝐸𝑠𝑢𝑚 = ± (𝐸 𝑥
2
+ 𝐸 𝑦
2
+ 𝐸𝑧
2
)
PREVIOUSLY KNOWN AS PROBABLE ERROR

16. CHECK THE PROBLEM

17. ERROR OF SERIES

18. CHECK THE PROBLEM

19. ERROR OF MEAN

21. WIEGHT MEASUREMENT