# Surveying Questions and Answers – Survey Adjustments and Errors Theory – Accidental Errors Laws

This set of Surveying Multiple Choice Questions & Answers (MCQs) focuses on “Survey Adjustments and Errors Theory – Accidental Errors Laws”.

1. The laws of accidental errors follow which of the following principle?
a) Normal equation
b) Probability law
c) Laws of weight
d) Most probable value

Explanation: Laws of accidental errors follow the probability law, which is having a definite law for accidental error occurrence. It defines the errors and helps in expressing them in the form of equations.

2. Which of the following does not indicate the feature in laws of accidental errors?
a) Negligible errors
b) Small errors
c) Large errors
d) Positive errors

Explanation: The features in laws of accidental errors include the tendency of small errors to be more frequent, positive and negative errors with equal frequency and making large errors occurrence impossible.

3. Most probable value is equal to which of the following?
a) Differentiation
b) Summation
c) Arithmetic mean
d) Normal equation

Explanation: Most probable value is equal to the arithmetic mean, in case all the taken weights are equal and in case of unequal weights, it is equal to the weighted arithmetic mean.

4. The value of mean square error can be given as__________
a) (∑v2+n)1/2
b) (∑v2*n)1/2
c) (∑v/n)1/2
d) (∑v2/n)1/2

Explanation: The mean square error is the ratio which is obtained by the taking mean of all the possible errors. It is taken as. It is useful in determining the possible error occurred and helps in reducing it by distributing it equally.

a) Normal equation
b) Frequency of errors
c) Probability curve
d) Probability equation

Explanation: The probability curve, which is established from the theory of probability, describes about the features like relative frequency of the errors in the form of curve. It is the basis for many mathematical derivations.
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6. Determine the probable error in a single measurement if the summation of the difference between mean and single observation is given as 8.76 in a series of 7 observations.
a) 0.98
b) 0.93
c) 9.08
d) 0.89

Explanation: The value of the probable error of single observation can be determined by using the formula,
Es = 0.6745*$$\sqrt{∑v^2/(n-1)}.$$ On substitution, we get
Es = 0.6745*$$\sqrt{8.76^2/(7-1)}.$$ Es = 0.98.

7. Determine the probable error of measurements by using the different probable errors, which are given as 5.64, 2.98, 0.98 and 2.54.
a) 3.96
b) 9.63
c) 6.93
d) 9.36

Explanation: The probable error of measurements can be given as,
Probable error of measurement = $$\sqrt{E1^2+E2^2+E3^2+E4^2}$$. On substitution, we get
= $$\sqrt{5.64^2+2.98^2+0.98^2+2.54^2}$$
= 6.93.

8. What will be the mean square error, if the readings were given as 2.654, 2.987, 2,432 and 2.543.
a) 3.305
b) 0.335
c) 0.305
d) 30.35

Explanation: The mean square error can be given as,
M.S.E = $$\sqrt{∑v^2/n}$$. The mean of the readings can be given as,
(2.645 + 2.987 + 2.432 + 2.543) / 4 = 2.651.
The values of v are obtained by difference of each reading with the mean. So, the ∑v can be given as
∑v = (2.651-2.645) + (2.987-2.651) + (2.651-2.432) + (2.652-2.543) = 0.67
On substitution, we get
M.S.E = $$\sqrt{∑v^2/n}$$
M.S.E = $$\sqrt{0.67^2/4}$$
M.S.E = 0.335.

9. If the value of error due to the single measurement is 6.54 for 10 observations, then calculate the value of average probable error.
a) 2.086
b) 2.608
c) 0.268
d) 2.068

Explanation: The average probable error can be calculated by using the formula,
Em = Es / $$\sqrt{n}$$. On substitution, we get
Em = 6.54 / $$\sqrt{10}$$
Em = 2.068.

10. Find the number of observations if the mean square error and the summation of the difference between the individual and the mean series are given as 0.987 and 3.654.
a) 14
b) 12
c) 10
d) 9

Explanation: The mean square error can be calculated by using the formula,
M.S.E = $$\sqrt{∑v^2/n}$$. On substitution, we get
0.987 = $$\sqrt{3.654^2/n}$$
n = 14 (approximately).

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