# Advice 1: How to determine the error of the instrument

The implementation of many educational and scientific-research works connected with carrying out a variety of measurements of physical quantities. After receiving the results of the instrumental measurements usually follows the treatment. For exact match the results of a calculation pattern of the experiment is required to take into account the error margin of measurements. Determining the error of measuring instruments is carried out by special methods.
Instruction
1
Use to determine absolute instrumental error determined by the design of the instrument, a special table, the errors of measuring instruments. For example, the drawing line length is 500 mm and the interval is 1 mm absolute instrumental error of plus or minus 1 mm; and for micrometer with measuring range of 25 mm and 0.01 mm, this value will be plus or minus 0.005 mm.
2
Determine the absolute error of reference. It is derived from not very accurate readings, starting with measuring instruments and devices. In most cases it is equal to the half the price of division of the instrument scale. When measuring time absolute error of reference take is equal to the division value of the stopwatch (hours).
3
Calculate the maximum absolute error of direct observation. It is defined as the sum of the absolute instrumental error and the absolute error count (if other types of errors can be neglected):

A' = AI + AO where

A' – maximum absolute error of direct observations;
AI – absolute instrumental error;
AO absolute accuracy of the countdown.
4
When determining absolute error of measurement instrument, we round it to one significant digit. The numerical value of the result of the measurement procedure are rounded so that its last digit were in the same category as the digit error.
5
If there is a need for instrument re-measurement undertaken in the same controlled conditions, then the margin of error, referred to here as the random, determine the arithmetic average of errors of all measurements.
6
To define an absolute sampling error of electrical measuring instrument, find out its accuracy. It usually indicate the scale of the device or technical data sheet (description).

# Advice 2 : How to calculate absolute error

Measurements can be performed with varying degrees of accuracy. It is absolutely accurate are not even precision instruments. Absolute and relative error may be small, but in reality they are almost always. The difference between the approximate and exact values of a certain magnitude is called the absolute error. The deviation can be both upwards and downwards.
You will need
• - measurement data;
• calculator.
Instruction
1
Before you can calculate absolute uncertainty, take for initial data a few postulates. Eliminate gross errors. Accept that the necessary amendments have already been calculated and included in the result. The amendment may be, for example, the transfer starting point of measurement.
2
Take as a starting position that is known and taken into account random error. This implies that they are less systematic, i.e., absolute and relative, are specific to this device.
3
Random errors affect the result, even high-precision measurements. Therefore, any result will be more or less close to absolute, but there will always be differences. Determine this interval. It can be expressed by the formula (Hism - HH)≤Chism ≤ (Hism+HH).
4
Determine the amount that approximated to the true value. In real measurements, the arithmetic mean, which can be found using the formula shown in the figure. Take the result for the true value. In many cases, as accurate a reading is taken of the reference device.
5
Knowing the true value of the measurement, you can find the absolute error, which should be considered in all subsequent measurements. Find the value of X1 – specific data measurement. Determine the difference between the HH, subtracting a larger number from a smaller. When error determination takes into account only the module of this difference.
Note
As a rule, in practice, absolutely accurate measurement is not possible to lead. Therefore, for the reference value is taken as the limit error. It represents the maximum value of the modulus of the absolute error.
Useful advice
In practical measurements the magnitude of the absolute error is usually taken as half the smallest scale. When operating with numbers over the absolute error is taken half the value of the digit that is in the following with accurate figures for the category.

To define the accuracy class of the instrument is more important is the ratio of absolute error to the measurement result or the length scale.

# Advice 3 : How to calculate measurement error

The result of any measurement is inevitably accompanied by a deviation from the true value. To calculate the measurement error in several ways depending on its type, for example, statistical methods for determining the confidence interval, standard deviation, etc.
Instruction
1
There are several reasons that give rise to error of measurement. This instrument inaccuracy, imperfection techniques, as well as errors caused by inattention of the operator performing the measurements. In addition, often the true value of the parameter take its actual value, which actually is merely the most probable, based on the analysis of statistical sample results a series of experiments.
2
Accuracy is a measure of the deviation of the measured parameter from its true value. According to the method of Kornfeld, determine the confidence interval, which ensures a certain degree of reliability. They find the so-called confidence limits, which varies the magnitude error is calculated as half the sum of these values:∆ = (xmax - xmin)/2.
3
This is interval estimation error, which is carried out in a small volume of the statistical sample. Point estimation is to calculate the mathematical expectation and standard deviation.
4
Mathematical expectation is an integral sum of a number of works by the two parameters of the observations. It actually measured value and its probability at these points:M = Σxi•pi.
5
The classic formula for calculating the standard deviation involves the calculation of the average values of the analyzed sequence of values of the measurand, and also takes into account the volume series of the experiments:σ = √(∑(xi – khsr)2/(n - 1)).
6
According to the method of expression also distinguish absolute, relative and reduced error. The absolute error is expressed in the same units as the measured value, and is equal to the difference between the estimated and true value is:∆x = x1 – x0.
7
The relative error measurements associated with the absolute, but is more efficient. It has no dimension, sometimes expressed in percentages. It is the ratio of absolute error to the true or calculated value of the measured parameters:σx = ∆x/x0 or σx = ∆x/x1.
8
Given the margin of error is expressed as the ratio between absolute error and some conventionally accepted value x, which is constant for all measurements and is determined by the calibration of the instrument scale. If the scale starts from zero (one-sided), this normalizing value equal to its upper limit, and if a double – width of its range:σ = ∆x/xn.

# Advice 4 : How to determine the measurement error

The deviation from the true value inevitably arises when constructing probabilistic models for some parameter. This concept is applied in order to determine the error of measurement, compare the results of a series of experiments with the aim of obtaining the true value.
Instruction
1
There are two ways to estimate the error of measurement: interval and point. This is due to the degree of reliability that you want to set. The first method involves finding the confidence interval, which obviously will block actual value of the measured parameter or its mathematical expectation.
2
The confidence interval represents the interval of possible values, i.e. a subset of the elements of the sample. The boundaries of the interval are called the confidence limits are on certain formulas. For example, the mathematical expectation they will be equal to:khsr – t•σ/√N < M(x) < khsr + t•σ/√N where:khsr – the arithmetic mean of the sample;σ – standard deviation;M(x) is the mathematical expectation;N is the sample size;t is the parameter of the function Laplace.
3
In the above formulas are two kinds of point of error: the standard deviation and mathematical expectation. They represent some value that is a measure of the deviation of the calculated values of a random variable from its true value. This is different from interval estimation, which involves a whole range of possible errors. The degree of reliability falling within this range is determined by the Laplace function.
4
The standard deviation, in turn, is calculated by three methods, the most common of them – classic, using the sample mean:σ = √(∑(XI – khsr)2/(N - 1)), where XI are the elements of the sample.
5
Mathematical expectation is the value, around which are distributed the elements of a sample. I.e. is the average of the expected values that can take the random variable. To calculate this kind of variation, you need to make sets of samples and their probabilities array of works of their couples and make all of the elements of the array:M(x) = Σхi•pi.
6
To determine another point , the error of measurement, variance, need to take the square root of the standard deviation or use the following formula relative to the expected value:D = (x – M(x))2 = Σpi•(XI – M(x))2.
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