You will need

- the results of measurements;
- calculator.

Instruction

1

First and foremost, spend several measurements of the same value to be able to calculate the actual value. The more measurements, the more accurate will be the result. For example, Apple weigh on the electronic scales. Let's say you got the results 0,106, 0,111, 0,098 kg.

2

Now calculate a valid value (valid, true because it is impossible to find). To do this, total the results and divide them by the number of measurements, i.e., find the arithmetic mean. In the example, a valid value is (0,106+0,111+0,098)/3=0,105.

3

To calculate the absolute error of the first measurement subtract from the result the actual value: 0,106-0,105=0,001. In the same way, calculate the absolute error of the remaining measurements. Please note, regardless, you get the result with a minus or plus sign of the error is always positive (i.e. you take module value).

4

To obtain the relative error of the first dimension, divide the absolute error to the actual value: 0,001/0,105=0,0095. Please note, usually the relative error is measured in percent, so multiply the resulting number by 100%: 0,0095х100%=0,95%. In the same way consider the relative error of the remaining measurements.

5

If the true value is already known, immediately start for the calculation of errors by eliminating the search arithmetic mean of measurement results. Immediately subtract from the true meaning of the result, you will find the absolute error.

6

Then divide the absolute error to the true value and multiply by 100% - this is relative error. For example, the number of students 197, but it was rounded up to 200. In this case, calculate the rounding error: 197-200=3, relative error: 3/197х100%=1,5%.

# Advice 2 : How to find absolute and relative error

In the measurement of any quantity there is always some deviation from the true value, since no instrument can not give the exact result. In order to determine possible deviations of the data obtained from the exact value, use the concepts of relative and absolute error.

You will need

- the results of measurements;
- calculator.

Instruction

1

First and foremost, spend several measurements of the same value to be able to calculate the actual value. The more measurements, the more accurate will be the result. For example, Apple weigh on the electronic scales. Let's say you got the results 0,106, 0,111, 0,098 kg.

2

Now calculate a valid value (valid, true because it is impossible to find). To do this, total the results and divide them by the number of measurements, i.e., find the arithmetic mean. In the example, a valid value is (0,106+0,111+0,098)/3=0,105.

3

To calculate the absolute error of the first measurement subtract from the result the actual value: 0,106-0,105=0,001. In the same way, calculate the absolute error of the remaining measurements. Please note, regardless, you get the result with a minus or plus sign of the error is always positive (i.e. you take module value).

4

To obtain the relative error of the first dimension, divide the absolute error to the actual value: 0,001/0,105=0,0095. Please note, usually the relative error is measured in percent, so multiply the resulting number by 100%: 0,0095х100%=0,95%. In the same way consider the relative error of the remaining measurements.

5

If the true value is already known, immediately start for the calculation of errors by eliminating the search arithmetic mean of measurement results. Immediately subtract from the true meaning of the result, you will find the absolute error.

6

Then divide the absolute error to the true value and multiply by 100% - this is relative error. For example, the number of students 197, but it was rounded up to 200. In this case, calculate the rounding error: 197-200=3, relative error: 3/197х100%=1,5%.

# Advice 3 : 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.

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 4 : How to determine the absolute measurement error

Calculation of errors

**of measurement**is the final stage of the calculation. It reveals the degree of deviation of the obtained value from the true. There are several types of such deviations, but sometimes it is enough to define only the absolute**error****of measurement**.Instruction

1

To determine the absolute

**error of****the measurement**, it is necessary to find the deviation of the actual value. It is expressed in the same units as estimated, and is equal to the arithmetic difference between the true and the estimated values: δ = x1 – x0.2

The absolute

**error**is often used to write some constant values with infinitely small or infinitely large value. This applies to many physical and chemical constants, e.g., Boltzmann's constant equal to 1,380 6488×10^(-23) ± 0,000 0013×10^(-23) j/K, where the value of the absolute error is separated from true by the sign ±.3

In the framework of mathematical statistics

**measurements**are made in a series of experiments, the result of which is some set of values. Analysis of this sample based on methods of probability theory and involves the construction of probabilistic models. In this case, the absolute**error****of measurement**is accepted by the standard deviation.4

To calculate standard deviation you need to determine the average or weighted average of sample points:khsr = Σxi/n is the arithmetic mean, where the xi are the elements of the sample, n is its volume;hvsw = ∑pi•xi/∑pi – weighted average.

5

As you can see, in the second case, taking into account the weight of the elements pi, which show how likely the measured value will take a value of an element of the sample.

6

The classic formula of the standard deviation as follows:σ = √(∑(xi – khsr)2/(n - 1)).

7

There is the concept of relative error, which is in direct dependence on the absolute. It is equal to the ratio of absolute error to the estimated or actual value of the variable, the choice of which depends on the requirements of a specific task.

Useful advice

For convenience, use the tabular method of recording, and even better – the Microsoft Excel program.