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 calculate the error

**The error**is a value which determines possible deviations of the data obtained from the exact value. There are concepts of relative and absolute error. Their presence is one of the tasks of mathematical analysis. In practice, however, more important is to calculate the error of the scatter of any measured indicator. Physical devices have their own margin of error. But not only it is necessary to consider the indicator. For the calculation of error scatter σ necessary to carry out several measurements of this magnitude.

You will need

- A device for measuring the desired value

Instruction

1

Measure device or other means of measuring the desired quantity. Repeat the measurement several times. The greater the obtained value, the higher the accuracy of determining the error of the scatter. Usually spend 6-10 measurements. Note the resulting set of values of the measurand.

2

If all values are equal, therefore, the error of variation is equal to zero. If a row has different values, compute the error of the scatter. For its determination, there is a special formula.

3

According to the formula, and calculate the first average value <x> of the resulting values. To do this, add up all the values and their sum divide by the number of measurements n.

4

Determine alternately the difference between each value and the mean value <x>. Record the results of the obtained differences. Then lift all the difference in the square. Find the sum of these squares. Save the last received result.

5

Compute the expression n(n-1), where n is the number of your measurements. Divide the result from previous calculations on the resulting value.

6

Take the square root of the private from division. This is the error dispersion σ measured you size.

# Advice 3: How to find the error

Through measurement, we can not guarantee the accuracy of, any instrument gives a certain

**error**. To know the measurement accuracy or the accuracy class of the instrument, it is necessary to determine the absolute and relative**error**.You will need

- - several measurement results or other sample;
- calculator.

Instruction

1

Measure at least 3-5 times to be able to calculate the actual value of the parameter. Total the results and divide them by the number of measurements you got a valid value, which is used in the problems is true (it is impossible to determine). For example, if the measurement gave the result 8, 9, 8, 7, 10, the actual value will be (8+9+8+7+10)/5=8,4.

2

Find the absolute

**error of**each measurement. From this measurement subtract the actual value, the signs of neglect. You will receive 5 of the absolute error, one for each dimension. In the example they are equal 8-8,4 = 0,4, 9-8,4 =0,6, 8-8,4=0,4, 7-8,4 =1,4, 10-8,4=1,6 (taken modules results).3

To find the relative

**error of**each measurement, divide the absolute**error**to the actual (true) value. Then multiply the result by 100%, it's usually at a percentage measured by this value. In the example locate the relative**error is**therefore: δ1=0.4 a/8,4=0,048 (or 4.8%), δ2=0,6/8,4=of 0.071 (or 7.1 %), δ3=0.4 a/8,4=0,048 (or 4.8%), δ4=1,4/8,4=0,167 (or 16.7%), δ5=1,6/8,4=to 0.19 (or 19%).4

In practice, for the most accurate display errors using the standard deviation. To find it, erected in the square of the absolute error measure and add together. Then divide this number by (N-1), where N is the number of measurements. Calculating the root of the result, you will get a standard deviation that characterizes

**the error**of measurement.5

To find the limit of the absolute

**error**, find the minimum number obviously exceeding the absolute**error**or equal to it. In the example just select the highest value of 1.6. It is also sometimes necessary to find the maximum relative**error**, in this case, find the number that is greater than or equal to the relative error in the example it is equal to 19%.# Advice 4: How to calculate measurement error

**Measurements**of physical quantities are always accompanied by one or another

**error**. It represents the deviation of measurement results from the true value of the measurand.

You will need

- measuring device:
- calculator.

Instruction

1

Errors can occur as a result of various factors. Among them are the imperfection of the means or methods of measurement inaccuracies in their manufacture, failure to comply with the special conditions in conducting research.

2

There are several classifications of errors. On the submission form they can be absolute, relative and given. The former represents the difference between the calculated and the actual value. Expressed in units of the measured phenomenon and are according to the formula:∆x = hisl - Hist. The second is determined by the ratio of the absolute error to the magnitude of the true value of the indicator.The calculation formula is:δ = ∆x/Hist. Measured in percentages or fractions.

3

Reduced error of the measuring device is as the ratio of ∆x to the fiducial value XH. Depending on the type of device it is taken either equal to the limit of measurement, either related to their specific range.

4

On the conditions of occurrence distinguish between basic and advanced. If the measurements were carried out in normal conditions, there is the first kind. Deviation due to output values outside the normal, is optional. For its evaluation documentation is typically a set of rules within which may change the magnitude of a breach of the conditions of measurement.

5

The errors physical measurements are divided into systematic, random and rough. The first is caused by factors that act at multiple repetition of the measurements. The second arises from the influence of reason and random. The mistake is the result of observation, which differs sharply from all the others.

6

Depending on the nature of the measured quantity can be used various ways to measure error. The first of these is the method of Kornfeld. It is based on the calculation of the confidence interval in the range from the minimum to the maximum result. The error in this case will represent half the difference of these results: ∆x = (hmag-xmin)/2. Another way is to calculate mean square error.

# Advice 5: 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 6: 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 7: What is the permissible error of the meter

Self-monitoring in diabetes is an important component of treatment. To measure blood sugar at home use blood glucose meter. The margin of error of this instrument is higher than in laboratory analyzers, blood glucose.

Measurement of blood sugar is necessary for evaluating the effectiveness of treatment of diabetes and the dose adjustment of drugs. From the therapy depends on how many times a month you will need to measure the sugar. Sometimes a blood analysis is needed many times during the day, sometimes just 1-2 times a week. Self-control is especially necessary for pregnant women and patients with type 1 diabetes.

The meter is not considered a precision instrument. It is designed only for approximate determination of the concentration of sugar in the blood.

The permissible error of the meter according to the world standards is 20% at glucose 4.2 mmol/L.

For example, if the self-control level sugar 5 mmol/l, the actual concentration value is in the range from 4 to 6 mmol/L.

The permissible error of the meter under standard conditions is measured in percentage and not in mg/DL. the higher, the larger the error in absolute numbers. For example, if the blood sugar reaches about 10 mmol/l, the error does not exceed 2 mmol/l, and if the sugar is about 20 mmol/l, the difference with results from laboratory measurements can be up to 4 mmol/L.

The standards allow for the excess of the stated measurement error in 5% of cases. This means that every twentieth research can significantly distort the results.

The meters are subject to mandatory certification. The accompanying device documents usually given the numbers of permissible measurement error. If you do not see in the instructions, the inaccuracy is 20%.

Some manufacturers of blood glucose meters, pay special attention to the accuracy of the measurements. There are devices for European companies, which have a margin of error of less than 20%. The best indicator to date is 10-15%.

Permissible error of measurement that describes the operation of the device. On the accuracy of the study is influenced by some other factors. Improperly prepared skin, too small or large the volume of the resulting drop of blood, unacceptable temperature mode - all this can lead to errors.

Only if all rules are self-enforced, you can count on the declared margin of error of the study.

The accuracy of the meter can be checked at the service center. The warranty obligations of the manufacturers provide free advice and Troubleshooting.

## The permissible error of the meter according to the world standards

The meter is not considered a precision instrument. It is designed only for approximate determination of the concentration of sugar in the blood.

The permissible error of the meter according to the world standards is 20% at glucose 4.2 mmol/L.

For example, if the self-control level sugar 5 mmol/l, the actual concentration value is in the range from 4 to 6 mmol/L.

The permissible error of the meter under standard conditions is measured in percentage and not in mg/DL. the higher, the larger the error in absolute numbers. For example, if the blood sugar reaches about 10 mmol/l, the error does not exceed 2 mmol/l, and if the sugar is about 20 mmol/l, the difference with results from laboratory measurements can be up to 4 mmol/L.

In most cases, the meter overestimates the indicators of glycemia.

The standards allow for the excess of the stated measurement error in 5% of cases. This means that every twentieth research can significantly distort the results.

## The margin of error of the blood glucose meters of different companies

The meters are subject to mandatory certification. The accompanying device documents usually given the numbers of permissible measurement error. If you do not see in the instructions, the inaccuracy is 20%.

Some manufacturers of blood glucose meters, pay special attention to the accuracy of the measurements. There are devices for European companies, which have a margin of error of less than 20%. The best indicator to date is 10-15%.

## The error of the meter with self-control

Permissible error of measurement that describes the operation of the device. On the accuracy of the study is influenced by some other factors. Improperly prepared skin, too small or large the volume of the resulting drop of blood, unacceptable temperature mode - all this can lead to errors.

Only if all rules are self-enforced, you can count on the declared margin of error of the study.

Rules of self-control with the help of a glucometer can be obtained from the attending physician.

The accuracy of the meter can be checked at the service center. The warranty obligations of the manufacturers provide free advice and Troubleshooting.