The root-mean-square value, also called root-mean-square value or effective value, is calculated by squaring, averaging and then finding the root. For example, a square wave signal with an amplitude of 100V and a duty ratio of 0.5 has a voltage of only 50V if calculated by the average value and 70.7 1V if calculated by the root mean square value.
Question 2: What is mean square and what is mean square?
Question 3: What do you mean by mean square root? The root mean square value is actually an effective value, which is the square root of the average of the squares of a set of statistics.
Rms = (x 1 square +x2 square +...+xn square) /n to the power of -65438 +0/2.
The junior high school teacher taught me to calculate the square by writing. The method of saying it three times is similar to that of square, but it is more complicated. Four times is twice squared, and then it's not clear.
I have answered the square root once, as follows:
Much like division. Let's take 5 as an example. The formula is as follows (underline indicates alignment), which is explained as follows:
_________2.2 3 ?
_________ -
________2|5.00 00 00
_________4
__________ -
______42 | 1.00
__________84
__________ -
______443| 16 00
__________ 13 69
________ -
____446? | 2 3 1 00
First judge the unit, 2*2=4, which is the largest square number less than 5, so the unit is 2; After subtraction, 1 is left, followed by two digits, and then (2 * 20+ 1 = 4 1, (2 * 20+2) * 2 = 84, and (2 * 20+3) * 3 are calculated. 100, so the second quotient is 2; Similarly, the third place should be 3, because (22*20+3)*3= 1369 and (22 * 20+4) * 4 =1776 >; 1600; According to this method, you can count as many places as you want, but the more you count, the more complicated it is!
To sum up, it is: 1, which is a double digit at a time, so it should be divided into two digits. For example, 3 15 is written as 3 15. 00 00; 2. Multiply the part that has been opened by 20, add a number, and multiply it by that ding each time. Everything else is the same as division!
Respondent: zhaomf- Scholar Level 2 3-29 2 1:30
Question 4: What does mean by mean square convergence? There are three meanings, 1: unity; 2: all, all; 3. Question 5: What does mean by mean square deviation? The mean square deviation is the same as the unit of sample data.
For example, if a set of data is 4cm, 4, 5cm, 5cm, 5 cm, 2 cm, then their mean square deviation unit is also cm.
Question 6: Do mean square error and root mean square error mean the same thing? Standard deviation or something, right? The standard deviation of the whole sample is different, and the formula is similar.
1. variance s = [(x1-x) 2+(x2-x) 2+... (xn-x) 2]/n (x is the average)
2. Standard deviation = arithmetic square root of variance
Standard deviation is also called standard deviation, or experimental standard deviation. The formula is as shown above. Simply put, the standard deviation is a measure of the degree to which a set of values deviates from the average. A large standard deviation means that most values differ greatly from their average values; A smaller standard deviation means that these values are closer to the average. For example, the average values of * * {0,5,9, 14} and {5,6,8,9} of two groups of numbers are all 7, but the standard deviation of the second * * * is smaller. Standard deviation can be used to measure uncertainty. For example, in physical science, the standard deviation of measured values * * * represents the accuracy of these measurements when repeated. When determining whether the measured value conforms to the predicted value, the standard deviation of the measured value plays a decisive role: if the measured average value is too far from the predicted value (compared with the standard deviation value at the same time), it is considered that the measured value is contradictory to the predicted value. This is easy to understand, because if the measured value falls outside a certain numerical range, it can be reasonably inferred whether the predicted value is correct or not. Standard deviation is applied to investment and can be used as an index to measure the stability of return. The greater the standard deviation, the higher the risk, because the income is far from the past average. On the contrary, the smaller the standard deviation, the more stable the income and the less the risk. For example, six students in Group A and Group B all took the same Chinese exam. Group A scored 95, 85, 75, 65, 55, 45, and Group B scored 73, 72, 765, 438+0, 69, 68, 67. The average value of these two groups is 70, but the standard deviation of group A is 18.7 1, and that of group B is 2. Touch 7 (this data is run in R statistical software), which shows that the gap between students in group A is much larger than that between students in group B. If it is a population, the number of roots of standard deviation formula is divided by n, and if it is a sample, the number of roots of standard deviation formula is divided by (n- 1). Because we are exposed to a large number of samples, the formula of dividing all numbers by (n- 1) is widely used, and the sum of squares is divided by the number of numbers (or the number minus one), and then the root number of the value obtained is 65438.
Standard deviation
Because variance is the square of the data, which is too different from the test value itself, it is difficult for people to measure it intuitively, so we often use the root sign of variance to convert it back, which is the standard deviation we want to talk about. In statistics, the average difference of samples is mostly divided by the degree of freedom (n- 1), which refers to the degree to which samples can be freely selected. When there is only one left, it can no longer be free, so the degree of freedom is n- 1.
What does rms mean? RMS is the root mean square value: RMS-root meam square, which was originally derived for sine waves, but actually applies to all waveforms. The basic process of calculation in the circuit is first square, then average (integral), finally root, and then absolute value rectification. RMS is a calculation method derived from the definition of effective value, so they are equivalent. When the circuit is realized, this calculation method is close. The root-mean-square value, also known as the effective value, is calculated by squaring first, then averaging and finally finding the root. For example, a square wave signal with an amplitude of 100V and a duty ratio of 0.5 has a voltage of only 50V if calculated by the average value and 70.7 1V if calculated by the root mean square value. Why is this? For example, there is a 100 volt battery pack, and it stops for 10 minutes after each power supply, which means that the duty cycle is half. If this battery drives a resistor of 10Ω, the current of 10a and the power of 1000W will be generated when the power is supplied for10 minutes, and the current and power will be zero when the power is cut off. Then its average power in a 20-minute period is 500W, which is equivalent to the power generated by 70.7 1V DC pair10 Ω resistance power supply. However, supplying power to the10 Ω resistor with 50V DC voltage can only generate 250W W. For motors and transformers, as long as the root mean square current does not exceed the rated current, it will not burn out even if it is overloaded in a certain period of time. It is the power handling capacity (or rated power) of the speaker, and it is an important technical parameter, representing the power input capacity of the speaker to withstand long-term continuous and safe work. The sound signal is not a sine wave signal, but a random signal. These random signals can be represented by three energy numbers. Effective value (RMS), also called root mean square value, is the measurement result of sine signal with equal amplitude at the signal peak, which is close to the average value and basically represents the heating energy of the signal. The peak value is the maximum level reached by the signal. For sine wave, the peak level is 3dB higher than the effective value level, and for music signal, the peak level can exceed the effective value 10- 15dB. Peak factor is used to explain the ratio of peak level to effective value level when evaluating the displacement ability of loudspeaker. For AES 2- 15dB,
RMS value is actually an effective value, that is, the square root of the average of the squares of a set of statistics.
Rms = (x 1 square +x2 square +...+xn square) /n to the 65438th power +0/2.
In DC circuit, the definition of voltage or current is very simple, but in AC circuit, it is more complicated and there are many ways to define it. Root mean square (rms) refers to the most common mathematical method to define the effective voltage or current of AC waves.
To obtain the root mean square value, you need to perform three mathematical operations on the function representing the AC waveform:
(1) Calculates the square of a waveform function (usually a sine wave).
(2) Calculate the time average of the function obtained in the first step.
(3) Find the square root of the function obtained in the second step.
In the circuit whose impedance is composed of pure resistance, the effective value of AC wave is usually called effective value or DC value. For example, if an AC power supply of 100V rms is connected to a resistor, and its current generates 50W of heat, then a power supply of 100V connected to this resistor will also generate 50W of heat.
For sine wave, the root mean square value is 0.707 times of the peak value, or 0.354 times of the peak value. Household voltage is represented by effective value. The so-called "1 17V" alternating current has a peak value (pk) of about 165V and a peak-to-peak value (pk-pk) of about 330V.