Must the standard deviation be less than the average

Must the standard deviation be less than the average

It may require that the standard deviation must be less than the mean. Given a group of data, any situation may occur. If the standard deviation is greater than the mean, it means that the data variation degree is great, so a group of data must not be normal distribution. Experience to judge whether a group of data is normal distribution, generally requires that the mean is greater than 2 times of the standard deviation. It is best to use SPSS and other statistical analysis software to accurately judge whether it is normal distribution

The average is 50, the standard deviation is 15, the number of samples is 64, the probability of greater than 53

First of all, let your normal distribution be x ~ n (50,15 ^ 2), that is, find P (x > 53)
By transforming it into standard normal distribution, we get the following results
P(X>53)=1-Φ[(53-50)/15]=1-Φ(0.2)
By looking up the table or using Minitab, we can get Φ (0.2) = 0.579260
So the probability of greater than 53 P (x > 53) = 1-0.579260 = 0.420740

Average and standard deviation of body weight in pounds
A study on the weight status of college students found that the average weight of boys is 60kg, the standard deviation is 5kg; the average weight of girls is 50kg, the standard deviation is 5kg
Requirements: (1) is there a big difference in weight between boys and girls? Why?
(2) Calculate the mean and standard deviation of body weight in pounds (1 pound = 2.2kg)
(3) Roughly, what percentage of boys weigh between 55kg and 65kg?
(4) Roughly estimated, what percentage of girls weigh between 40kg and 60kg?
It is mainly the calculation process of the second question

（1）
Mathematical expectation does not affect variance (or standard deviation)
（2）
I use M for boys and W for girls. Variance is the square of standard deviation. D is variance. E is mathematical expectation, which is mean
E（m）=60 D（m）=5
And because M = m / 2.2
So e (m) = e (M / 2.2) = e (m) / 2.2 = 60 / 2.2 = 27.2727
D（M）=D（m/2.2）=D（m）/2.2²=D（m）/4.84=1.0330578512397
Similarly, e (W) = 22.7273
D（W）=1.0330578512397
Note: if standard deviation is needed, root the variance
（3）
The normal distribution probability model is used here
m ~ N（60,5²）
Then (M-60) / 5 ~ n (0,1)
Because 55 ≤ m ≤ 65
So - 1 ≤ (M-60) / 5 ≤ 1
The probability is p (m) = Φ (1) - Φ (- 1) = 2 Φ (1) - 1 = 0.6286
(4) The same as (3)
p（w）=2Φ（2）-1=0.9544

Which is larger, the mean or the standard deviation

The standard deviation is generally larger than the average
But the two are not comparable
The mean is the mathematical median of a sequence, different from the median
The standard deviation is based on the variance. It is the density of the numbers in the series

How to apply the chemical formula PV = NRT and what are its variations?

1、 Corollary of Avogadro's law
We can use Avogadro's law and the relationship between the mass of matter and the number of molecules and the molar mass to obtain the following useful inferences
(1) At the same temperature and pressure: ① V1: V2 = N1: N2 = N1: N2; ② ρ 1: ρ 2 = M1: m2; ③ at the same mass: V1: V2 = M2: M1
(2) At the same temperature and volume: ④ P1: P2 = N1: N2 = N1: N2; ⑤ at the same mass: P1: P2 = M2: M1
(3) At the same temperature, same pressure and same volume: 6. ρ 1: ρ 2 = M1: M2 = M1: M2
The reasoning process is as follows:
(1) Under the same temperature and pressure, gases with the same volume contain the same number of molecules. Therefore, it can be seen that: under the same temperature and pressure, the volume of gases is directly proportional to the number of molecules, that is, to the amount of their substances, that is, v = kn for any gas; therefore, V1: V2 = N1: N2 = N1: N2, according to n = m / m, there is formula ②; if the mass of gases is the same at this time, there is formula ③
(2) According to Avogadro's law, when the temperature, volume and the number of gas molecules are the same, the pressure is also the same, that is, when the temperature and volume are the same, the gas pressure is proportional to the number of molecules
(3) According to n = m / M and ρ = m / V, there is formula 6. Of course, these conclusions are not only applicable to two kinds of gases, but also to many kinds of gases
2、 Relative density
Under the same temperature and pressure, as in the above conclusion, the density ratio in formula 2 and formula 6 is called the relative density of gas d = ρ 1: ρ 2 = M1: m2. Note: ①. D is called the relative density of gas 1 relative to gas 2, which has no unit. For example, the density of oxygen to hydrogen is 16. ②. If the volume is the same at the same time, it is also equal to the mass ratio, that is, d = M1: m2

There are many kinds of materials directly composed of carbon atoms

The materials directly composed of carbon atoms are (diamond) (graphite) (carbon black)

What is the unit of density in PM = ρ RT (M is the molar mass and ρ is the density)?

The unit of density in PM = ρ RT is g / m3, i.e. g / m3

Schematic diagram of carbon atom structure

Carbon atom: write + 6 in the middle nucleus, and there are two electron layers on the outside, with the number of electrons of 2 and 4 respectively
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The specific meaning of the formula PV = NRT

PV = NRT the Clapeyron equation is usually expressed as follows: PV = NRT ① P is the pressure, V is the volume of gas, n is the amount of material, t is the absolute temperature, R is the gas constant. All gases have the same r value. If the pressure, temperature and volume are in Si, r = 8.314 PA · m3 / mol · K

The structural characteristics of organic compounds are: each carbon atom usually forms several covalent bonds with other atoms, what other atoms can be?
The four bonds of carbon atom can be -, -, -

Each carbon atom usually forms four covalent bonds with other atoms
Other atoms can be C, h, O, N, etc
The four bonds of carbon atom can be single bond, double bond and three bond
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