Examples of standards in the following topics:
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- The standard normal distribution is a normal distribution of standardized values called z-scores.
- A z-score is measured in units of the standard deviation.
- For example, if the mean of a normal distribution is 5 and the standard deviation is 2, the value 11 is 3 standard deviations above (or to the right of) the mean.
- The mean for the standard normal distribution is 0 and the standard deviation is 1.
- The value x comes from a normal distribution with mean µ and standard deviation σ.
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- Although they are often used interchangeably, the standard deviation and the standard error are slightly different.
- The standard error is the standard deviation of the sampling distribution of a statistic.
- Secondly, the standard error of the mean can refer to an estimate of that standard deviation, computed from the sample of data being analyzed at the time.
- However, the mean and standard deviation are descriptive statistics, whereas the mean and standard error describes bounds on a random sampling process.
- Standard deviation will be unaffected by sample size.
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- The standard error is the standard deviation of the sampling distribution of a statistic.
- Quite simply, the standard error is the standard deviation of the sampling distribution of a statistic.
- The standard error and the standard deviation of small samples tend to systematically underestimate the population standard error and deviations.
- The standard error and standard deviation are often considered interchangeable.
- Paraphrase standard error, standard error of the mean, standard error correction and relative standard error.
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- The standard error of the mean is the standard deviation of the sample mean's estimate of a population mean.
- In general terms, the standard error is the standard deviation of the sampling distribution of a statistic.
- The standard error of the mean (i.e., standard error of using the sample mean as a method of estimating the population mean) is the standard deviation of those sample means over all possible samples (of a given size) drawn from the population.
- As mentioned, the standard error of the mean (SEM) is the standard deviation of the sample-mean's estimate of a population mean.
- Note that the standard error and the standard deviation of small samples tend to systematically underestimate the population standard error and deviations because the standard error of the mean is a biased estimator of the population standard error.
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- In principle, the choice of standard state is arbitrary, although the International Union of Pure and Applied Chemistry (IUPAC) recommends a conventional set of standard states for general use.
- A standard pressure of 1 bar (101.3 kilopascals) has been accepted.
- Strictly speaking, temperature is not part of the definition of a standard state; the standard state of a gas is conventionally chosen to be 1 bar for an ideal gas, regardless of the temperature.
- The standard state should not be confused with standard temperature and pressure (STP) for gases, or with the standard solutions used in analytical chemistry.
- The standard enthalpy of formation, or standard heat of formation, of a compound is the change in enthalpy that accompanies the formation of one mole of the compound from its elements in their standard states.
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- If the standard deviation were zero, then all men would be exactly 70 inches tall.
- This quantity is known as the standard deviation.
- The sample standard deviation, $s$, is a statistic known as an estimator.
- As mentioned above, most often the standard deviation is estimated using the corrected sample standard deviation (using $N-1$).
- Dark blue is one standard deviation on either side of the mean.
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- In order to consider a normal distribution or normal approximation, a standard scale or standard units is necessary.
- In order to consider a normal distribution or normal approximation, a standard scale or standard units is necessary.
- The standard score is the number of standard deviations an observation or datum is above the mean.
- Standard scores are also called $z$-values, $z$-scores, normal scores, and standardized variables.
- Includes: standard deviations, cumulative percentages, percentile equivalents, $Z$-scores, $T$-scores, and standard nine.
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- The standard Gibbs Free Energy is calculated using the free energy of formation of each component of a reaction at standard pressure.
- These same definitions apply to standard enthalpies and internal energies.
- Don't confuse these thermodynamic standard states with the "standard temperature and pressure" (STP) widely employed in gas law calculations.
- To accomplish this, combine the standard enthalpy and the standard entropy of a substance to get the standard free energy of a reaction:
- As with standard heats of formation, the standard free energy of a substance represents the free energy change associated with the formation of the substance from the elements in their most stable forms as they exist under the standard conditions of 1 atm pressure and 298K.
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- The standard enthalpy of reaction is the enthalpy change that occurs in a system when a chemical reaction transforms one mole of matter under standard conditions.
- In order to calculate the standard enthalpy of a reaction, we can sum up the standard enthalpies of formation of the reactants and subtract this from the sum of the standard enthalpies of formation of the products.
- Note that because it exists in its standard state, the standard enthalpy of formation for oxygen gas is 0 kJ/mol.
- Next, we sum up our standard enthalpies of formation.
- A calculation of standard enthalpy of reaction (∆H°rxn) from standard heats of formation (∆H°f)
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- State the mean and standard deviation of the standard normal distribution
- A normal distribution with a mean of 0 and a standard deviation of 1 is called a standard normal distribution.
- Since the distribution has a mean of 0 and a standard deviation of 1, the Z column is equal to the number of standard deviations below (or above) the mean.
- This process of transforming a distribution to one with a mean of 0 and a standard deviation of 1 is called standardizing the distribution.
- A portion of a table of the standard normal distribution