Math and Arithmetic

Statistics

Probability

789

standard deviation is the square roots of variance, a measure of spread or variability of data . it is given by (variance)^1/2

The set of X1, X2, ..., XN is called X. Given that mean(X), is the sum of all X divided by N, the variance of X is mean((Xi - mean(X))2). The standard deviation of X is the square root of the variance.

The mean and standard deviation do not, by themselves, provide enough information to calculate probability. You also need to know the distribution of the variable in question.

A standard deviation calculator allows the user to find the mean spread away from the mean in a statistical environment. Most users needing to find the standard deviation are in the statistics field. Usually, the data set will be given and must be typed into the calculator. The standard deviation calculator will then give the standard deviation of the data. In order to find the variance of the data, simply square the answer.

49.30179172 is the standard deviation and 52 is the mean.

Pooled variance is a method for estimating variance given several different samples taken in different circumstances where the mean may vary between samples but the true variance (equivalently, precision) is assumed to remain the same. A combined variance is a method for estimating variance from several samples, given the size, mean and standard deviation of each. Mathematically, a combined variance is equal to the calculated variance of the set of the data from all samples. See links.

You need the mean and standard deviation in order to calculate the z-score. Neither are given.

A single number, such as 478912, always has a standard deviation of 0.

Standard deviations are measures of data distributions. Therefore, a single number cannot have meaningful standard deviation.

You can't. You need an estimate of p (p-hat) q-hat = 1 - p-hat variance = square of std dev sample size n= p-hat * q-hat/variance yes you can- it would be the confidence interval X standard deviation / margin of error then square the whole thing

The actual rate is the total dollars divided by total hours or pieces. The actual formula is not dependant on any standard rate. The rate variance, however, cannot be determined without the standard rate. The rate variance is the difference between actual rate and standard rate.

A standard deviation in statistics is the amount at which a large number of given values in a set might deviate from the average. A percentile deviation represents this deviation as a percentage of the range.

idk about normal distribution but for Mean "M" = (overall sum of "x") / "n" frequency distribution: 'M' = Overall sum of (' x ' * ' f ') / overall sum of ( ' f ' ) M = Mean x = Mid Point f = frequiency n = number of variables ALL FOR STANDARD DEVIATION * * * * * A general Normal distribution is usually described in terms of its parameters, and given as N(mu, sigma2) where mu is the mean and sigma is the standard deviation. The STANDARD Normal distribution is the N(0, 1) distribution, that is, it has mean = 0 and variance (or standard deviation) = 1.

If the probability distribution function for the random variable X is f(x), then first calculate E(X) = integral of x*f(x)dx over the whole real line. Noxt calculate E(X2) = integral of x2*f(x)dx over the whole real line. Then Variance(X) = E(X2) - [E(X)]2 and finally, SD(X) = sqrt[Variance(X)].

Risk reflects the chance that the actual return on an investment may be very different than the expected return. One way to measure risk is to calculate the variance and standard deviation of the distribution of returns.Consider the probability distribution for the returns on stocks A and B provided below.StateProbabilityReturn onStock AReturn onStock B120%5%50%230%10%30%330%15%10%320%20%-10%The expected returns on stocks A and B were calculated on the Expected Return page. The expected return on Stock A was found to be 12.5% and the expected return on Stock B was found to be 20%.Given an asset's expected return, its variance can be calculated using the following equation:whereN = the number of states,pi = the probability of state i,Ri = the return on the stock in state i, andE[R] = the expected return on the stock.The standard deviation is calculated as the positive square root of the variance.Note: E[RA] = 12.5% and E[RB] = 20%Stock AStock B

You cannot from the information provided.

Given a set of n scores, the variance is sum of the squared deviation divided by n or n-1. We divide by n for the population and n-1 for the sample.

Standard deviation helps planners and administrators to arrive at a figure that could be used to determine a range that can effectively describe a given set of numerical information/data; and based on which a decision concerning a system of those data can be made.

standard deviation only measures the average deviation of the given variable from the mean whereas the coefficient of variation is = sd\mean Written as "cv" If cv>1 More variation If cv<1 and closer to 0 Less variation

For data sets having a normal distribution, the following properties depend on the mean and the standard deviation. This is known as the Empirical rule. About 68% of all values fall within 1 standard deviation of the mean About 95% of all values fall within 2 standard deviation of the mean About 99.7% of all values fall within 3 standard deviation of the mean. So given any value and given the mean and standard deviation, one can say right away where that value is compared to 60, 95 and 99 percent of the other values. The mean of the any distribution is a measure of centrality, but in case of the normal distribution, it is equal to the mode and median of the distribtion. The standard deviation is a measure of data dispersion or variability. In the case of the normal distribution, the mean and the standard deviation are the two parameters of the distribution, therefore they completely define the distribution. See: http://en.wikipedia.org/wiki/Normal_distribution

You probably mean the Greek letter sigma since this is the probability area.Lower-case sigma is usually reserved to represent a population standard deviation. When it is squared it represents a population variance. With a caret ('hat') over it it represents an estimator of the population standard deviation.Upper-case sigma is most often used to mean summation (adding up) of terms given by the expression after the sigma. The limits of summation are given above and below the sigma symbol in terms of one of the variables in the expression.

Z-score is the x value minus the mean, all divided by the standard deviation; or z=(x-mu)/sigma. The "x" value needs to be given to answer the question.

You also know that x is 1.036 times the standard deviation of the variable above its mean. Anything more than that would require further information about the mean and/or the variance of the variable.

The Empirical Rule states that 68% of the data falls within 1 standard deviation from the mean. Since 1000 data values are given, take .68*1000 and you have 680 values are within 1 standard deviation from the mean.

Given a set of numbers, and its mean, we can find the difference between each of the numbers and the mean. If we take the mean of these differences, the result is called the mean deviation of the numbers.

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