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Q: Is the expected value the same as the standard deviation?

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Standard deviation has the same unit as the data set unit.

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The formula for standard deviation has both a square (which is a power of 2) and a square-root (a power of 1/2). Both must be there to balance each other, to keep the standard deviation value's magnitude similar to (having the same units as) the sample numbers from which it's calculated. If either is removed from the formula, the resulting standard deviation value will have different units, reducing its usefulness as a meaningful statistic.

Either when there is a single data item, or when all data items have exactly the same value.

Standard deviation is a measure of the scatter or dispersion of the data. Two sets of data can have the same mean, but different standard deviations. The dataset with the higher standard deviation will generally have values that are more scattered. We generally look at the standard deviation in relation to the mean. If the standard deviation is much smaller than the mean, we may consider that the data has low dipersion. If the standard deviation is much higher than the mean, it may indicate the dataset has high dispersion A second cause is an outlier, a value that is very different from the data. Sometimes it is a mistake. I will give you an example. Suppose I am measuring people's height, and I record all data in meters, except on height which I record in millimeters- 1000 times higher. This may cause an erroneous mean and standard deviation to be calculated.

Related questions

A standard deviation of zero means that all the data points are the same value.

No.

The expected value of the standard normal distribution is equal to the total amount of the value. It is usually equal to it when the value works out to be the same.

Standard error of the mean (SEM) and standard deviation of the mean is the same thing. However, standard deviation is not the same as the SEM. To obtain SEM from the standard deviation, divide the standard deviation by the square root of the sample size.

The standard deviation is defined as the square root of the variance, so the variance is the same as the squared standard deviation.

The members all have the same value.

Standard deviation has the same unit as the data set unit.

The smaller the standard deviation, the closer together the data is. A standard deviation of 0 tells you that every number is the same.

No. The average of the deviations, or mean deviation, will always be zero. The standard deviation is the average squared deviation which is usually non-zero.

If the standard deviation of 10 scores is zero, then all scores are the same.

The lower case sigma character (σ) represents standard deviation.

The standard deviation is the square root of the variance.

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