Q: For a set of 100 observations with a mean of 46 and a standard deviation of 0 What is the value of the smallest observation in the set?

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If there is zero deviation all the observations are 50.

A single observation cannot have a sample standard deviation.

Strictly speaking, none. A quartile deviation is a quick and easy method to get a measure of the spread which takes account of only some of the data. The standard deviation is a detailed measure which uses all the data. Also, because the standard deviation uses all the observations it can be unduly influenced by any outliers in the data. On the other hand, because the quartile deviation ignores the smallest 25% and the largest 25% of of the observations, there are no outliers.

It is a measure of the spread of the distribution. The greater the standard deviation the more variety there is in the observations.

If all four numbers are the same, there is no standard deviation. The mean will be equal to all 4 numbers, resulting in a 0 standard deviation. Ex) 5,5,5,5

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If there is zero deviation all the observations are 50.

The standard deviation for a single observation is 0.

A single observation cannot have a sample standard deviation.

Suppose there are n observations. Put them in ascending order (smallest first) of size. Calculate k = n/4. Round up to the next integer, if necessary. Then Q1 is the kth observation in the ordered sets. Also Q3 is the 3kth observation in the ordered sets. IQR = Q3 - Q1 Calculation of the standards deviation is a lot more work. First find the mean = sum of all the observations, divided by the number of observations. Call that number M. Next find the mean "sum of squares", MSS. Square the value of each observation and add them together. Then divide this sum by the number of observations. Then the Variance is V = MSS - M2 Finally, the standard deviation is sqrt(V).

Strictly speaking, none. A quartile deviation is a quick and easy method to get a measure of the spread which takes account of only some of the data. The standard deviation is a detailed measure which uses all the data. Also, because the standard deviation uses all the observations it can be unduly influenced by any outliers in the data. On the other hand, because the quartile deviation ignores the smallest 25% and the largest 25% of of the observations, there are no outliers.

The standard deviation of a single observation is not defined. With a single observation, the mean of the observation(s) would be the same as the value of the observation itself. By definition, therefore, the deviation (difference between observation and mean) would always be zero. Rather a pointless exercise!

It is a measure of the spread of the distribution. The greater the standard deviation the more variety there is in the observations.

The standard deviation of a set of data is a measure of the spread of the observations. It is the square root of the mean squared deviations from the mean of the data.

A standard deviation of 0 implies all of the observations are equal. That is, there is no variation in the data.

If all four numbers are the same, there is no standard deviation. The mean will be equal to all 4 numbers, resulting in a 0 standard deviation. Ex) 5,5,5,5

A single observation, such as 50486055535157526145 cannot have a standard deviation cube test compressive result.

use this link http://www.ltcconline.net/greenl/Courses/201/probdist/zScore.htm Say you start with 1000 observations from a standard normal distribution. Then the mean is 0 and the standard deviation is 1, ignoring sample error. If you multiply every observation by Beta and add Alpha, then the new results will have a mean of Alpha and a standard deviation of Beta. Or, do the reverse. Start with a normal distribution with mean Alpha and standard deviation Beta. Subtract Alpha from all observations and divide by Beta and you wind up with the standard normal distribution.