Select all of the true statements about the standard deviation of a quantitative variable. Standard deviation represents how far a group of values are from the mean of those values, on average. Standard deviation is always a nonnegative value. OIf a set of values has a mean of 0 and a standard deviation that is not 0, then adding a new data point with a value of 0 will have no effect on the standard deviation. Standard deviation is resistive to unusual values. Changing the units of a set of values (e.g., converting from inches to feet) does not affect its standard deviation. The standard deviation of a set of values is equal to 0 if and only if all of the values are the same.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
1. Standard deviation represents how far a group of values are form the mean of those value on average, because variance is taken as average of sum of squares of each value from the mean and it's square root is standard deviation. Therefore it is true.
2. Standard deviation is always non-negative because it is the average squared deviation of the observations from the mean and it is the square root of variance. Therefore it is true.
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