To measure variability, why is the standard deviation usually preferred over the range? Give an example of a data sets to illustrate your answer. (Data sets should have the same range but very different standard deviations.)
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.
(a)
The standard deviation is used to calculate the variability of the data set. It tells us about the spread of the data points from the mean value. The standard deviation is the square root of the average squared differences of each value from the mean value. To calculate the standard deviation, one should know the mean value. The standard deviation of the data depends on the center of the dataset.
The difference between the maximum and minimum values of the data is called the range of the data. As a measure of dispersion, the range has some limitations. The range is not dependent on the exact value of every measurement because the range uses the maximum and minimum values to find the variability.
consider two data sets:
A: 8, 2,4,6,7,9,4, 3, 6, 5
B: 12,7,8,9,10,11,5,6, 10,9
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