In this problem, we explore the effect on the standard deviation of multiplying each data value in a data set by the same constant. Consider the data set 15, 10, 9, 7, 6. (a) Use the defining formula, the computation formula, or a calculator to compute s. (Round your answer to four decimal places.) (b) Multiply each data value by 7 to obtain the new data set 105, 70, 63, 49, 42. Compute s. (Round your answer to four decimal places.)
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.
In this problem, we explore the effect on the standard deviation of multiplying each data value in a data set by the same constant. Consider the data set 15, 10, 9, 7, 6.
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