9. a. After 3 points have been added to every score in a sample, the mean is found to be M 83 and the standard deviation is s 8. What were the values for the mean and standard deviation for the original sample? b. After every score in a sample has been multiplied by 4, the mean is found to be M 48 and the standard deviation is s 12. What were the values for the mean and standard deviation for the original sample?
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.
9. a. After 3 points have been added to every score in a
sample, the mean is found to be M 83 and the
standard deviation is s 8. What were the values
for the mean and standard deviation for the original
sample?
b. After every score in a sample has been multiplied
by 4, the mean is found to be M 48 and the
standard deviation is s 12. What were the values
for the mean and standard deviation for the original
sample?
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