A student was asked to compute the mean and standard deviation for the following sample of n 5 scores: 81, 87, 89, 86, and 87. To simplify the arithmetic, the student first subtracted 80 points from each score to obtain a new sample consisting of 1, 7, 9, 6, and 7. The mean and standard deviation for the new sample were then calculated to be M 6 and s 3. What are the values of 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.
10. A student was asked to compute the
standard deviation for the following sample of n 5
scores: 81, 87, 89, 86, and 87. To simplify the
arithmetic, the student first subtracted 80 points from
each score to obtain a new sample consisting of 1, 7,
9, 6, and 7. The mean and standard deviation for the
new sample were then calculated to be M 6 and
s 3. What are the values of the mean and standard
deviation for the original sample?
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