Consider the set of sample data for scores on a Stat 1 exam: {0, 5, 7, 7, 7, 11, 15, 18, 22, 23, 30}; ?⎯⎯⎯x¯ = 13.2; ?s = 9.2; ?n = 11. Find the third quartile, ?3Q3
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.
Consider the set of sample data for scores on a Stat 1 exam:
{0, 5, 7, 7, 7, 11, 15, 18, 22, 23, 30}; ?⎯⎯⎯x¯ = 13.2; ?s = 9.2; ?n = 11.
- Find the third
quartile , ?3Q3 . - A student not included in this data set scored 33.5 points on this same exam. Using the statistics give above, convert this student's score in points to a z-score, rounded to two decimal places. (Do not recalculate the mean and standard deviation.)
- Compared to the sample of 11 scores, is this student's score (33.5 points) usual or unusual, based on the z-score? Explain your answer.
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