In a city with three high schools, all the ninth graders took a Standardized Test, with these results: High School Mean Test Score Number of ninth graders (Frequency) Glenwood 81 284 Central 95 323 Lincoln 69 154 The city's PR manager, who never took statistics, claimed the mean score of all ninth graders in the city was the average of 81, 95, and 69, which is 81.7. Of course, that is incorrect. What is the mean score for all ninth graders in the city? Round to one decimal place. mean of all ninth grader's scores =
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.
Mean :
For sample data {x1, …, xm} with corresponding frequency counts of f1, …, fm respectively and sample size n = f1 + f2 + … + fm, then the sample mean is :
Where, n is the sum of all frequencies .
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