Percentiles a) Consider a set of (n=25) ordered data points x1, x2, ..., x24, x25. Find the percentile for each of the following data points: x8; x21. Find the data point the corresponds to each of the following percentiles: 68th percentile, 42nd percentile (or if it is the average of two, give in the form such as (x9+x10)/2) b) Consider a set of (n=48) ordered data points x1, x2, ..., x47, x48. Find the percentile for each of the following data points: x14; x45. Find the data point the corresponds to each of the following percentiles: 75th percentile, 57th percentile (or if it is the average of two, give in the form such as (x9+x10)/2)
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.
Percentiles
a) Consider a set of (n=25) ordered data points
x1, x2, ..., x24, x25.
Find the percentile for each of the following data points: x8; x21.
Find the data point the corresponds to each of the following percentiles: 68th percentile, 42nd percentile
(or if it is the average of two, give in the form such as (x9+x10)/2)
b) Consider a set of (n=48) ordered data points
x1, x2, ..., x47, x48.
Find the percentile for each of the following data points: x14; x45.
Find the data point the corresponds to each of the following percentiles: 75th percentile, 57th percentile
(or if it is the average of two, give in the form such as (x9+x10)/2)
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