8. Do 5 number summary and box plot of the following data: 3,7, 2, 10, 8, 12, 14, 18, 21, 16, 8
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.
Given data:
3, 7, 2, 10, 8, 12, 14, 18, 21, 16, 8
To find 5 number summary and to construct box plot for the given data.
Minimum value = 2
Median is the middle value that divides the data into equal parts. One half containing data values greater than it and the other half containing data values less than it.
Arrange the data in ascending order:
2, 3, 7, 8, 8, 10, 12, 14, 16, 18, 21
Middle value which divides the data into two equal parts is 10.
Thus, median is 10
First Quartile is the middle value of the lowest half of the data: {2, 3, 7, 8, 8}
Middle value of this lower half is 7.
Thus, First Quartile is 7
Third Quartile is the middle value of upper half: {12, 14, 16, 18, 21}
Middle value of this upper half is 16.
Thus, Third Quartile 16
Maximum value = 21
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