Problem 18: The following data give the number of books purchased by a sample of 16 adults during the past I year. 5 5 8 8 9. 10 11 12 13 14 15 20 20 26 1. Calculate mean, median and mode. Comment on the shape of the distribution. 2. Calculate variance, standard deviation and range. (You can use calculator to calculate the standard deviation and derive the variance from that) 3. Calculate the maximum, minimum and three quartiles. 4. Find the value of 90th percentile. 5. Calculate interquartile range (IQR). 5. Draw the box plot and comment on the shape of the distribution. 7. Find the outliers (if any). Compare the results of parts I and 6.
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.
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