The data below represents the number of hours 45 hospital patients slept following the administration of a certain anaesthetic. 7, 10, 12, 4, 8, 7, 3, 8, 5, 12, 11, 3, 8, 1, 1, 13, 10, 4, 4, 5, 5, 8, 7, 7, 3, 2, 3, 8, 13, 1, 7, 17, 3, 4, 5, 5, 3, 1, 17, 10, 4, 7, 7, 11, 8. From the data answer the following questions; a) What type of data is this? b) Construct a frequency distribution with relative frequencies and cumulative relative frequencies c) Construct a Box plot for this data d) Describe this data relative to symmetry and skewness e) Determine, the mean, median and mode, Using the data f) Determine, the standard deviation and the coefficient of variation g) What conclusion would you make regarding the data based on measures of central tendency and measures of variation?
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.
The data below represents the number of hours 45 hospital patients slept following the administration of a certain anaesthetic. 7, 10, 12, 4, 8, 7, 3, 8, 5, 12, 11, 3, 8, 1, 1, 13, 10, 4, 4, 5, 5, 8, 7, 7, 3, 2, 3, 8, 13, 1, 7, 17, 3, 4, 5, 5, 3, 1, 17, 10, 4, 7, 7, 11, 8. From the data answer the following questions; a) What type of data is this? b) Construct a frequency distribution with relative frequencies and cumulative relative frequencies c) Construct a Box plot for this data d) Describe this data relative to symmetry and skewness e) Determine, the mean, median and
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