The following data set represents the record high temperatures in degree Fahrenheit (°F) for each of the 50 US states: 106 98 96 108 90 93 89 103 104 119 111 85 97 102 85 109 93 120 98 102 90 96 114 108 91 100 96 105 89 96 107 99 113 125 88 122 110 85 99 90 93 102 123 110 111 101 92 96 89 116
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 following data set represents the record high temperatures in degree Fahrenheit (°F) for each of
the 50 US states:
106 98 96 108 90 93 89 103 104 119
111 85 97 102 85 109 93 120 98 102
90 96 114 108 91 100 96 105 89 96
107 99 113 125 88 122 110 85 99 90
93 102 123 110 111 101 92 96 89 116
i. Construct a suitable frequency distribution table using interval 85 – 95, 95 – 105 and so on.
ii. Determine the mean,
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