1. Sample data for the number of deaths attributed to UV radiation in African countries in the year 2002 is given in table. 50 84 31 338 504 40 7 58 204 15 27 39 1 45 174 98 94 199 9. 27 58 356 45 94 26 171 13 57 138 39 3 171 41 1177 102 123 433 35 40 456 125 (a) Find the mean and standard deviation. (b) Use Chebyshev's theorem to find an interval centered about the mean number of deaths from UV radiation in which you would expect at least 75% of the numbers to fall.
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.
1.
(a)
The descriptive analysis is conducted using EXCEL. The software procedure is given below:
- Enter the data.
- Select Data > Data Analysis >Descriptive Statistics> OK.
- Enter Input Range as Data column.
- Mark Labels in First Row.
- Mark Summary Statistics.
- Click OK.
The output using EXCEL is as follows:
From the output, the mean is 130.98, and the standard deviation is 205.44.
Thus, the mean value is 130.98, and the standard deviation is 205.44.
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