A company has 30 employees, including a director. The lowest salary among the 30 employees is $22,000. The director’s salary is $180,000, which is more than twice as much as anyone else’s salary. Decide for each of the following statements about the 30 salaries whether it is true, false, or you cannot tell on the basis of the information at hand. • The median salary is below $60,000. • The average salary is below $60,000. • If all salaries are increased by $1,000, that adds $1,000 to the average.
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.
A company has 30 employees, including a director. The lowest salary among the 30 employees is $22,000. The director’s salary is $180,000, which is more than twice as much as anyone else’s salary. Decide for each of the following statements about the 30 salaries whether it is true, false, or you cannot tell on the basis of the information at hand.
• The median salary is below $60,000.
• The average salary is below $60,000.
• If all salaries are increased by $1,000, that adds $1,000 to the average.
• If the director’s salary is doubled, and all other salaries remain the same, that increases the average salary.
• If the director’s salary is doubled, and all other salaries remain the same, that increases the median salary.
• The standard deviation of the salaries is larger than $180,000
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