An investigator took a random sample of Chief Financial Officers (CFOs) of public listed firms in Singapore, recorded their annual salaries and found that the salary distribution was skewed to the right. She then proceeded to calculate three measures of location for this data, namely the mean, median and mode. The mean was found to be SGD ($) 230,000.35 with a standard deviation of SGD ($) 50,000.85 but the mode was not available. You are required to state and explain which you expect to have a larger value: their mean annual salary or their median annual salary. Explain whether the mode will make a good measure of location of annual salaries and why it may not show up in standard computer output. Interpret the value for the standard deviation of annual salaries of CFOs in Singapore.
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. An investigator took a random sample of Chief Financial Officers (CFOs) of public listed firms in Singapore, recorded their annual salaries and found that the salary distribution was skewed to the right. She then proceeded to calculate three measures of location for this data, namely the
- You are required to state and explain which you expect to have a larger value: their mean annual salary or their median annual salary.
- Explain whether the mode will make a good measure of location of annual salaries and why it may not show up in standard computer output.
- Interpret the value for the standard deviation of annual salaries of CFOs in Singapore.
- Explain why the coefficient of variation can be a better measure of dispersion in certain circumstances.
b. Take 50 observations at random
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