What is the best measure of central tendency to describe the salaries of employees of a company?
The median as the measure of central tendency is most appropriate for determining the average salary because it does not depend on outliers or the least and largest numbers (Siegel 54). These outliers can influence the average, but they do not represent the actual situation. When the salary is measured with the help of the mean, the highest salaries of top managers and CEO are also calculated in order to present the average, and the final number can be higher than the salary that is received by the majority of employees. In this context, the median that is not influenced by such outliers presents the adequate average salary or the middle score for all payments received in the company.
The number of vacation days taken by employees of a company is normally distributed with a mean of 14 days and a standard deviation of 3 days. For the next employee, what is the probability that the number of days of vacation taken is less than 10 days? More than 21 days?
In order to calculate the probability, the number of vacation days should be presented as X, the mean is presented as μ = 14, and the standard deviation is presented as σ = 3. The probability (P) is presented as the z-value. The formula used for calculating z is z = (X – μ) / σ.
For the period that can be less than 10 days, it is necessary to use P(X<10), z = (10-14) / 3 = -1.33. According to the table with z-values, z = 0.09, and P(X<10) = 9%. For the period that can be more than 21 days, it is necessary to use P(X>21), z = (21-14) / 3 = 2.33. According to the table with z-values, z = 0.99, and P(X>21) = 1 – 0.99 = 0.01 = 1%.
Sampling methods and examples of sampling situations
Simple Random Sampling is an approach to selecting a sample from the larger population when each unit can be chosen randomly, and there is an equal opportunity for all units to be selected (Weiers 24). Units are usually assigned with a certain number, and the selection is made with the help of the random number generator.
Systematic Random Sampling is a method based on selecting every next unit after the determined interval (Berenson et al. 38). For instance, the researcher can decide to select every tenth person from the large population to be assigned to the sample.
Stratified Random Sampling is a method when persons are assigned to different strata or sub-groups (for instance, persons are divided by gender or age), and the random selection is conducted in each stratum in order to guarantee that the sample is representative.
Cluster Random Sampling is an approach characterized by identifying clusters or heterogeneous areas among the population and selecting research participants from these clusters randomly (Black 223).
When a researcher aims at identifying differences in business strategies of male and female leaders, he should use the stratified random sampling to guarantee that both genders are equally represented in the study (Downing and Clark 151). When a researcher wants to study differences typical of business situations in certain districts of a city, it is reasonable to use the cluster sampling method to choose units or participants from the areas of interest randomly.
Regression technique in business
The purpose of regression is to examine relationships between certain factors or variables when one or more independent variables can cause changes in the dependent variable. In business, regression is also used to analyze trends and risks in the sphere. If the relationship is determined for one independent variable and one dependent variable, the simple regression analysis is used (Wegner 118).
The example of this situation is when a researcher investigates the relationship between the price’s increase and the customers’ interest in the product. The multiple regression analysis is used when several independent variables affect a dependent variable. The example in the business world is the study of the relationship between the gender and buying capacity of customers and the demand for the certain product.
Works Cited
Berenson, Mark, David Levine, Kathryn Szabat, and Timothy Krehbiel. Basic Business Statistics: Concepts and Applications. New York: Pearson Higher Education, 2012. Print.
Black, Ken. Business Statistics: Contemporary Decision Making. New York: John Wiley & Sons, 2009. Print.
Downing, Douglas, and Jeffrey Clark. Business Statistics. New York: Barron’s Educational Series, 2010. Print.
Siegel, Andrew. Practical Business Statistics. New York: Academic Press, 2011. Print.
Wegner, Trevor. Applied Business Statistics: Methods and Excel-Based Applications. New York: Juta and Company Ltd, 2010. Print.
Weiers, Ronald. Introduction to Business Statistics. New York: Cengage Learning, 2010. Print.