Overview of the scenario
The scenario involves analyzing the distribution of salaries for different jobs in the state of Minnesota. The client is interested in the distribution of salaries for jobs with salaries ranging from $40,000 to $120,000. Data on 364 different jobs in the state were collected from the Bureau of Statistics. The data will be analyzed by determining the measures of central tendency and dispersion to understand the distribution of salaries.
Quantitative and qualitative variable
In this scenario, the job title is the qualitative variable since it cannot be measured numerically. On the other hand, salary is the quantitative variable since it is measured numerically in US dollars.
Discrete and continuous variable
Salary is a continuous variable since it can be measured in decimals. Discrete variables can only be measured in whole numbers. Both discrete and continuous variables are quantitative variables. Thus, the job title is neither a discrete nor continuous variable since it is a qualitative variable.
Level of measurement
The job title is a nominal level of measurement since letters are used to distinguish the data. In this case, there is no ordering of data (Graham, 2008). For instance, Accountants and Auditors are the first in the list, but it does not mean it is more superior to the other jobs. Salary, on the other hand, is measured on an ordinal level. The salaries for the different jobs can be ranked from the lowest to the highest.
Measures of center/central tendency
They are summary measures describing a data set with a single value the represents the middle of the distribution (Graham, 2008). They help in understanding and analyzing data as well as making inferences about the population. For instance, it is not possible to describe the salaries of all the 364 job titles one by one, but it is easier through a measure of center like the mean, median, among other measures.
Measures of variation
These measures show the extent to which values in a data set deviate from the mean or any other measure of central tendency (Graham, 2008). They help in understanding the distribution of values in a data set.
Descriptive statistics
As shown above, the mean is $62,306.13 implying that the average salary for the 364 jobs in Minnesota is $62,306.13. The mode is $46,100 indicating that more jobs are paying $46,100 than any other salary. The median is $56,520 showing that the middle salary for the 364 jobs is $56,520. The sample variance is 3.67E+08 and the standard deviation is 19149.21. This means that the salaries of the 364 jobs deviated by an average of 19149.21 of the mean salary. The range is $79,680 implying that the difference between the highest salary and lowest salary is $79,680. The midrange is $80,010 implying that the average between the highest and lowest salaries is $80,010.
Conclusion
The average salary is $62,306.13 while the median salary is $56,520 implying that salaries are positively skewed. This implies that the most jobs had salaries below the mean salary, but a few jobs had higher salaries that pushed the mean above the median. There is also a large gap between the lowest salary and the highest salary as shown by the range.
References
Graham, A. (2008). Statistics (1st ed.). Blacklick, OH: McGraw-Hill.
