# Sample and Population, Case Study Example

In order for a business to be successful, the management of challenges is necessary.  Management analysts assist in these challenges.

A management analyst is a position that is more commonly referred to as a management consultant.  The management analysts examine, analyze data statistically and recommend solutions in order for a company to increase its composition, proficiency and profits.  The demand for management analysts are in both public and private companies; however, they are most often used in private companies as they need management analysts to support the challenges and competiveness they are faced with in business. (U.S. Bureau of Labor Statistics, 2009)

Central Tendency Measurements is a set of data or measurements that tend to cluster around specific value or a set of values. In business, this type of statistic is used by management analysts to analyze the internal workings of a company.  For instance, a business analyst many analyze payroll, profits, or sales.  The analyst’s then compare the data to other reported data from business markets in order to suggests or propose a new strategy in order to make profits or save in overall costs.  (Hartman, 2011)

There are different types of statistics that are used in central tendency for business statistics. These include sample mean and population mean.  (Waner, 2003; Arsham, 1994)

• The sample mean of a variable X is the sum of the X results for the sample of a given population divided by the actual sample size.
• The population mean is the mean of the entire population instead of just a sample size.

Sample Mean Formula

 X= ∑Xi/n = sum of values/sample size

X:   Sample Mean

∑=Sum

Xi=X values

n=Sample size

Sample Population Formula

 µ= ∑Xi/n = sum of values/Population size

µ=   Sample Population

∑=Sum

Xi=X values

n=Population size

The population mean as noted previously are the values for the entire population, not just the sample.  The µ replaces the X in this equation.  It should also be noted that the sample mean is used to make and implication in regard to the population. (Waner, 2003)

Example problem: (Waner, 2003)

You are the manager of a business department with a staff of 40 employees whose salaries are represented in the frequency table below.

 Annual Salary \$10,000 \$15,000 \$25,000 \$30,000 \$40,000 \$50,000 # of employees 10 9 5 6 6 4

What would the mean salary be earned by an employee?

Solution: In order to find the average salary, the first thing needed is to find the sum of the salaries earned.

10 employees at \$10,000: 10×10,000 = 100,000

9 employees at \$15,000: 9×15,000 = 135,000

5 employees at \$25,000: 5×25,000 = 125,000

6 employees at \$30,000: 6×30,000 = 180,000

6 employees at \$40,000: 6×40,000 = 240,000

4 employees at \$50,000: 4×50,000 = 200,000

_______________________________________________________

Total = \$980000.00

 µ= ∑Xi/n = sum of values/Population size

We then use our formula:

• We determine the values for each of the variables in the formula:
• µ = the average salary
• ∑Xi= Sum of all employee salaries \$(980000.00)
• n= number of employees (40)

Therefore, the average annual salary is μ = 980000.00/40= 24,500.00

Resources

Arsham, H. (1994).  Statistical Thinking for Managerial Decisions.
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