Practical Applications of Statistics

Practical Applications of Statistics

What Is Statistics?
American Heritage Dictionary® defines statistics as: "The mathematics of the collection, organization, and interpretation of numerical data, especially the analysis of population characteristics by inference from sampling."
The Merriam-Webster’s Collegiate Dictionary® definition is: "A branch of mathematics dealing with the collection, analysis, interpretation, and presentation of masses of numerical data." The steps of statistical analysis involve collecting information, evaluating it, and drawing conclusions. Statisticians provide crucial guidance in determining what information is reliable and which predictions can be trusted. They often help search for clues to the solution of a scientific mystery, and sometimes keep investigators from being misled by false impressions. Statisticians work in a variety of fields, including medicine, government, education, agriculture, business, and law.

What Do Statisticians Do?
Statisticians help determine the sampling and data collection methods monitor the execution of the study and the processing of data, and advise on the strengths and limitations of the results. They must understand the nature of uncertainties and be able to draw conclusions in the context of particular statistical applications. Survey statisticians collect information from a carefully specified sample and extend the results to an entire population.

Sample surveys might be used to:
• Determine which political candidate is more popular.
• Discover what foods teenagers prefer for breakfast.
• Estimate the number of children living in a given school district.
Government statisticians conduct experiments to aid in the development of public policy and social programs. Such experiments include:

• Consumer prices
• Fluctuations in the economy
• Employment patterns
• Population trends
Statistical sciences are used to enhance the validity of inferences in:
• Radiocarbon dating to estimate the risk of earthquakes
• Clinical trials to investigate the effectiveness of new treatments
• Field experiments to evaluate irrigation methods
• Measurements of water quality
• Psychological tests to study how we reach the everyday decisions in our lives
Statisticians quantify unknowns in order to optimize resources. They:
• Predict the demand for products and services
• Check the quality of items manufactured in a facility
• Manage investment portfolios
Many people with degrees in statistics do not work with the title "statistician." They are business analysts, professors, economists, mathematicians, statistical software engineers, risk analysts, quality analysts, investigators, environmentalists, pharmaceutical engineers, and researchers who use statistics on a daily basis to perform the functions of their jobs. Some of the key statistical concepts used in this field are:
• Mean, mode, and median
• Frequency distribution
• Standard deviation
• Sampling

The Median, the Mean and the Mode
Before you can begin to understand statistics; there are four terms you will need to fully understand. The first term \'average\' is something we have been familiar with from a very early age when we start analyzing our marks on report cards. We add together all of our test results and then divide it by the sum of the total number of marks there are. We often call it the average. However, statistically it\'s the Mean.
The Mean
Example:
Four tests results: 15, 18, 22, 20
the sum is: 75
Divide 75 by 4: 18.75
The \'Mean\' (Average) is 18.75 (Often rounded to 19)
The Median
The Median is the \'middle value\' in your list. When the totals of the list are odd, the median is the middle entry in the list after sorting the list into increasing order. When the totals of the list are even, the median is equal to the sum of the two middle (after sorting the list into increasing order) numbers divided by two. Thus, remember to line up your values, the middle number is the median! Be sure to remember the odd and even rule.
Examples:
Find the Median of: 9, 3, 44, 17, 15 (Odd amount of numbers)
Line up your numbers: 3, 9, 15, 17, 44 (smallest to largest)
The Median is: 15 (The number in the middle)
Find the Median of: 8, 3, 44, 17, 12, 6 (Even amount of numbers)
Line up your numbers: 3, 6, 8, 12, 17, 44
Add the 2 middles numbers and divide by 2: 8 + 12 = 20 ÷ 2 = 10
The Median is 10.
The Mode
The mode in a list of numbers refers to the list