# 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-Websters 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 of numbers that occur most frequently. A trick to remember this one is to remember that mode starts with the same first two letters that most does. Most frequently – Mode.

Examples:

Find the mode of:

9, 3, 3, 44, 17, 17, 44, 15, 15, 15, 27, 40, 8,

Put the numbers is order for ease:

3, 3, 8, 9, 15, 15, 15, 17, 17, 27, 40, 44, 44,

The Mode is 15 (15 occurs the most at 3 times)

*It is important to note that there can be more than one mode and if no number occurs more than once in the set, then there is no mode for that set of numbers. Occasionally in Statistics you’ll be asked for the ‘range’ in a set of numbers. The range is simply the smallest number subtracted from the largest number in your set. Thus, if your set were 9, 3, 44, 15, and 6 – The range would be 44-3=41. Your range is 41.

A natural progression once the 3 terms in statistics are understood is the concept of probability. Probability is the chance of an event happening and is usually expressed as a fraction.

Frequency Distribution

A frequency distribution shows the number of observations falling into each of several ranges of values (Lane 2004). Frequency distributions are portrayed as frequency tables, histograms, or polygons. Frequency distributions can show either the actual number of observations falling in each range or the percentage of observations. In the latter instance, the distribution is called a relative frequency distribution.

Standard Deviation

The standard deviation is a concept that measures the amount of variation or deviation that might be expected between the actual indicator value and the forecasted value. And it is given in the same units as the indicator (Lane 2004). As an example, retail sales’ forecasts are given in U.S. dollars and thus the standard deviation is also in U.S. dollars.

Given a forecasted value and a standard deviation the possible range of actual values can be found. From statistics there is a 68% chance that the actual value will be either one standard deviation above or one standard deviation below the forecasted value or +/- 1 standard deviation. It also works out that there is a 95% chance the actual value will be within +/- 2 standard deviations and there is a 99.7% chance the actual value will be within +/- 3 standard deviations. Statistics also says there is always some small chance the actual value can be any number of standard deviations from the forecasted value but usually the actual value will be within 3 standard deviations of the forecasted value. Thus the standard deviation is a very concise and powerful way of conveying the amount of uncertainty in the forecasts. The smaller the standard deviation, the less the uncertainty.

Sampling

Sampling is the act, process, or technique of selecting a suitable sample, or a representative part of a population for the purpose of determining parameters or characteristics of the whole population. The purpose of sampling is to draw conclusions about populations from samples; inferential statistics are used to determine a populations characteristics by directly observing only a portion (or sample) of the population. A sample, rather than a complete enumeration (a census) of the population, is used for many reasons. Obviously, it is cheaper to observe a part rather than the whole, but the dangers of using samples are still high. Some samples are better than others but all may yield data that is inaccurate and unreliable. Potential error is the price that must be paid for the convenience and savings the samples provide.

Careers and Opportunities in Statistics – Business and Industry

Jobs for statisticians in business and industry are found in both not-for-profit and for-profit public and private companies. Statisticians work in areas such as market research, quality control, financial planning, insurance, and management of all types of industries.

Future statisticians should study statistics and mathematics as well as economics, finance, marketing, operations management, computer science, and writing. Communication skills are important in order to convey statistical aspects of business decisions to stockholders, employees, the general public, and other professionals.

Fields of Application

Statisticians who work in business and industrial statistics can look forward to promising careers in numerous fields, including the following:

Insurance

Engineering

Writing

Finance

Marketing

Manufacturing

Insurance

Statisticians work in all aspects of insurance, including pension plans, life tables, risk assessment, customer retention, and operations management. They assist in financial decisions regarding interest, annuities, mortgages, and bonds, and help determine pricing and product design for the firm. Analysts in the insurance industry are educated in a variety of disciplines, including statistics, finance, economics, and business, mathematics, and computer science.

Engineering

Engineers work in a range of industries, including electronics, chemicals, aerospace, pollution control, and construction. They may be responsible for leading large projects with significant costs, technical complexity, and responsibility. Statistical methods allow engineers to make a consistent product, detect problems early, minimize chemical waste, and predict product life.

Writing

Science writers are employed by the mass media, universities, and corporations to produce news briefs, articles, news releases, and other reports. Writers with scientific backgrounds are especially in demand because of their ability to explain complicated statistical or scientific data in easy-to-understand articles for non-statisticians and the general public.

Finance

Financial statisticians build models that help an organization avoid risk and exploit opportunities. Statisticians build prediction models from historic business or economic information. Financial statisticians also work in the areas of consumer credit and fraud detection. Use of these models in decision-making sharpens our understanding of the world we live in and improves our quality of life.

Marketing

Statistics is used to quantify the extent of variation in customers’ needs and wants. Statisticians design experiments for new products, conduct focus groups and sample surveys to gather consumer feedback, and perform field experiments in test markets to determine product viability. Statistics and data mining are also used to analyze sales data and predict future trends.

Manufacturing

Industrial statisticians help build products and deliver services that satisfy customers and increase the company’s market share and profitability. Statisticians help design the best possible product, guide the transition from design to manufacturing, ensure a consistently excellent product, help manage customer satisfaction, and ensure a financially beneficial bottom-line. Industry professionals use statistical methods for quality control in nearly all manufactured goods.

Works Cited

Cooper (2004). Statistics & Research Methods for Managerial Decisions [Custom Electronic Text for University of Phoenix] Thomson Custom Publishing, 2001. Retrieved May 17, 2004 from the University of Phoenix, Resource, QNT/530 Statistics and Research Methods for Managerial Decisions Website https://mycampus.phoenix.edu/secure/resource/resource.asp

Lane, D. (2004) Frequency distribution, Website http://davidmlane.com/hyperstat/A26308.html, Retrieved 5/17/04

Market Research International (2002) Financial Forecast Center, Website http://www.neatideas.com/stdev.htm, Retrieved 5/17/04

Shoder (2004) Introduction to Statistics: Mean, Median, and Mode. Shoder Education

Foundation. Website http://www.shodor.org/interactivate/lessons/sm1.html, Retrieved 5/17/04