The study of statistics is usually divided into two categories: descriptive statistics and inferential statistics.
The definition of statistics given earlier referred to organizing, presenting, analyzing
data. This facet of statistics is usually referred to as descriptive statisticsMethods of organizing, summarizing, and presenting data in an informative way..
For instance, the United States government reports the population of the United States was 179,323,000 in 1960; 203,302,000 in 1970; 226,542,000 in 1980; 248,709,000 in 1990, and 265,000,000 in 2000. This information is descriptive statistics. It is descriptive statistics if we calculate the percentage growth from one decade to the next. However, it would not be descriptive statistics if we used these to estimate the population of the United States in the year 2010 or the percentage growth from 2000 to 2010. Why? Because these statistics are not being used to summarize past populations but to estimate future populations. The following are some other examples of descriptive statistics.
There are a total of 42,796 miles of interstate highways in the United States. The interstate system represents only 1 percent of the nations total roads but carries more than 20 percent of the traffic. The longest is I-90, which stretches from Boston to Seattle, a distance of 3,081 miles. The shortest is I-878 in New York City, which is 0.70 of a mile in length. Alaska does not have any interstate highways, Texas has the most interstate miles at 3,232, and New York has the most interstate routes with 28.
According to the Bureau of Labor Statistics, the average hourly earnings of production workers were $17.73 for January 2006. You can review the latest information on wages and productivity of American workers by going to the Bureau of Labor Statistics website at: http://www.bls.gov/home.htm and selecting Average Hourly Earnings.
Masses of unorganized datasuch as the census of population, the weekly earnings of thousands of computer programmers, and the individual responses of 2,000 registered voters regarding their choice for president of the United Statesare of little value as is. However, statistical techniques are available to organize this type of data into a meaningful form. Data can be organized into a frequency distributionA grouping of data into mutually exclusive classes showing the number of observations in each class.. (This procedure is covered in Chapter 2.) Various chartsSpecial graphical formats used to portray a frequency distribution, including histograms, frequency polygons, and cumulative frequency polygons. Other graphical devices used to portray data are line charts, bar charts, and pie charts. They are very useful, for example, for depicting the trend in long-term debt or percent changes in profit from last year to this year. may be used to describe data; several basic chart forms are also presented in Chapter 4.
Specific measures of central location, such as the mean, describe the central value of a group of numerical data. A number of statistical measures are used to describe how closely the data cluster about an average. These measures of central tendency and dispersion are discussed in Chapter 3.
The second type of statistics is inferential statisticsThe methods used to estimate a property of a population on the basis of a sample.also called statistical inference. Our main concern regarding inferential statistics is finding something about a population from a sample taken from that population. For example, a recent survey showed only 46 percent of high school seniors can solve problems involving fractions, decimals, and percentages. And only 77 percent of high school seniors correctly totaled the cost of salad, a burger, fries, and a cola on a restaurant menu. Since these are inferences about a population (all high school seniors) based on sample data, we refer to them as inferential statistics. You might think of inferential statistics as a best guess of a population value based on sample information.
Note the words population and sample in the definition of inferential statistics. We often make reference to the population living in the United States or the 1.31 billion population of China. However, in statistics the word population has a broader meaning. A populationThe entire set of individuals or objects of interest or the measurements obtained from all individuals or objects of interest. may consist of individualssuch as all the students enrolled at Utah State University, all the students in Accounting 201, or all the CEOs from the Fortune 500 companies. A population may also consist of objects, such as all the Cobra G/T tires produced at Cooper Tire and Rubber Company in the Findlay, Ohio, plant; the accounts receivable at the end of October for Lorrange Plastics, Inc.; or auto claims filed in the first quarter of 2006 at the Northeast Regional Office of State Farm Insurance. The measurement of interest might be the scores on the first examination of all students in Accounting 201, the tread wear of the Cooper Tires, the dollar amount of Lorrange Plasticss accounts receivable, or the amount of auto insurance claims at State Farm. Thus, a population in the statistical sense does not always refer to people.
To infer something about a population, we usually take a sampleA portion, or part, of the population of interest. from the population.
Reasons for sampling
Why take a sample instead of studying every member of the population? A sample of registered voters is necessary because of the prohibitive cost of contacting millions of voters before an election. Testing wheat for moisture content destroys the wheat, thus making a sample imperative. If the wine tasters tested all the wine, none would be available for sale. It would be physically impossible for a few marine biologists to capture and tag all the seals in the ocean. (These and other reasons for sampling are discussed in Chapter 8.)
As noted, using a sample to learn something about a population is done extensively in business, agriculture, politics, and government, as cited in the following examples:
Television networks constantly monitor the popularity of their programs by hiring Nielsen and other organizations to sample the preferences of TV viewers. For example, in a sample of 800 prime-time viewers, 320, or 40 percent, indicated they watched CSI: Crime Scene Investigation on CBS last week. These program ratings are used to set advertising rates or to cancel programs.
Gamous and Associates, a public accounting firm, is conducting an audit of Pronto Printing Company. To begin, the accounting firm selects a random sample of 100 invoices and checks each invoice for accuracy. There is at least one error on five of the invoices; hence the accounting firm estimates that 5 percent of the population of invoices contain at least one error.
A random sample of 1,260 marketing graduates from four-year schools showed their mean starting salary was $42,694. We therefore estimate the mean starting salary for all accounting graduates of four-year institutions to be $42,694.
The relationship between a sample and a population is portrayed below. For example, we wish to estimate the mean miles per gallon of SUVs. Six SUVs are selected from the population. The mean MPG of the six is used to estimate MPG for the population.
We strongly suggest you do the Self-Review exercise.
Following is a self-review problem. There are a number of them interspersed throughout each chapter. They test your comprehension of the preceding material. The answer and method of solution are given at the end of the chapter. You can find the answer to the following Self-Review on page 19. We recommend that you solve each one and then check your answer.
Click here for Solution.
The Atlanta-based advertising firm, Brandon and Associates, asked a sample of 1,960 consumers to try a newly developed chicken dinner by Boston Market. Of the 1,960 sampled, 1,176 said they would purchase the dinner if it is marketed.
What could Brandon and Associates report to Boston Market regarding acceptance of the chicken dinner in the population?
Is this an example of descriptive statistics or inferential statistics? Explain.
Chapter Exercises 6, 7, 8, 13, 14