1.2 Types of Statistics?
The study of statistics is usually divided into two categories: descriptive statistics and inferential statistics.
Descriptive Statistics
The definition of statistics given earlier referred to “organizing, presenting, analyzing the data.” This facet of statistics is usually referred to as descriptive statistics.
DESCRIPTIVE STATISTICS Methods of organizing, summarizing, and presenting data in an informative way.
For instance, the Cambodia government reports the population of the Cambodia was 14,363,532 in 2010; 16,396,860 in 2020. This information is descriptive statistics. It is descriptive statistics if we calculate the percentage growth from one 2010 to the 2020. However, it would not be descriptive statistics if we used these to estimate the population of Cambodia in the year 2030 or the percentage growth from 2020 to 2030. Why? The reason is these statistics are not being used to summarize past populations but to estimate future populations.
The following are some other examples of descriptive statistics:
The average person spent $51.5 on traditional Valentine’s Day merchandise in 2020. This is an increase of $0.50 from 2019. As in previous years, men will spend nearly twice the amount women spend on the holiday.
The average man spent $67.75 to impress the people in his life while women only spent $33.83.
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 Next Chapter.
Types of descriptive statistics
There are 3 main types of descriptive statistics:
The distribution concerns the frequency of each value.
The central tendency concerns the averages of the values.
The variability or dispersion concerns how spread out the values are.
Inferential Statistics
The second type of statistics is inferential statistics—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 a salad, 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.
INFERENTIAL STATISTICS The methods used to estimate a property of a population on the basis of a sample.
Note: the words population and sample in the definition of inferential statistics. We often make reference to the population of 308.8 million people living in the United States or the 1,336.1 million people living in China. However, in statistics the word population has a broader meaning.
A population may consist of individuals—such as all the students enrolled at RUPP University, all the students in Accounting 201, or all the CEOs from the Royal Group or Planning for your interviews, you will need to know about each company’s mission, profitability, products, and markets.
Two terms of Inferential Statistics:
POPULATION The entire set of individuals or objects of interest or the measurements obtained from all individuals or objects of interest. To infer something about a population, we usually take a sample from the population.
SAMPLE A portion, or part, of the population of interest.
Inferential statistics have two main uses:
making estimates about populations (for example, the mean SAT score of all 11th graders in the US).
testing hypotheses to draw conclusions about populations (for example, the relationship between SAT scores and family income).
Most of the time, you can only acquire data from samples, because it is too difficult or expensive to collect data from the whole population that you’re interested in.
While descriptive statistics can only summarize a sample’s characteristics, inferential statistics use your sample to make reasonable guesses about the larger population.
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:
A random sample of 1,260 marketing graduates from four-year schools showed their mean starting salary was $550. We therefore estimate the mean starting salary for all marketing graduates of four-year institutions to be $550.
Television networks constantly monitor the popularity of their programs by hir- ing 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, indi- cated they watched American Idol on Fox last week. These program ratings are used to set advertising rates or to cancel programs.
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