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Descriptive statistics

Descriptive statistics describe the main features of a collection of data quantitatively. Descriptive statistics are distinguished from inferential statistics (or inductive statistics), in that descriptive statistics aim to summarize a data set quantitatively without employing a probabilistic formulation, rather than use the data to make inferences about the population that the data are thought to represent. Even when a data analysis draws its main conclusions using inferential statistics, descriptive statistics are generally also presented. For example in a paper reporting on a study involving human subjects, there typically appears a table giving the overall sample size, sample sizes in important subgroups (e.g., for each treatment or exposure group), and demographic or clinical characteristics such as the average age, the proportion of subjects of each sex, and the proportion of subjects with related comorbidities.

Inferential statistics

Inferential statistics tries to make inferences about a population from the sample data. We also use inferential statistics to make judgments of the probability that an observed difference between groups is a dependable one, or that it might have happened by chance in this study. Thus, we use inferential statistics to make inferences from our data to more general conditions; we use descriptive statistics simply to describe what's going on in our data.

Use in statistical analyses

Descriptive statistics provide simple summaries about the sample and the measures. Together with simple graphics analysis, they form the basis of quantitative analysis of data.

Descriptive statistics summarize data. For example, the shooting percentage in basketball is a descriptive statistic that summarizes the performance of a player or a team. This number is the number of shots made divided by the number of shots taken. A player who shoots 33% is making approximately one shot in every three. One making 25% is hitting once in four. The percentage summarizes or describes multiple discrete events. Or, consider the scourge of many students, the grade point average. This single number describes the general performance of a student across the range of their course experiences.

Describing a large set of observations with a single indicator risks distorting the original data or losing important detail. For example, the shooting percentage doesn't tell you whether the shots are three-pointers or lay-ups, and GPA doesn't tell you whether the student was in difficult or easy courses. Despite these limitations, descriptive statistics provide a powerful summary that may enable comparisons across people or other units.

Univariate analysis

Univariate analysis involves the examination across cases of a single variable, focusing on three characteristics: the distribution; the central tendency; and the dispersion. It is common to compute all three for each study variable.


The distribution is a summary of the frequency of individual or ranges of values for a variable. The simplest distribution would list every value of a variable and the number of cases who had that value. For instance, computing the distribution of gender in the study population means computing the percentages that are male and female. The gender variable has only two, making it possible and meaningful to list each one. However, this does not work for a variable such as income that has many possible values. Typically, specific values are not particularly meaningful (income of 50,000 is typically not meaningfully different from 51,000). Grouping the raw scores using ranges of values reduces the number of categories to something for meaningful. For instance, we might group incomes into ranges of 0-10,000, 10,001-30,000, etc.

Frequency distributions are depicted as a table or as a graph. Table 1 shows an age frequency distribution with five categories of age ranges defined. The same frequency distribution can be depicted in a graph as shown in Figure 2. This type of graph is often referred to as a histogram or bar chart.

Central tendency

The central tendency of a distribution locates the "center" of a distribution of values. The three major types of estimates of central tendency are the mean, themedian, and themode.

The mean is the most commonly used method of describing central tendency. To compute the mean, take the sum of the values and divide by the count. For example, the mean quiz score is determined by summing all the scores and dividing by the number of students taking the exam. For example, consider the test score values:

15, 20, 21, 36, 15, 25, 15

The sum of these 7 values is 147, so the mean is 147/7 =21.

The median is the score found at the middle of the set of values, i.e., that has as many cases with a larger value as have a smaller value. One way to compute the median is to sort the values in numerical order, and then locate the value in the middle of the list. For example, if there are 500 values, the median is the average of the two values in 250th and 251st positions. If there are 501 values, the value in 250th position is the median. Sorting the 7 scores above produces:

15, 15, 15, 20, 21, 25, 36

There are 7 scores and score #4 represents the halfway point. The median is 20. If there are an even number of observations, then the median is the mean of the two middle scores. In the example, if there were an 8th observation, with a value of 25, the median becomes the average of the 4th and 5th scores, in this case 20.5.

The mode is the most frequently occurring value in the set. To determine the mode, compute the distribution as above. The mode is the value with the greatest frequency. In the example, the modal value 15, occurs three times. In some distributions there is a "tie" for the highest frequency, i.e., there are multiple modal values. These are called multi-modal distributions.

Notice that the three measures typically produce different results. The term "average" obscures the difference between them and is better avoided. The three values are equal if the distribution is perfectly "normal" (i.e., bell-shaped).


Dispersion is the spread of values around the central tendency. There are two common measures of dispersion, the range and the standard deviation. The range is simply the highest value minus the lowest value. In our example distribution, the high value is 36 and the low is 15, so the range is 36 − 15 = 21.


From Yahoo Answers

Question:I asked a question which featured this film, and got a lot of answers claiming that the film is propaganda and factually flawed. Could someone advise me where in the film it gets the facts wrong? Links or sources would be appreciated PS, simply saying you don't agree with or like Michael Moore isn't any kind of answer

Answers:http://www.davekopel.com/Terror/Fiftysix-deceits-in-Fahrenheit-911.htm there u go


Answers:Definition: Adjectives are words that function to describe nouns. Specifically, adjectives describe the action, state, or quality that nouns refer to. Descriptive adjectives are the largest class of the four types of adjectives, the others being adjectives of quantity, demonstrative adjectives, and pronominal adjectives When using multiple descriptive adjectives in a sentence, there is an order in which they should be arranged. Adjectives that describe opinion typically preceded adjectives that describe color, size, shape, etc. For example, the sentence The ugly red chair sat in the corner is preferable to The red ugly chair sat in the corner. In addition, adjectives are usually arranged in a sentence from those that are more general in scope to those that are more specific. For example, "The big Egyptian mask hanging on the wall" is preferable to The Egyptian big mask hanging on the wall and "The blue silken curtains hanging in the bedroom" is preferable to The silken blue curtains hanging in the bedroom. Writers and speakers can refer to a list of descriptive adjectives for ideas on how to better explain the action, state, or quality that a noun in a sentence refers to. Understanding that there are three main types of descriptive adjectives can provide further insight on how these important words can be used. With a good descriptive adjective resource and a little creativity, you can begin to add more flavor to your ideas when speaking or writing in English.

Question:I have to make a non-factual question but i'm not sure how to start it. My teacher gave us 5 words but it's last minute and I can't find the paper with the words on it. Please help ASAP. Thanks so much!

Answers:To make a non-factual question - I'm guessing you need to use words that make it an opinion instead. Like what is the best tasting whatever. Obviously an opnion. Often words like favorite show it is an opinion. Using favorite instead of best. For example show that it is someone's opinion not factual. Hope this helps.

Question:1. what the responsibilties of finance in the company? 2. I want an example of work background of finance manager. Also, education background of any finance manager. THANX in Advance.

Answers:Almost every firm, government agency, and other type of organization has one or more financial managers who oversee the preparation of financial reports, direct investment activities, and implement cash management strategies. Because computers are increasingly used to record and organize data, many financial managers are spending more time developing strategies and implementing the long-term goals of their organization. The duties of financial managers vary with their specific titles, which include controller, treasurer or finance officer, credit manager, cash manager, and risk and insurance manager. For duties of each of these titles, pls click on the link below. A bachelor s degree in finance, accounting, economics, or business administration is the minimum academic preparation for financial managers. However, many employers now seek graduates with a master s degree, preferably in business administration, economics, finance, or risk management. These academic programs develop analytical skills and provide knowledge of the latest financial analysis methods and technology. Experience may be more important than formal education for some financial manager positions most notably, branch managers in banks. Banks typically fill branch manager positions by promoting experienced loan officers and other professionals who excel at their jobs. Other financial managers may enter the profession through formal management training programs offered by the company. The American Institute of Banking, which is affiliated with the American Bankers Association, sponsors educational and training programs for bank officers through a wide range of banking schools and educational conferences.

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Factorial Design (Part A): Scenario & Descriptive Statistics :An Example of a 2x2 Factorial Design: Designing the study, collecting data, recording data, interpreting the descriptive statistics