Descriptive Statistics PDF

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Module 4Mathematics as a ToolAt the end of the fourth module, you must have: applied a variety of statistical tools to process and manage numerical data; utilized the methods of linear regression and correlations to predict the value of a variable given certain conditions; and 3. advocated the use o...

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Module 4 Mathematics as a Tool At the end of the fourth module, you must have: 1. applied a variety of statistical tools to process and manage numerical data; 2. utilized the methods of linear regression and correlations to predict the value of a variable given certain conditions; and 3. advocated the use of statistical data in making important decisions. ______________________________________________________________________________________________________________ Lesson 4.1 Descriptive Statistics Definition of Statistics  In its plural sense, statistics is a set of numerical data.  In its singular sense, Statistics is the science of collecting, analyzing, presenting, and interpreting data, as well as of making decisions based on such analyses.

Types of Statistics Descriptive Statistics consists of methods for organizing, displaying, and describing data by using tables, graphs, and summary measures.

Case Study 1-1: How Women Rate Their Lives

Case Study 1-2: How Much Did Companies Spend on Ads in 2011?

Inferential Statistics consists of methods that use sample results to help make decisions or predictions about a population.

Population versus Sample A population consists of all elements – individuals, items, or objects – whose characteristics are being studied. The population that is being studied is also called the target population.

A portion of the population selected for study is referred to as a sample. 1|Page

Figure 1.1 Population and Sample A survey that includes every member of the population is called a census. The technique of collecting information from a portion of the population is called a sample survey. A sample that represents the characteristics of the population as closely as possible is called a representative sample.

Basic Terms  An element or member of a sample or population is a specific subject or object (for example, a person, firm, item, state, or country) about which the information is collected.  A variable is a characteristic under study that assumes different values for different elements. In contrast to a variable, the value of a constant is fixed.  The value of a variable for an element is called an observation or measurement.  A data set is a collection of observations on one or more variables.  A parameter refers to any numerical value describing a characteristic of a population and is usually represented by Greek letters such as µ and σ.  The term statistic is used to refer to any numerical value describing a characteristic of a sample. It is usually represented by lower case letters of the English alphabet, such as x and s.

Table 1.1 Total Revenues for 2010 of Six Companies

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______________________________________________________________________________________________________________ Types of Variables  Quantitative Variables  Discrete Variables  Continuous Variables  Qualitative or Categorical Variables A variable that can be measured numerically is called a quantitative variable. The data collected on a quantitative variable are called quantitative data. A variable whose values are countable is called a discrete variable. In other words, a discrete variable can assume only certain values with no intermediate values. A variable that can assume any numerical value over a certain interval or intervals is called a continuous variable. Figure 1.2 Types of Variables

Levels of Measurement 1. Nominal Level (Classificatory Scale)  The nominal level is the weakest level of measurement where numbers or symbols are used simply for categorizing subjects into different groups.  Classifies data into various distinct categories in which no ranking is implied on the categories. Example: Sex (male, female), Marital Status (single, married, widowed), Type of stocks owned (growth, value, other) 2. Ordinal Level (Ranking Scale)  The ordinal level of measurement contains the properties of the nominal level, and in addition, the numbers assigned to categories of any variable may be ranked or ordered in some low-to-high manner. Example: Product Satisfaction (very unsatisfied, fairly unsatisfied, neutral, very satisfied), Student Classification (freshmen, sophomore, junior, senior) 3|Page

3. Interval Level  The interval level has the properties of the nominal and ordinal levels, and in addition, the distances between any two numbers on the scale are known sizes. An interval scale must have a common and constant unit of measurement. Furthermore, the unit of measurement is arbitrary and there is no “true zero” point. Example: IQ, temperature (in Celsius), Standardized Exam Score (NCAE) 4. Ratio Level  The ratio level of measurement contains all the properties of the interval level, in addition, it has a “true zero” point. Example: Weight (in kilograms), number of correct answers in an exam, salary

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Republic of the Philippines SOUTHERN LEYTE STATE UNIVERSITY – TOMAS OPPUS San Isidro, Tomas Oppus, Southern Leyte ACTIVITY IN DESCRIPTIVE STATISTICS Name: ___________________________________________________ Date: _______________________ Course & Section: _________________________

Score: _________________

_____________________________________________________________________________________________________________ General Instructions: a. Write all your answers in a clean sheet of bond paper. b. Show all your solution and box your final answer. c. Take a picture of your answer and send it through messenger. ______________________________________________________________________________________________________________ A. DIRECTIONS: Classify the following as Qualitative or Quantitative. If a variable is quantitative, further classify it as Discrete or Continuous. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

gender general point average occupation unemployment rate Number of hours children watch television Number of bicycles sold in 1 year by a large sporting goods store Classification of children in a day-care center (infant, toddler, preschool) The number of defective computers produced by a manufacturer. The time needed to finish the test. The number of dropout in a school district for a period of 10 years.

B. DIRECTIONS: Classify each as Nominal-Level, Ordinal-Level, Interval-Level, or Ratio-Level of measurement. 1. Ratings of excellent, above average, average, below average, or poor for painting exhibits. 2. Temperatures (in degrees Celsius) of a sample of restless demonstrators who are against the government. 3. Colors of a sample of Binitin Shirts. 4. Cars described as compact, intermediate, or full-sized. 5. Ages of students in a classroom. C. DIRECTIONS: Give 5 examples of Descriptive Statistics and 5 examples of Inferential Statistics. Example: 

The average Amazon.com rating of the book The Complete Idiot’s Guide to Statistics by 26 reviewers is 4.6 on a scale of 1 to 5. (Descriptive

Statistics) 

A study has concluded that the average credit card debt of college graduates has increased from the year 20019 to 2020. (Inferential

Statistics) 5|Page...