BASIC STATISTICSChapter 1: Introduction

DEFINITION:Statistics is a group of methods that are used to

collect, organize, present, analyze, and interpret data to make decisions.

Collection refers to the gathering of information or data.

Organization or presentation involves summarizing data or information in textual, graphical, or tabular forms.

Analysis involves describing the data by using statistical methods and procedures.

Interpretation refers to the process of making conclusions based on the analyzed data.

Descriptive Statistics

Inferential Statistics

TYPES OF STATISTICS

Descriptive Statistics - is a statistical procedure concerned with

describing the characteristics and properties of a group of persons, places, or things.- Involves gathering, organizing, presenting,

and describing data.

For example, we may describe a collection of persons by stating how many are poor and how many are rich, how many are literate and how many are illiterate, how many fall into various categories of age, height, civil status, IQ, and many more.

Descriptive Statistics can answer the questions like:

1. How many students are interested to take Statistics online?

2. What are the highest and lowest scores obtained by STENEX applicants this year?

3. What are the characteristics of the most likable teacher according to students?

4. What proportion of SRSTHS students likes Mathematics?

Inferential Statistics is a statistical procedure that is used to draw

inferences or information about the properties or characteristics by a large group of people, places, or things on the basis of the information obtained from a small portion of a large group.

also called inductive reasoning or inductive statistics.

Example: Suppose we want to know the most favorite brand

of toothpaste of a certain barangay and we do not have enough time and money to interview all the residents of that barangay, we may just ask selected residents. With the data obtained from the interviews, we shall draw or make conclusion as to the barangay’s favorite brand of toothpaste.

Inferential Statistics can answer the questions like:

1. Is there a significant difference in the academic performance of male and female sophomore students in Statistics?

2. Is there a significant difference between the proportions of students who prefer Coke than Pepsi?

3. Is there a significant relationship between amount of time studied and grades received?

4. Is there a significant difference between the Biology scores of 30 students before and after taking Memory Plus for 15 days?

DESCRIPTIVE VS. INFERENTIAL

Descriptive

Definition of Terms

Sampling Techniques

Presentation of data

Summation

Calculator Exercises

Summary Measures of Data

Normal Distribution

InferentialSampling Distribution

Hypothesis Testing

• Z – test• T – test• F – test• Test on Proportion• Chi-square test

Correlation and Regression

CLASS EXERCISE 1Tell whether the following situations will make

use of descriptive statistics or inferential statistics.

1. A teacher computes the average grade of her students and then determines the top ten students.

2. A manager or a business firm predicts future sales of the company based on the present sales.

3. A psychologist investigates if there is a significant relationship between mental age and chronological age.

4. A researcher studies the effectiveness of a new fertilizer to increasing food production.

5. A janitor counts the number of various furniture inside the school.

6. A sports journalist determines the most popular basketball player for this year.

7. A school administrator forecast future expansion of a school.

8. A market vendor investigates the most popular brand of vinegar.

9. An engineer calculates the average height of the buildings along Taft Avenue.

10. A dermatologist tests the relative effectiveness of a new brand of medicine in curing pimples and other skin diseases.

DESCRIPTIVE OR INFERENTIAL?

In this survey conducted by Pulse Asia:1. Who were surveyed by Pulse

Asia?2. Is there anyone among you

who was a respondent in this research?

3. Why do you think Pulse Asia was able to conclude the 69% favor RH bill?

POPULATION VS. SAMPLE A population consists of all

elements – individuals, items, or objects – whose characteristics are being studied. The population being studied is called the target population.

A portion of the population selected for

study is referred to as a sample.

EXAMPLES: Population – total number of SRSTHS

students during SY 2010-2011: 877 students

Sample – Second year students of SRSTHS during SY 2010-2011: 228 students

Give your own examples!

BASIC TERMS Elements or Members of a sample or population is a

specific subject or object(for example, a person, firm, item, state or country)

Example: YOU as a member of the SRSTHS population.

Variable is a characteristic or property of a population or sample which makes the members different from each other.

Example: in II-Pasteur, gender is a variable Constant is a property or characteristic of a population

or sample, which makes the members of the group similar to each other. Example: if a class is composed of all boys, gender is constant.

Data (singular form is datum)are numbers or measurements that are collected as a result from observation, interview, questionnaire, experimentation, test and so forth.

Parameter is any numerical or nominal characteristic of a population. It is a value or measurement obtained from a population. It is usually referred to as the true or actual value.

Example: The researcher uses the whole population of SRSTHS to get the average allowance of SRSTHS students.

Statistic is an estimate of a parameter. It is any value or measurement obtained from a sample.

Example: The researcher uses the sample (n=200) to get the average allowance of SRSTHS students.

DATA TYPES Qualitative data are data which can

assume values that manifest the concept of attributes. These are sometimes called categorical data.

Example: gender, nationality Quantitative data are data which are

numerical in nature. These are data obtained from counting or measuring.

Example: Height, test scores

Discrete Variables Continuous Variables Dependent Variables Independent Variables

TYPES OF VARIABLES

Discrete Variables – is one that can assume a finite number of values. In other words, it can assume specific values only. The values of a discrete variable are obtained through the process of counting.

Example: the number of chairs in a room

Continuous Variables – A variable that can assume any numerical value over a certain interval or interval. The values of a continuous variable are obtained through measuring.

Example: The height of Kuya Ronil.

Dependent Variable is a variable which is affected or influenced by another variable.

Independent Variable is one which affects or influences the dependent variable.

Example:In a research problem entitled,

“The Effect of Technology-based Instruction on the Students’ Mathematics Achievement”. The independent variable here is the technology-based instruction, while the dependent variable is the academic achievement of students.

CLASS EXERCISE 2.A. Classify the following as quantitative or

qualitative data1. Color of the eye2. Number of typewriters in a room3. Civil status4. Address5. Telephone numbers6. Age of teachers7. Rank of students8. Speed of a car9. Birth rates10. Score in mathematics examination

B. Identify each of the following as continuous or discrete.

1. Weight of a body2. Length of a rod3. Number of chairs in the room4. Dimensions of a table5. Number of possible outcomes in throwing a die6. Number of hairs on your head7. Amount of sales in a business firm8. All rational numbers9. Speed of light10. Area of a land11. Lifetime of television tubes and batteries12. Life span of a person13. Number of passengers in a plane.

OUTPUT 1A. Google search or cut out newspaper clippings on a

research article on any topic. It should contain the results of any survey conducted locally(preferred) or abroad.

Guidelines:1. Clip the whole article if taken from a magazine or

newspaper. If it comes from the Internet, download the whole article. If it is more than two pages, summarize it.

2. Indicate the name of magazine/newspaper, date of publication, title of article and author. Highlight the population/sample/margin of error used in the article.

3. Identify statements which belong to: (a)descriptive statistics (b) inferential statistics

4. Find out the population/sample used in the survey.5. Enumerate the data gathered and classify whether

they are: a) qualitative b) quantitative

Stay happy!