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statistics an introduction




STATISTICS – a branch of mathematics that has applications in almost every facet of man’s daily life. The word STATISTICS is used in two senses: 1. Statistics (singular sense) – a field of science that deals with the collection, organization or presentation, analysis, and interpretation of data.
Collection of data refers to the process of obtaining measurements. Data can be gathered using interviews, surveys, experiments, observations, documentary analysis, registration, and other methods.  Organization or presentation of data refers to the tabulation of data into graphs or charts, so that logical conclusions can be derived from the collected measurements.  Analysis of data involves extracting of relevant information from the given data where numerical description can be formulated.  Interpretation of data is referred to as the task of drawing conclusions whether in narrower or broader sense.


Statistics (plural sense) – refers to the data set on certain variables.

Reasons why some knowledge of statistics important to the competence of every professional:


Statistical literacy is necessary in reading and evaluating reports and other literature critically and intelligently. Statistical literacy is important to professionals if they are going to undertake an investigation that involves the collection, processing, and analysis of data on their own account. Statistics is an important research tool.

As a research tool, it:
Permits us to use the most exact kind of description (math and statistics are parts of descriptive language). Forces us to be definite and exact in our procedure in our thinking. Enables us to summarize the results in a meaningful and convenient form. Enables us to draw general conclusions. Enables us to predict “how much” of a thing will happen under conditions we know and have measured and also how much faith we place in our prediction. Enables us to analyze some of the causal factors underlying complex and otherwise bewildering events.

LIMITATION OF STATISTICS: Statistics can help an investigator describe data, design experiments, and test the relationships among things or events of interest. It should be noted that statistics never proves anything. Rather, it indicates the likelihood of the results of an investigation being the product of chance.


DESCRIPTIVE STATISTICS – involves techniques concerned with collecting and describing a set of data so as to yield meaningful information.

It includes basic descriptive statistics (percentages, ratios, tables, and graphs).  Measures of Central Tendency (mean, median, mode).  Measures of Variability or Dispersion (range, standard deviation, variance, coefficient of variation).

Examples: 1. Employees’ ranks in the final job interview. 2. Tabulating the total scores of students in the final exam. 3. Reporting the incidence of HIV cases among Filipinos. 4. Line graph of company’s gross profit for 2012. 5. Average scores of elementary pupils in the district achievement test.

INFERENTIAL STATISTICS – is concerned with techniques that use
the obtained sample data to infer or draw conclusions about a larger set of data. This area of statistics is mostly concerned with making inferences about the population and categorized under this area are:  Sampling procedures  Estimation procedures  Hypothesis testing EXAMPLES: 1. Comparing the lifespan of smokers and non-smokers. 2. Comparing the LET ratings of men and women. 3. Relating global warming with industrial smokes. 4. Relating poverty with unemployment rate. 5. Comparing the research capabilities of college professors who are masters’ and non-masters’ degree holders.






VARIABLE is a characteristic that changes or varies over a period of time and/or for different individuals or objects under consideration. Examples:
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Blood type Educational attainment Age Sex Religious Affiliation Scores of students in the exam Number of children in the family Occupation Monthly salary, etc.

DATA SET is a collection of facts and figures.

A UNIVARIATE data results when a single variable is measured on a single experimental unit.
A BIVARIATE data results when two variables are measured on a single experimental unit. A MULTIVARIATE data results when more than two variables are measured on a single experimental unit.


QUALITATIVE VARIABLES Measure a quality or characteristic on each experimental unit. These variables produce data that can be categorized according to similarities or differences and therefore also referred to as categorical data. Examples: 1. Sex (Male or Female) 2. School Type (Public or Private) 3. Favorite color of a shirt (black, red, white, blue, etc.) QUANTITATIVE VARIABLES Measure a numerical quantity or amount on each experimental unit. Examples: 1. Age (in years) 2. Score in the exam 3. Weekly allowance (in Php)


Can assume only finite or countable (whole numbers) number of values. Examples: 1. Number of pages in a book 2. Number of children in the family 3. Number of balls in a box CONTINUOUS VARIABLE/DATA Can assume the infinitely many values corresponding to the points on the line interval (can take decimal value). Examples: 1. Age 2. Height 3. Grade point average (GPA)


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