What is Frequency Distribution?

• A common, very helpful way to summarize data collections method shows the frequency (no. of occurrences) in each of several categories.

• Frequency Distribution can be summarize large volume of data values so decision makes can extract useful information directly from the collection.

• Frequency Distribution is a tabular arrangement of data showing its classification or grouping according to magnitude or size.

• Large masses of data presented without any arrangement or classification given very little information. In order for these data to give useful information they should be summarized or organized into a reduced form more appropriate for an effective analysis. One way of doing this is to summarize the data and compress them into a frequency distribution.
  

Classification of Variables

A. According to continuity of values

1. Continuous variables. These are variables that can take the form of decimals.
Example. Weight, length, height, school achievement.

2. Discrete or discontinuous variable. These are variables that can’t take the form of
decimals.
Example: number of students, number of houses, size of a family, etc.

B. According to scale and measurements

1. Nominal variable. This property allows one to make statements of similarities or
differences.
Example: sex- member of population may be classified as male or female,
socio-economic status – the member of the group may be classified
as those belonging to high, average or low socio-economic status

2. Ordinal variable. This variable refers to a property whereby members of a group are
ranked.

Example: one can judge and rank the contestants in a beauty contest.

3. Internal variable. This property allows one to make statements of equality of intervals.

Example: height, weight, temperature, test scores, etc.

4. Ratio variable. This property permits making statements of quality of ratios.

Example: If Cora is 48 yrs. old and Philline is 22 years old. Their ages can be expressed in the ratio of 48:22 or 24:11 (twenty-four is to eleven)

C. According to Functional Relationship

1. Independent variable. This is sometimes termed as predictor variable.

2. Dependent variable. This is sometimes called criterion variable.

Example: Academic achievement is dependent on I.Q . I.Q. is independent variable and academic achievement is the dependent variable

Methods of Collecting Data

a. Direct or Interview Method – This is a personal communication with the individual you want to interview.

b. Indirect or Questionnaires Method – This is done by sending questionnaires to the person from whom like to get the information.

c. Registration – Utilizing existing records

Example: records of births, marriages and deaths at the National Census of Statistics Office
(NCSO)

d. Observation – This can be done directly or indirectly.

e. Experiment – This is done by making or conducting scientific inquiry.

Definition of Terms

Data
It is a facts or figures from which conclusions may be drawn. The statistical facts, historical facts, principles, opinions and item of various sources like scores, age, I.Q., Income, etc.

Data Collection and Presentation The data collected must be valid, reliable, relevant, and consistent with other information to the problem at hand. Data collected may be classified as primary, secondary, internal or external.

Primary Data
Refer to the data obtained directly from an original source by means of actual observations or by conducting interview. The direct source could be an individual or family groups, business entities or private and government agencies.

Secondary Data
Refer to data or information that come from existing records (published and/or unpublished) in usable form such as surveys, census, business journals and magazines, newspapers, commercial publications and other such as theses and dissertation and research papers, etc.

Internal Data
Data taken from the company’s own records of operations such as sales records, production records, personal records, etc.

External Data
Data that come from outside sources and not from the company’s own record.

Variable
It is a characteristic or phenomena which may take on different values. Example: weight, I.Q., and sex, age, marital status, eye color, etc.

Quantitative variable
If the outcomes are expressed numerically. Example: height, weight, age and numerical values.

Qualitative variable
It the outcomes refer to non-numerical qualities or attributes. Ex. Sex, marital status, eye color.

Division of Statistics

Statistics may be divided into:

1. Descriptive Statistics – which is concerned with the collection, classification, and presentation of data designed to summarize and describe the group characteristics of the data.

Examples: the measure of location, measures of variability, skewness and kurtosis

2. Inferential Statistics – refers to the drawing of conclusions or judgment about a population based or representative sample systematically taken from the same population. It’s aim is to give concise information about large group of data without dealing with each and every element of these groups. So that, if the sample taken is small, certain assumptions and inferences are made based on limited information and if the sample drawn is large, it may be treated as equal to that of the whole observation.

Populations and Sample

Population. It is the totality of all the actual or concerable objects of a certain class under consideration. It is a complete set of individuals, objects or measurements having some common observable characteristics.

Sample. It is a finite number of objects selected from the population.

Importance of Statistics

Statistics or statistical method is playing an important role in nearly all fields of human endeavor. The influence of statistics has spread out in almost all fields such as education, agriculture, business, psychology, economics, physics, government, chemistry, sociology, and other branches of science and engineering.

We are aware of the activities in our school. Our teacher give us the grades which are the result of our performance based in recitation, quizzes, tests, homework and other classroom activities. Evaluation of student’s performance in the classroom makes use of statistical method. The school administrator evaluates teachers’ performance, keeps record of no. of students enrolled, gathers information about the students and collect data pertinent to efficient operation, These data are then analyzed and interpreted such activities make use of statistics.

In the sciences, statistical methods are used in the formulation of laws, principles, and established facts. In companies, results of statistics serve as bases for the formulation of policies for a more efficient operation of the business.

Some of the most important subject areas which make use of statistical theory and techniques are as follows:

Biology – Research and experimentation in life processes of plants and animals to promote growth or prolong life

Education – Teaching – Learning processes, measurement and evaluation, educational studies, enrollment, management and finance.

Engineering – Design and Test of performance and quality control

Sports – Points made out of so many attempts from the field or foul from the line such as in basketball, football, etc.

What is Statistics?

Statistics is not really a new subject. It has been existence since the earliest man on earth.

The earliest tribes have been using statistics in keeping records of the:

• No. of individuals in their tribes
• No. of animals they have
• No. of enemies they killed and other similar data.
  

The early astronomers, through careful observations and accurate recordings of data were able to predict the changing courses of the stars and other heavenly bodies.

Statistics is a branch of mathematics which deals with the collection, organization, analysis and interpretation of numerical data which maybe used for prediction and verification of relationships among variables.

Course Outline

• Introduction what statistics is?, Some term and their definition used in statistics
• Methods of Collection of data and Kinds of sampling
• Kinds of data and their examples
• Classification of variable
• Frequency Distribution, and construction
• Graphical presentation for continuous data and Graphical Presentation for discontinuous data
• Measures of Central Tendency(Mean, Median, Mode)
• Quartiles, Percentiles, and Deciles
• Dispersion
• Standard score and normal curve
• Linear regression and coefficient of correlation
• Hypothesis testing and Measures of difference

Course Objectives

1. Know the importance of collected and organized data to statistical analysis.
2. Give a clear understanding to some terms to be used that will facilitate its computation in statistics.
3. Learn and present a number of common statistical method for summarizing large data set.
4. Give an insight how to find the appropriate measure of dispersion and how to examine several quantitative methods for describing the shape of distribution and how to interpret these statistics.
5. Determine the importance of the normal distribution in the analysis and evaluation of every aspect of experimental data.
6. Determine the difference among correlation, coefficient of correlation and regression.
7. Know the role of probability to inferential statistics.

Course Description

The word statistics refers in common usage to numerical data but it has an additional meaning that is more specialized. Statistics also refer to the methodology for the collection, presentation and analysis of data and for the use of such data.

The collection and summarization of data are important first steps in the process of using data for analysis and decision making. The statistical methodology for analyzing data and making decisions is called statiscal inference. The logical foundation of statistical inference is the mathematical theory of probability. We define probability as the likelihood that a given event will occur relative to all other events that can occur. We usually define probabilities based on the number or frequency with which events can occur.