Introduction to statistics

1. Jimma University
College of Natural Science
Department of Statistics
By Abebe.N
Gmail:abe1621n@gmail.com

2. General course objectives
Students will be familiarize with.
• Data collection, processing and organization
• Summarization and exploration
• Probability and probability distribution
• Random variable and sampling technique
• Estimation and hypotheses testing

3. Chapter-One
Introduction
At the end of this chapter students will be able to know.
• define Statistics, population, census, sample survey, parameter and variable
• distinguish descriptive statistics and inferential statistics
• identify the types of variables and level of measurement
• identify applications, uses, and limitations of statistics

4. Definition and classification of statistics
Statistics: A field of study concerned with methods and procedures for:
 Collection of data.
 Presentation of the collected data.
 Analysis and interpretation of the results.
 Making decisions on the basis of such analysis
 To make scientific inferences about a body of data when only a small part of the
data is observed.

5. Classification of statistics
Statistics is broadly divided into two categories based on how the collected data are used.
I. Descriptive Statistics: It is an area of statistics which is mainly concerned with the
methods and techniques used in collection, organization, presentation, and analysis of a set of
data without making any conclusions or inferences.
• Descriptive statistics summarizes or describes the characteristics of a data set.
• Descriptive statistics consists of two basic categories of measures: measures of central tendency
and measures of variability.
• descriptive statistics concerned with summary calculation, graph, chart, and table.
Example: From sample we have 40% employee suggest positive attitude toward the management of
the organization

6. Conti….
I. Inferential Statistics: Inferential statistics is an area of statistics which deals with
the method of inferring or drawing conclusion about the population based upon
the results of a sample.
• It consists of performing hypothesis testing, determining relationships among variables
and making predictions.
• is a method used to generalize from a sample to a population
For example: the average income of all families (the population)in Ethiopia can be
estimated from figures obtained from a few hundred (the sample) families.

7. Stage of statistical investigation
There are five stages or steps in any statistical investigation
Collection of data: This is the process of obtaining data by measurements or counts or obtaining raw
data.
Data may be collected either from primary source or secondary or from both the sources depending
upon the objective/s of the investigation
• Data can be collected in a variety of ways one of the most common methods is sample or census
survey.
• Survey can also be done in different ways
• Telephone survey
• Mailed questionnaire
• Personal interview methods

8. Conti….
Organization of data: summarization of data in some meaningful ways
• Classify the set of observation on the same group e.g table form
• it is necessary to edit these data in order to correct any apparent
inconsistencies, ambiguities, and recording errors.

9. Conti….
Presentation of data: The processes of re-organization, classification, compilation
and summarization of data to present in meaningful ways.
• After the data have been collected and organized they can be presented in the form
of tables, charts, diagrams and graphs.
• The raw data organized and present in clear and meaningful ways.
• This presentation useful to facilitates the understanding as well as analysis of data

10. Conti….
Analysis of data: the basic purpose of data analysis is to dig out useful information for
decision making
• The processes of cleaning, transforming and modeling data to discover useful
informations
Interpretation of data: Interpret and drawing conclusions from the data output.
• Correct interpretation will lead to a valid conclusion of the study.

11. Definitions of some basic statistical terms
Population: All subjects possessing a common characteristic that is being studied.
• The complete set of possible measurement for which inference are made
• A population is a totality of things, objects, peoples, etc. about which information is being collected
• The population represents the target of an investigation, and the objective of the investigation is to
draw conclusions about the population hence we sometimes call it target population.
Example: All students in JU taking probability and statistics course in this semester
• Population of households
Sample : A sample is a subset or part of a population selected to draw conclusions about the
population.

12. Conti….
Sample survey: data are collected sub-part of the population and sample are representative
of the whole population
• Data are used to estimate the characteristics of the whole population
• cheaper, practical, and convenient.
• Save time and energy.
• Easy to handle and analysis.
Census: complete enumeration of the whole population and data about all individual unit
are collected in the population studying without considering sample.

13. Conti….
Sampling: The process of selecting a sample from the population is called sampling.
Parameter: Characteristic or measure obtained from a population.
• It is the population measurement used to describe the population or quantity computed from values in
population.
Example: population mean(µ), population standard deviation(𝜹), population proportion(𝑷).
Statistic: Characteristic or measure obtained from a sample or quantity computed from values in sample
Example: sample mean(𝒙),sample standard deviation(𝒔), sample proportion(𝒑)
Sampling frame: A list of people, items or elements from which the sample is taken.
Example: list of household income
Sample size: The number of elements or observation to be included in the sample.
Variable: It is an item of interest that can take on many different numerical values.

14. Application, Uses and Limitation of Statistics
Application
Today the field of statistics is recognized as a highly applied and useful discipline in decision
Statistics is used to analyze and interpret large amounts of data in order to extract meaningful
insights and make informed decisions.
• Statistics is used to build models that can predict future outcomes based on past data and
patterns.
• Statistics is used to design and analyze surveys and experiments in order to collect data and
make inferences about populations.
• Statistics is used in medical research to analyze data from clinical trials and studies, and to
make inferences about the effectiveness of treatments and interventions.

15. Conti…..
Uses of Statistics
• It present fact in definite and precise form
• Data reduction
• Measuring the magnitude of variation in data
• Estimating unknown population characteristics
• Testing and formulating of hypothesis
• Study the relationship between two or more variables

16. Conti….
Limitation of statistics
• statistics deals with aggregate of facts and no with individual data items
• Statistics are true on average so a single observation is not a statistic.
• Statistical data are only approximately and not mathematical correct
• It does not deal with qualitative characteristics directly

17. Types of Variables & Measurement Scales
Types of Variables: There are two types of variables
I. Qualitative variables: variable which assume non numerical values and can not be measured
• Example: - religion, gender, race, beauty, religion,, place of birth, ethnic group, stages of
breast cancer (I, II, III, or IV), degree of pain (minimal, moderate, severe or unbearable).
II. Quantitative variables: that can be quantified or can have numerical values and it can be measured
and counting.
• Example: weight, height, age, production, blood pressure, heart beat, number of patients on a given
hospital etc.
• A quantitative variable can be grouped in to two types discrete or continuous.

18. Conti…..
I. Discrete variables: are variables which can assume only a specific number of values.
• Discrete variables are a result of counting and values are usually whole numbers
• Example: the number of items purchased, the number of HIV patient indifferent year, number of students in
Jimma university, number of chairs, number of accidents in a given year.
II. Continuous variable: continuous variables are variables that can have any value with in an interval.
• The values of continuous variables are obtained by measurement.
• Example: weight, height, blood pressure, age, expenditure, productions, rainfall generally any
measurable quantity etc.

19. Scale of measurement
Measurement: A procedure where qualities or quantities are assigned to characteristics of subjects,
objects or events.
• All measurements are not the same.
E.g., Measuring weight = e.g., 40kg, 40,000g.
Measuring the status of a patient on scale =“improved”, “stable”, “not improved”.
There are four type of measurement scale
 Nominal scale
 Ordinal scale
 Interval scale
 Ratio scale

20. Conti….
1. Nominal scale:
• Data that represent categories or names
• There is no implied order to the categories of nominal data.
• No arithmetic and relational operation can be applied.
• E.g.
• Blood type (A, B, O and AB)
• Eye color (brown, black, blue, etc.)

21. Conti…
2. Ordinal
 Categories that can be ranked, but differences Between ranks do not exist
Although non‐numerical, can be considered to have a natural ordering
 Arithmetic operations are not applicable.
 Ordering is the sole property of ordinal scale.
E.g.
• Degree of pain (minimal, moderate, severe)
• Rating scales (Excellent, Very good, Good, Fair, poor)
• Letter grade (A, B, C, D and F)

22. Conti….
3. Interval
 Data that can be ranked and differences are meaningful. However, there is no
meaningful zero, so ratios are meaningless.
 All arithmetic operations except division and relational operations are also possible.
E.g.
 IQ
 Temperature in degree Fahrenheit (30F is not as much as two times of 15F)

23. Conti….
4. Ratio
• Data can be ranked, differences are meaningful, and there is a true zero.
• All arithmetic and relational operations are applicable.
• E.g.
• Age (30 year individual is two times of 15 years)
• Weight (0kg is to mean, no weight)
• Number of drugs