Course: STA101
Introduction to Statistics
Farzana Zaman
Adjunct Faculty (Statistics)
Department of Mathematics and Natural Sciences (MNS)
BRAC University
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Outline
Lecture 01, 02 & 03
❖ Introduction
❖ Definition and Scope of Statistics
❖ Basic Statistical terms
❖ Sources of Data
❖ Variables & Classification of variables
❖ Level of Measurements
❖ Summarization & Graphical presentation of Qualitative data
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Introduction
Introduction to Statistics
✦ In simple words, statistics is the study of data.
✦ Examples of statistics are:
– The inflation rate is 2%.
– Your grade point average is 3.5.
– The price of a new Tesla Model S sedan is $79, 570.
✦ Each of these statistics is a numerical fact and communicates a very
limited piece of information that is not very useful by itself.
However, if we recognize that each of these statistics is part of a
larger discussion, then the question “what is statistics” is applicable.
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Introduction
Introduction to Statistics
✦ According to Fisher (1947), the science of statistics is essentially a
branch of applied mathematics and may be regarded as mathematics,
applied to observational data.
✦ Statistics is the set of knowledge and skills used to organize,
summarize, and analyze data.
✦ In other words, statistics is the science of collecting, organizing,
presenting, analyzing, and interpreting data to assist in making more
effective decisions.
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Scopes & Applications
Scopes of Statistics
Population, health and family
planning
Socio-economic study
Biology
Medicine
Business and commerce
Psychology and education
Agriculture
Production industry
Physical science
Astronomy etc.
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Scopes & Applications
Real Life Applications
Life Sciences:
Studying the Effectiveness of a New Drug
A pharmaceutical company is testing a new drug. They conduct a
clinical trial with two groups: one receives the new drug, and the
other receives a placebo.
Economics:
Analyzing Unemployment Rates
An economist wants to understand the relationship between education
levels and unemployment rates across different regions.
Business:
Customer Feedback Analysis
A restaurant collects customer feedback on service quality on a scale
of 1 to 5.
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Scopes & Applications
Real Life Applications
Molecular Biology: Analysis of microarray data
Ecology: Describing quantitatively how individuals in various animal
and plant populations are spatially distributed
Public health: Identifying sources of diseases and ways to treat them
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Basic Statistical Terms & Ideas
Types of Statistics
Broadly speaking, applied statistics can be divided into two areas:
– Descriptive Statistics
– Inferential Statistics
Descriptive Statistics: Methods for organizing, summarizing and
presenting data in an informative way.
Example: (Student Exam Scores)
A teacher wants to summarize/find the average of the performance of
40 students on a math exam. The teacher collects data from all the
students or a portion of students and then present it in an organized
way. Then he calculates the mean score by adding all the students’
scores and dividing by 40. This gives the average performance of the
class.
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Basic Statistical Terms & Ideas
Types of Statistics
Inferential Statistics: Methods for making a valid conclusion of a
population on the basis of a sample data.
Example: (Student Exam Scores)
Based on a sample of 20 students, the teacher estimates the average
performance of all the students in the class. Suppose the calculated
average score is 75 out of 100. On the basis of the sample data, the
teacher makes predictions/conclusions about the average performance
of the entire class.
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Basic Statistical Terms & Ideas
Population
Population is the collection of all items or individuals with at least
one common characteristic for which we have an interest at a
particular time or study.
Population Size: The number of elements in the population is called
the population size and is denoted by N.
Examples:
– All students in Fall 2024 semester at BRACU
– All daily newspapers published in the Bangladesh
– All the ages of students enrolled in the BRAC University
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Basic Statistical Terms & Ideas
Sample
A sample is a small but representative part of a population.
Sample Size: The number of elements in the sample is called the
sample size and is denoted by n.
Examples:
– Students in section 31, Fall 2024 semester at BRACU
– Daily newspapers - The Daily Star, Prothom Alo, The Bangladesh
Today, Kaler Kantho
– Ages of students in section 31, Fall 2024 semester at BRACU
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Basic Statistical Terms & Ideas
Example: Population & Sample
Example: Student Housing
A survey is carried out at Penn State to estimate the proportion of all
undergraduate students living at home during the current term. Of the
3,838 undergraduate students enrolled at the campus, a random sample
of 100 was surveyed.
Population: All 3,838 undergraduate students at Penn State
Sample: The 100 undergraduate students surveyed
We can use the data collected from the sample of 100 students to make
inferences about the population of all 3,838 students.
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Basic Statistical Terms & Ideas
Exercise: Population & Sample
Example: Polling Teachers
Educational policy researchers randomly selected 400 teachers at random
from the National Science Teachers Association database of members and
asked them whether or not they believed that evolution should be taught
in public schools. They received responses from 252 teachers.
Q. Identify the population and sample from the given scenario.
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Basic Statistical Terms & Ideas
Parameter & Statistic
Parameter: A constant which
is a function or characteristic
of population values and is
usually unknown, is called a
parameter.
Statistic: Any function of
sample values which is an
estimate of the parameter and
which is a known value is
called a statistic.
Example:
Average height of all students
in Fall 2024 semester at
BRACU (µ).
Example:
Average height of students in
section 31, Fall 2024 semester
at BRACU (x̄).
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Basic Statistical Terms & Ideas
Example: Mean screen time
Suppose a teacher is interested in finding out the mean screen time of all
BRAC University students. For this purpose, a survey is carried out and
responses from 3000 students were recorded.
Q. Identify the population, sample, parameter and statistic from the given
scenario.
Population: All BRAC University students
Sample: The 3000 students surveyed
Parameter: Average/ Mean screen time of all students at BRACU
(Population Mean)
Statistic: Average/ Mean screen time of 3000 surveyed students at
BRACU (Sample Mean)
The teacher can use the data collected from the sample of 3000 students
to make inferences about the screen time of the population of all BRACU
students.
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Basic Statistical Terms & Ideas
Variable
A variable is a measurable quantity, which can vary within its domain.
A variable is a characteristic, often but not always quantitatively
measured, containing two or more values or categories that can vary
from person to person, object to object or from phenomenon to
phenomenon.
Examples:
– Gender : Male, Female
– Family Size: 1-member family, 2-member family etc.
– Hair color: black, brown, white etc.
– Age/ Height/ Weight of individuals
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Basic Statistical Terms & Ideas
Types of Variables
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Basic Statistical Terms & Ideas
Qualitative & Quantitative Variables
Qualitative Variable: A qualitative variable is one for which
numerical measurement is not possible.
An individual is simply assigned to any one of the several mutually
exclusive categories on the basis of the observation made on the
individual.
Examples:
– Gender : Male, Female
– Hair color: black, brown, white etc.
– Religion: Muslim, Hindu, Christian, etc.
Quanitative Variable: A quantitative variable is one for which the
resulting observations are numeric and thus possesses a natural
ordering.
Examples:
– Family Size: 1-member family, 2-member family etc.
– Age/ Height/ Weight of individuals
– Number of accidents
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Basic Statistical Terms & Ideas
Discrete & Continuous Variables
Observations on quantitative variables may be further classified as
discrete or continuous.
Discrete Variable: When a variable can assume only the isolated
values, which are countable within a given range is called discrete
variable.
Examples:
– Number of members/ children in a family
– Number of accidents in a city per day
– Number of fishes caught in a sweep of a net
Continuous Variable: If a variable can theoretically assume any value
within a continuous range or ranges, is called continuous variable.
Examples:
– Height/ Weight of individuals
– Price of a commodity
– Time
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Basic Statistical Terms & Ideas
Scale/ Level of Measurement
Measurement is a process of assigning numbers to some
characteristics or variables or events according to scientific rules.
Variables in a study can be measured under four levels or scales of
measurement:
1. Nominal
2. Ordinal
3. Interval
4. Ratio
Nominal Scale: Nominal is the weakest level of measurement.
The measurement scale, in which numbers are assigned to the
categories or variable values for identification only, is called a nominal
scale.
Example: Gender, Religion, Region, Hair color, Race etc.
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Basic Statistical Terms & Ideas
Scale/ Level of Measurement
Ordinal Scale: The measurement scale in which numbers are
assigned to the categories or variable values for identification as well
as ranking is called an ordinal scale.
Example: Economic status, Educational Status etc.
Interval Scale: The measurement scale in which numbers are
assigned to the variable values in such a way that the level of
measurement is broken down on a scale of equal units and the zero
value on the scale is not absolutely zero, is called an interval scale.
Example: Temperature, IQ score, Test score etc.
Ratio Scale: The measurement scale in which numbers are assigned
to the variable values in such a way that the level of measurement is
broken down on a scale of equal units and the zero value on the scale
is absolutely zero, is called a ratio scale.
Example: Age, Height, Weight, Pulse rate etc.
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Basic Statistical Terms & Ideas
Comparison between Four Levels of Measurement
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Basic Statistical Terms & Ideas
Exercise
Q. Identify the level of measurement for each variable and determine if
each is qualitative or quantitative, as well as discrete or continuous.
ˆ Jersey numbers of football players
ˆ Your rank in class
ˆ Temperature
ˆ Number of patients seen
ˆ Number of sales calls made
ˆ Distance to class
ˆ Amount of income tax paid
ˆ Time
ˆ Yearly rainfall in Dhaka
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Data
Data
Data are raw, disorganized facts and figures collected from any field
of inquiry.
A data is said to be primary data if it is obtained from an investigation
conducted for the first time. Thus the data collected for the first time
by the investigator as original data are known as primary data.
Example:
Census Data
National income data collected by the government
Data collected on exam scores of the students of STA101
When a statistical analysis is conducted on a data set available from a
prior investigation is called a secondary data.
Example:
Primary data become secondary data for those who use them.
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Data
Source of Data
In broad sense, the sources of data can be divided into:
– Primary Sources
– Secondary Sources
Primary Sources of data:
– Census
– Survey
– Observation and Records etc.
Secondary Sources of data:
– BBS (Bangladesh Bureau of Statistics)
– NIPORT
– Bangladesh Bank
– Word Bank etc.
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Summarization & Graphical Presentation of Data
How to Prepare Data for Further Statistical Operations
The most frequently used methods for data condensation and
representation are:
– Tabulation
– Graphical Representation
Tabulation: A statistical method of data condensation that
represents summary information of one or more variables.
Construction of a Table: A statistical table is the logical listing of
collected data in vertical columns and horizontal rows of numbers
with sufficient explanatory and qualifying words, terms and
statements in the form of titles, headings and notes which make clear
the full meaning of data and their origin.
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Summarization & Graphical Presentation of Data
Principles of Table Construction
Some basic principles to consider when constructing a table are as
follows:
1. The table should be self-explanatory. The title describing the
contents of the table should be clear, concise and to the point.
2. The table should be as simple as possible. Two or three tables are
often preferable to a large table containing too many details and
variables.
3. The specified units of measurements for the data should be given.
4. Necessary code or symbols used in table should be explained in a
footnote.
5. Sources of data should be mentioned.
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Summarization & Graphical Presentation of Data
Frequency Distribution for Qualitative Data
Recall that qualitative data are values of a qualitative
(non-numerically valued) variable and we use Nominal & Ordinal
scale of measurement for such data.
One way of organizing qualitative data is to construct a table that
gives the number of times each distinct value occurs.
The number of times a particular distinct value occurs is called its
frequency (or count).
A frequency distribution of qualitative data is a listing of the distinct
values and their frequencies.
A frequency table is a grouping of qualitative data into mutually
exclusive and collectively exhaustive classes showing the number of
observations in each class.
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Summarization & Graphical Presentation of Data
Construction of a Frequency Distribution
Steps for constructing a frequency distribution:
Step 1 List the distinct values of the observations in the data set in
the first column of a table.
Step 2 For each observation, place a tally mark in the second column
of the table in the row of the appropriate distinct value.
Step 3 Count the tallies for each distinct value and record the totals
in the third column of the table.
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Summarization & Graphical Presentation of Data
Frequency Distribution
Example 1: Political Party Affiliations
Professor Weiss asked his statistics students to state their political party
affiliations as Democratic (D), Republican (R), or Other (O). The
responses of the 40 students in the class are given below. Determine a
frequency distribution of these data.
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Summarization & Graphical Presentation of Data
Frequency Distribution
Example 1: Political Party Affiliations
Table: Frequency distribution for the political party affiliation data
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Summarization & Graphical Presentation of Data
Relative Frequency Distribution for Qualitative Data
In addition to the frequency that a particular distinct value occurs, we
are often interested in the relative frequency, which is the ratio of the
frequency to the total number of observations and the percentage:
Relative frequency = NumberFrequency
of observations
Percentage = Relative frequency × 100
From the previous example,
Frequency of Democrats
Number of observations
13
=
= 0.325
40
Relative frequency of Democrats =
In terms of percentages, 32.5% of the students are Democrats.
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Summarization & Graphical Presentation of Data
Construction of a Relative Frequency Distribution
Steps for constructing a relative frequency distribution:
Step 1 Obtain a frequency distribution of the data.
Step 2 Divide each frequency by the total number of observations.
For the Example 1: Political Party Affiliations,
Table: Relative Frequency distribution for the political party affiliation
data
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Summarization & Graphical Presentation of Data
Exercise: Class Levels
Earlier in this section, we considered the political party affiliations of the
students in Professor Weiss’s statistics course. The class levels of those
students are as follows, where Fr, So, Jr, and Sr denote freshman,
sophomore, junior, and senior, respectively.
For the given data set,
ˆ determine a frequency distribution,
ˆ obtain a relative-frequency distribution.
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Summarization & Graphical Presentation of Data
Graphical Representation of Qualitative Data
ˆ Another method for organizing and summarizing data is to draw a
picture of some kind.
ˆ A graph or chart of a data set often provides the simplest and most
efficient display.
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Summarization & Graphical Presentation of Data
Bar Chart for Qualitative Data
Two common methods for graphically displaying qualitative data are
– bar charts
– pie charts .
A bar chart displays the distinct values of the qualitative data on a
horizontal axis and the relative frequencies (or frequencies or
percents) of those values on a vertical axis.
The relative frequency of each distinct value is represented by a
vertical bar whose height is equal to the relative frequency of that
value.
The bars should be positioned so that they do not touch each other.
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Summarization & Graphical Presentation of Data
Construction of a Bar Chart
Steps for constructing a bar chart:
Step 1 Obtain a relative frequency distribution of the data.
Step 2 Draw a horizontal axis on which to place the bars and a
vertical axis on which to display the relative frequencies.
Step 3 For each distinct value, construct a vertical bar whose height
equals the relative frequency of that value.
Step 4 Label the bars with the distinct values, the horizontal axis
with the name of the variable, and the vertical axis with “Relative
frequency.”
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Summarization & Graphical Presentation of Data
Bar Chart
Example 1: Political Party Affiliations
Figure: Bar chart of the political party affiliation data
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Summarization & Graphical Presentation of Data
Types of Bar Chart
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Summarization & Graphical Presentation of Data
Pie Chart for Qualitative Data
A pie chart is a disk divided into wedge-shaped pieces proportional to
the relative frequencies of the qualitative data.
Steps for constructing a pie chart:
Step 1 Obtain a relative-frequency distribution of the data.
Step 2 Divide a disk into wedge-shaped pieces proportional to the
relative frequencies.
Step 3 Label the slices with the distinct values and their relative
frequencies.
Calculation of Angles for categories:
Angle = Relative frequency × 360
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Summarization & Graphical Presentation of Data
Pie Chart
Example 1: Political Party Affiliations
Figure: Pie chart of the political party affiliation data
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Summarization & Graphical Presentation of Data
Exercise: Class Levels
Earlier in this section, we considered the political party affiliations of the
students in Professor Weiss’s statistics course. The class levels of those
students are as follows, where Fr, So, Jr, and Sr denote freshman,
sophomore, junior, and senior, respectively.
For the given data set,
ˆ draw a pie chart
ˆ construct a bar chart.
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Summarization & Graphical Presentation of Data
References
❑ Statistical Techniques in Business and Economics- Douglas A Lind,
William G. Marchal & Samuel A. Wathen.
❑ Introductory Statistics- Neil A. Weiss.
❑ Introductory Statistics- PREM S. MANN
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