2. What is Statistics ?
In today’s world we have access to more data than ever. For example, data
are collected for business applications from:
• Direct observation or measurement
• Customer surveys
• Political polls
• Economic surveys
• Marketing surveys
• Scanner data
This topic introduces various statistical concepts.
In this topic, we also introduce various methods of data collection.
3. What is Statistics?
• Statistics is a body of principles and methods concerned with
extracting useful information from a set of data to help people make
informed business decisions.
4. Statistics
• ‘Statistics is a way to get information from data to make informed
decisions.’
• Data Statistics Information
• Data: Mostly numerical facts collected from direct observations,
measurements or surveys.
• Information: Knowledge communicated concerning some particular
fact, which can be used for decision making.
5. Example Stats anxiety…
• A student enrolled in a business program is attending his first lecture
of the compulsory business statistics course. The student is somewhat
apprehensive because he believes the myth that the course is
difficult. To alleviate his anxiety, the student asks the lecturer about
last year’s exam marks of the business statistics course. The lecturer
obliges and provides a list of the final marks. The marks are composed
of all the within-semester assessment items plus the end-of-semester
final exam. What information can the student obtain from the list?
6. Two major branches of Statistics
1. Descriptive Statistics
2. Inferential Statistics
7. Descriptive Statistics
• Descriptive statistics deals with methods of organising, summarising,
and presenting data in a convenient and informative way. One form of
descriptive statistics uses graphical techniques, which allow statistics
practitioners to present data in ways that make it easy for the reader
to extract useful information.
• Another form of descriptive statistics uses numerical measures to
summarize data. The mean and median are popular numerical
measures to describe the location of the data. The range, variance
and standard deviation measure the variability of the data
8. Inferential Statistics
• Descriptive statistics describe the data set that is being analysed, but
does not provide any tools for us to draw any conclusions or make
any inferences about the data. Hence we need another branch of
statistics: inferential statistics. Inferential statistics is also a set of
methods, but it is used to draw conclusions or inferences about
characteristics of populations based on sample statistics calculated
from sample data.
9. Key Statistical concepts
• Population
A population is the group of all items (data) of interest. Population is
frequently very large; sometimes infinite. E.g.
1. All current million or so members of an automobile club
2. All goats available on eid at the ‘bakramandi’ in Islamabad.
10. Sample
• A sample is a set of items (data) drawn from the population of
interest. Sample could potentially be very large, but much less than
the population. E.g.
1. A sample of 500 members of the automobile club selected.
2. A sample of 1000 goats selected from different sections of the
‘Bakramandi’.
11. Key statistical concepts
• Parameter
A descriptive measure of a population.
• Statistic
A descriptive measure of a sample.
12. Methods of collecting data
• Recall, Statistics is a tool for converting data into useful information
But
• where then does data come from?
• How is it gathered?
• How do we ensure its accuracy?
• Is the data reliable?
• Is it representative of the population from which it was drawn?
13. Data quality
• The reliability and accuracy of the data affect the validity of the
results of a statistical analysis. The reliability and accuracy of the data
depend on the method of data collection.
14. Sources of data
Four of the most popular sources of statistical data are:
• Published data
1. Primary data
2. Secondary data
• Observational data
• Experimental data
• Data collected from surveys
15. Variable & Types of variables
• What is a variable?
• Types of variables
• Dependent variable
• Independent variable
• Binary variable
• Discrete variable
• Continuous variable
16. Measurement scale
The scale of measurement determines the amount of information contained
in the data and indicates the most appropriate data summarization &
statistical analyses.
• Nominal scale
When the data for a variable consist of labels or names used to identify an
attribute of the element e.g.
Gender: male or female
City: Islamabad, Karachi, Lahore
• Ordinal scale
Data is classified in to categories & rank of the data is meaningful e.g.
Superior, good, average , inferior
17. Measurement scale
• Interval scale
The data have properties of ordinal data and interval b/w values is
expressed in terms of fixed unit of measure. e.g.
3 students with SAT scores of 620,550 and 470
• Ratio scale
The data have properties of interval scale and the ratio of two values is
meaningful e.g. height, weight, distance.
18. Structure of the data
• Time series data
• Cross sectional data
• Panel data
19. Frequency distribution
• It is a tabular summary of data showing the number of
observations(Frequency) in each category.
• For qualitative data
Example
Data from 50 individuals for the soft drink purchases
20. RELATIVE FREQUENCY
Formula is:
Relative frequency = frequency of the particular class/n
For example;
Relative frequency of pepsi= frequency of pepsi class/n
21. Frequency distribution for Quantitative data
Example
• Sample of 20 clients for a small accounting firm.
1. Determine the number of classes
2. Determine the width of each class
3. Determine the class limit
22. Graphical representation
• Histogram
This display can be prepared for the data summarized in either frequency,
relative frequency or percent frequency distribution.
Horizontal axis variable of interest e.g. audit days
Vertical axis frequency/ relative frequency/percent frequency
• Cumulative frequency distribution
A variation of the frequency distribution that provides another tabular
summary of quantitative data.
23. Graphical representation
• Frequency polygon
A frequency polygon is obtained by plotting the frequency of each class
above the midpoint of that class and then joining the points with a
straight line.
• Time series graph
Line chart
years x-axis
variables y-axis
24. Graphical representation
• Scatter diagram
The relationship between two numerical variables e.g.
advertising expenditure
sales
• Pie chart
The size of a slice of the circle is proportional to the percentage
corresponding to that category.
25. Example
Magzine Proportion of readers(%age) Angle of the slice
Australian women’s weekly 17.4 17.4*3.6= 62.4𝑜
NZ women’s weekly 21.7 21.7*3.6= 78.0𝑜
NZ New Idea 13.3 13.3*3.6=48.0𝑜
NZ women’s Day 28.3 28.3*3.6= 102.0𝑜
Next 9.3 9.3*3.6=33.6𝑜
That’s life 10.0 10.0*3.6= 36𝑜
