Stats

1. Introduction to Stats
By Miss Kehkashan Nizam

2. Contents
• Statistics
• Applications of Statistics in Business and Economics
• Descriptive Statistics
• Inferential Statistics
• Data
• Data Sources

3. Statistics
Statistics is the discipline that concerns the collection, organization,
analysis, interpretation and presentation of data. In applying statistics
to a scientific, industrial, or social problem, it is conventional to begin
with a statistical population or a statistical model to be studied

4. Application of Statistics
For the effective functioning of the State, Statistics is indispensable. Different department and authorities require various facts and figures on different matters. They
use this data to frame policies and guidelines in order to perform smoothly.
Traditionally, people used statistics to collect data pertaining to manpower, crimes, wealth, income, etc. for the formation of suitable military and fiscal policies.
Over the years, with the change in the nature of functions of the State from maintaining law and order to promoting human welfare, the scope of the application of
statistics has changed too.
Today, the State authorities collect statistics through their agencies on multiple aspects like population, agriculture, defense, national income, oceanography, natural
resources, space research, etc.
Further, nearly all ministries at the Central as well as State level, rely heavily on statistics for their smooth functioning. Also, the availability of statistical information
enables the government to frame policies and guidelines to improve the overall working of the system.

5. Application of Statistics
Economics is about allocating limited resources among unlimited ends in the most optimal manner. Statistics offers information to answer some basic questions in
economics
What to produce?, How to produce?, For whom to produce?
Statistical information helps to understand the economic problems and formulation of economic policies. Traditionally, the application of statistics was limited since
the economic theories were based on deductive logic. Also, most statistical techniques were not developed enough for application in all disciplines.
However, today, with computers and information technology, statistical data and advanced techniques of statistical analysis are a boon to many.
In economics, many scholars have now shifted their stand from deductive logic to inductive logic in order to explain any economic proposition. This inductive logic
requires the observation of economic behavior of a large number of units. Hence, it needs strong statistical support in the form of data and techniques.

6. Application of Statistics
According to Chao, “Statistics is a method of decision-making in the face of uncertainty on the basis of numerical data and
calculated risks.” Hence, statistics provides information to businesses which help them in making critical decisions.
• Accounting--Public accounting firms use statistical sampling procedures when conducting audits for their clients.
• Finance--Financial advisors use a variety of statistical information, including price-earnings ratios and dividend yields, to
guide their investment recommendations.
• Marketing--Electronic point-of-sale scanners at retail checkout counters are being used to collect data for a variety of
marketing research applications..

7. Application of Statistics
• Production-- A variety of statistical quality control charts are used to monitor the
output of a production process.
• Economics--Economists use statistical information in making forecasts about the
future of the economy or some aspect of it.
• Industry--Statistics helps in the field of Quality Control

8. Statistical methods used in data analysis
Two main statistical methods are used in data analysis:
• Descriptive statistics
• Inferential Statistics

9. Descriptive Statistics
Descriptive statistics are graphical representations of data in tabular, graphical, and
numerical methods in order to summarize data.
A graphical representation of data is a useful method of analysis. Examples of this
visual representation are histograms, bar graphs and pie graphs, to name a few.
Using these methods, the data is described by compiling it into a graph, table or
other visual representation.
This provides a quick method to make comparisons between different data sets and
to spot the smallest and largest values and trends or changes over a period of time.

10. Descriptive Statistics
Descriptive statistics are most often concerned with two sets
of properties of a distribution (sample or population):
• Central tendency (or location) seeks to characterize the distribution's central or
typical value, Use the mean or the median to locate the center of the dataset.
This measure tells you where most values fall.
• Dispersion (or variability) characterizes the extent to which members of the
distribution depart from its center and each other. You can use the range or
standard deviation to measure the dispersion. A low dispersion indicates that the
values cluster more tightly around the center. Higher dispersion signifies that data
points fall further away from the center. We can also graph the frequency
distribution.

11. EXAMPLE
The manager of Hudson Auto would like to have a better understanding of the cost
of parts used in the engine tune-ups performed in the shop. She examines 50
customer invoices for tune-ups. The costs of parts, rounded to the nearest dollar,
are listed below. Find out mean, frequency and percentages. Make the histrogram.
91 78 93 57 75 52 99 80 97 62
71 69 72 89 66 75 79 75 72 76
104 74 62 68 97 105 77 65 80 109
85 97 88 68 83 68 71 69 67 74
62 82 98 101 79 105 79 69 62 73

12. EXAMPLE
Numerical Descriptive Statistics
• The most common numerical descriptive statistic is the average (or mean).
• Hudson’s average cost of parts, based on the 50 tune-ups studied, is $79
(found by summing the 50 cost values and then dividing by 50).

13. Inferential Statistics
Statistical inference is the process of using data obtained from a small group of
elements (the sample) to make estimates and test hypotheses about the
characteristics of a larger group of elements (the population).
Inferential statistics takes data from a sample and makes inferences about the
larger population from which the sample was drawn. Because the goal of
inferential statistics is to draw conclusions from a sample and generalize them to a
population, we need to have confidence that our sample accurately reflects the
population. This requirement affects our process. At a broad level, we must do the
following:
• Define the population we are studying.
• Draw a representative sample from that population.
• Use analyses that incorporate the sampling error.

14. Inferential Statistics’ s Methodologies
The most common methodologies in inferential statistics are
• hypothesis tests
• confidence intervals
• regression analysis

15. Inferential Statistics’ s Methodologies

16. Data and Data Sets
Data are characteristics or information, usually numerical, that are collected
through observation.
In a more technical sense, data is a set of values of qualitative or quantitative
variables about one or more persons or objects, while a datum (singular of data) is
a single value of a single variable.
The data collected in a particular study are referred to as the data set

17. Definitions
• The elements are the entities on which data are collected.
• A variable is a characteristic of interest for the elements.
• The set of measurements collected for a particular element is called an
observation.
• The total number of data values in a data set is the number of elements
multiplied by the number of variables.

18. Definitions

19. Scales of Measurement
Scales of measurement include:
• Nominal
• Ordinal
• Interval
• Ratio
• The scale determines the amount of information contained in the
data.
• The scale indicates the data summarization and statistical analyses
that are most appropriate.

20. Scales of Measurement
Nominal
Data are labels or names used to identify an attribute of the element.
A nonnumeric label or a numeric code may be used.
Example:
Students of a university are classified by the school in which they are
enrolled using a nonnumeric label such as Business, Humanities,
Education, and so on.
Alternatively, a numeric code could be used for the school variable (e.g.
1 denotes Business, 2 denotes Humanities, 3= denotes Education, and
so on).

21. Scales of Measurement
Ordinal
• The data have the properties of nominal data and the order or rank of
the data is meaningful.
A nonnumeric label or a numeric code may be used.
Example:
Students of a university are classified by their class standing using a
nonnumeric label such as Freshman, Sophomore, Junior, or Senior.
Alternatively, a numeric code could be used for the class standing
variable (e.g. 1 denotes Freshman, 2 denotes Sophomore, and so on).

22. Scales of Measurement
Interval
The data have the properties of ordinal data and the interval between
observations is expressed in terms of a fixed unit of measure.
Interval data are always numeric.
Example:
Melissa has an SAT score of 1205, while Kevin has an SAT score of 1090.
Melissa scored 115 points more than Kevin.

23. Scales of Measurement
Ratio
The data have all the properties of interval data and the ratio of two
values is meaningful.
Variables such as distance, height, weight, and time use the ratio scale.
This scale must contain a zero value that indicates that nothing exists
for the variable at the zero point.
Example:
Melissa’s college record shows 36 credit hours earned, while Kevin’s
record shows 72 credit hours earned. Kevin has twice as many credit
hours earned as Melissa.

24. Qualitative and Quantitative Data
Data can be further classified as being qualitative or quantitative.
The statistical analysis that is appropriate depends on whether the data
for the variable are qualitative or quantitative.
In general, there are more alternatives for statistical analysis when the
data are quantitative

25. Qualitative Data
Qualitative data are labels or names used to identify an attribute of
each element.
Qualitative data use either the nominal or ordinal scale of
measurement.
Qualitative data can be either numeric or nonnumeric.
The statistical analysis for qualitative data are rather limited.

26. Quantitative Data
Quantitative data indicate either how many or how much.
Quantitative data that measure how many are discrete.
Quantitative data that measure how much are continuous because
there is no separation between the possible values for the data..
Quantitative data are always numeric.
Ordinary arithmetic operations are meaningful only with quantitative
data.

27. Cross-Sectional and Time Series Data
Cross-sectional data are collected at the same or approximately the
same point in time.
Example: data detailing the number of building permits issued in June
2000 in each of the counties of Texas
Time series data are collected over several time periods.
Example: data detailing the number of building permits issued in Travis
County, Texas in each of the last 36 months

28. Cross-Sectional and Time Series Data
Primary data: Data collected by the investigator himself/ herself for a specific purpose.
Examples: Data collected by a student for his/her thesis or research project. ...
Secondary data: Data collected by someone else for some other purpose , from existing
Sources
• Data needed for a particular application might already exist within a firm. Detailed
information is often kept on customers, suppliers, and employees for example.
• Substantial amounts of business and economic data are available from organizations that
specialize in collecting and maintaining data.
• Government agencies are another important source of data.
• Data are also available from a variety of industry associations and special-interest
organizations.
• The Internet has become an important source of data

29. Types of Data
Primary data: Data collected by the investigator himself/ herself for a specific purpose.
Examples: Data collected by a student for his/her thesis or research project. ...
Secondary data: Data collected by someone else for some other purpose , from existing
Sources
• Data needed for a particular application might already exist within a firm. Detailed
information is often kept on customers, suppliers, and employees for example.
• Substantial amounts of business and economic data are available from organizations that
specialize in collecting and maintaining data.
• Government agencies are another important source of data.
• Data are also available from a variety of industry associations and special-interest
organizations.
• The Internet has become an important source of data

30. Data Acquisition Considerations
Time Requirement--Searching for information can be time consuming.
Information might no longer be useful by the time it is available.
Cost of Acquisition--Organizations often charge for information even
when it is not their primary business activity.
Data Errors--Using any data that happens to be available or that were
acquired with little care can lead to poor and misleading information.

31. Data Acquisition Considerations
Time Requirement--Searching for information can be time consuming.
Information might no longer be useful by the time it is available.
Cost of Acquisition--Organizations often charge for information even
when it is not their primary business activity.
Data Errors--Using any data that happens to be available or that were
acquired with little care can lead to poor and misleading information.