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## Statistical Indicators and Statistical Thinking

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### Statistical Indicators and Statistical Thinking Dr. T S G Peiris Department of Mathematics * – PowerPoint PPT presentation

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Title: Statistical Indicators and Statistical Thinking

1
Statistical IndicatorsandStatistical Thinking
Dr. T S G Peiris Department of Mathematics
1
2
• What is statistics?

• Why do we do statistics?

To understand and explain the variability
2
3
Why data
• As the global economy becomes increasingly
electronic , the application of statistics to
business and day to day applications has been
increasing fast.

3
4
Why data are needed?
• Obtaining appropriate data is essential in
• Data contain information needed to make a more
informal decision in a particular situation.

4
5
The growth and development of statistics
to an ever increasing application of statistical
• Today managers face problems/burdens, not having
to make more and more decisions based on larger
and larger volumes of data.

5
6
• Why we want to know about statistics?

amount of data. Lack of knowledge of data and
its variability by the managers is difficult to
survive due to competition. That is to use
available data to make decisions
6
7
• A market researcher needs to assess product
characteristics to distinguish one product from
another
• An investor wants to determine what firms are
likely to have accelerated growth
• A lecturer wants to know the duration of which
students access his notes in the website

7
8
• Dean of a Faculty wants to how students performed
in an exam
• Students wants compare marks with others
• An engineer wants to know how traffic pass at a
busy junction
• Farmer wants to about prices of vegetables

8
9
In todays world
• we are constantly being bombarded with
statistics and statistical information. For
example
• customer surveys
• medical news
• political polls
• economic predictions
• marketing information
• scanner data
• How can we make sense out of all this data?
• How do we differentiate valid from flawed claims?
• What is statistics?

9
10
Statistics
Data
Information
• Statistics is a way to get information from data

Information Knowledge communicated concerning
some particular fact.
Data Facts,, collected together for reference or
information.
Statistics is a tool for creating new
understanding from data.
10
11
Key statistical concepts (Statistical Thinking)
Population
Sample
Subset
Parameters
Statistics
11
12
Key statistical concepts (Statistical
Thinking)
• Population
• A population is the group of all items of
interest to a statistics practitioner.
• Frequently very large sometimes infinite.
• Sample
• A sample is a set of data drawn from the
population.
• Potentially very large, but less than the
population.
• .

12
13
Key statistical concepts (Statistical Thinking)
• Parameters
• A descriptive measure of a population.
• Statistics
• A descriptive measure of a sample.

13
14
Statistical inference (Decisions)
• Statistical inference is the process of making an
estimate, prediction, or decision about a
population based on a sample.

Population
Sample
Inference
Statistic
Parameter
What can we infer about a populations parameters
based on a samples statistics?
14
15
Stats anxiety
• A student is anxious about his statistics course,
after he had heard that the course is difficult.
The lecturer provides last semesters final exam
marks to the student. What can be discerned from
this list of numbers?

Statistics
Data
Information
List of last terms marks.
New information derived about the statistics
class.
95 89 70 65 78 57
e.g. Class average, proportion of class
receiving Fs, most frequent mark, marks
distribution, etc.
15
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Thus statistic
• is a quantity that is calculated from a sample of
data.
• It is used to give information about unknown
values in the corresponding population.

16
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Statistical Indicator
• Derived from the sample
• A single or composite value to represent a
variability of the population
• Students performance indicators
• University performance indicators
• Educational indicators
• Ecological indicators
• Human Resource Indicators
• Sport indicators
• Health indicators
• Climate indicator

18
Statistical Thinking
• As today's good decisions are driven by data.
Professionals are increasingly required to
justify decisions on the basis of data
• Statistical thinking is a science assisting you
to make decisions under uncertainties
• To make thinking easier we use statistical
indicators

19
Indicators to measure central tendency
20
Indicators to measure central tendency
• Mean

Weighted mean
In some cases, the data are weighted according to
its importance
21
Variation in weighted mean
22
Are both are the same?
What is the indicator to check the association?
23
Median67 - as an indicator
24
Selecting Mode as an indicator
25
Indicators to Measure dispersion
• (a) Sample variance

68, 12.9
(b) Range
37,93
26
Use of Standard Deviation (SD) as an indicator
27
Quality of information and variation are
inversely related
• The larger the variation in the data, the lower
the quality of the data (i.e., information) the
Devil is in the Deviations

28
• Other indicators to measure dispersion are Mean
Absolute Deviation (MAD) and Coefficient of
Variability (CV)

29
Why indicator CV is useful?
• Eg. A manufacturer of television tubes has two
types of tubes namely A and B. Mean life time
tubes A and B are 1495 hrs and 1875 and SD of
tubes are 220 hrs and 310 hrs respectively.
• The CV of A 14.7
• and CV of B 16.5

30
Indicators to Measure Percentiles
• First quartile (Q1) The sample 25th percentile
(P25)
• Second quartile (Q2) The sample 50th
percentile (P50) median
• Third quartile (Q3) The sample 75th percentile
(P75)
• Inter quartile range (IQR) Q3 Q1
• Desired Percentile

31
Indicator to measure association between two
variables
Correlation Coefficient
32
Use of statistical indictors for decision making
• Use of Z Score

Consumer Price Index CCPI is an indicator to
measure of the average change in the prices paid
by consumers for a specific basket of goods and
services over time in a country
33
Z Score as a statistical indicator
Distribution of raw marks
34
Z Score as a statistical indicator
Distribution of new indicator Z score
35
Relationship between raw marks and Z score
36
Consumer Price Index CCPI
• It is a statistical indicator to measure of the
average change in the prices paid by consumers
for a specific basket of goods and services over
time in a country.

Colombo Consumer Price Index (CCPI)
37
Weights used for Colombo Consumer Price Index
(CCPI) CCPI_N
Items Weight
Food and Beverages 46.71
Cloth and Footwear 3.08
Housing, Water, Electricity 18.29
Furnishing 3.22
Health 4.18
Transport 9.47
Communication 4.42
Recreation Culture 2.18
Education 5.79
Miscellaneous 2.65
38
39
Use of statistical indictors for decision making
• Body Mass Index
• Body Mass Index (BMI) is an indicator
calculated from a person's weight and height.
• BMI provides a reliable indicator of body
fatness for most people and is used to screen for
weight categories that may lead to health
problems .
• HAS THIS UPDATED TO SL?

40
BMI - Indicator
• BMI indicates you are
• Underweight for BMI less than 18.5,
• Normal - 18.5 - 24.9
• Overweight - 25.0 - 29.9
• Obese gt 30.0

41
BMI - Indicator
• high blood pressure (hypertension)
• low HDL-cholesterol ("good" cholesterol)
• high triglycerides
• high blood glucose (sugar)
• family history of premature heart disease
• physical inactivity
• cigarette smoking

42
Use of statistical indictors for decision making
• Human Development Index
• is an indicator
• to rank countries by level of "human
development", which usually also implies whether
a country is a developed, developing or under
developing

43
HDI - Indicator
• Go to Websites

44
Thank youandBest Wishes