1 Statistical Indicators and Statistical Thinking 1 Dr. T S G Peiris Department of Mathematics

2 Why do we do statistics? 2 What is statistics? To understand and explain the “variability”

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 conducting business/teaching/etc Data contain information needed to make a more informal decision in a particular situation. 4

5 The growth and development of statistics Widespread availability of software tools had led to an ever increasing application of statistical methods to business decision making. 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? Managers/Processionals have access to a large 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 today’s 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 is a way to get information from data ’ Data Statistics Information Data: Facts,, collected together for reference or information. Information: Knowledge communicated concerning some particular fact. Statistics is a tool for creating new understanding from data. 10

11 Parameters Population Sample Statistics Subset Key statistical concepts (Statistical Thinking) 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 Parameters A descriptive measure of a population. Statistics A descriptive measure of a sample. Key statistical concepts (Statistical Thinking ) 13

14 Statistical inference (Decisions) Statistical inference is the process of making an estimate, prediction, or decision about a population based on a sample. Parameter Population Sample Statistic Inference What can we infer about a population’s parameters based on a sample’s 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 semester’s final exam marks to the student. What can be discerned from this list of numbers? Data Statistics Information List of last term’s marks New information derived about the statistics class. e.g. Class average, proportion of class receiving F’s, most frequent mark, marks distribution, etc. 15

16 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

17 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 Business indicators

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 Median=67 - as an indicator

24 Selecting Mode as an indicator

25 Indicators to Measure dispersion (a) Sample variance: (b) Range [37,93} 68, 12.9

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 ItemsWeight Food and Beverages46.71 Cloth and Footwear3.08 Housing, Water, Electricity18.29 Furnishing 3.22 Health 4.18 Transport9.47 Communication4.42 Recreation & Culture2.18 Education5.79 Miscellaneous2.65

38 Grade Point Average _GPA

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 Overweight Obese > 30.0

41 BMI - Indicator high blood pressure (hypertension) high LDL-cholesterol ("bad" cholesterol) 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 you and Best Wishes