1. Dr. Engr. Sami ur Rahman Data Analysis Lecture 2: Basic Concepts of Statistical Methods

2. University Of Malakand | Department of Computer Science | UoMIPS | Dr. Engr. Sami ur Rahman | 2 Introductory Statistics  Why Use Statistics  Types of Statistical Analysis  Common Types of Descriptive Statistics  Basic Concepts  Central Tendency

3. University Of Malakand | Department of Computer Science | UoMIPS | Dr. Engr. Sami ur Rahman | 3 Why Use Statistics?  Statistics are powerful tools that help people understand interesting phenomena.  “Whether you are a student, a researcher, or just a citizen interested in understanding the world around you, statistics can offer methods for helping you make sense of your environment” (Urdan, 2001).

4. University Of Malakand | Department of Computer Science | UoMIPS | Dr. Engr. Sami ur Rahman | 4 Types of Statistical Analysis  Descriptive  Used to describe and summarize data  Inferential  Used to make inferences or predictions about the similarity of a sample to the population from which the sample is drawn.

5. University Of Malakand | Department of Computer Science | UoMIPS | Dr. Engr. Sami ur Rahman | 5 Common Types of Descriptive Statistics  Percentage  The number per 100 individuals who achieved a certain score.  Mean  The arithmetic average of a distribution of scores  Standard Deviation  The average deviation between the individual scores in the distribution and the mean for the distribution

6. University Of Malakand | Department of Computer Science | UoMIPS | Dr. Engr. Sami ur Rahman | 6 Basic Concepts  Population: the whole set of a “universe”  Sample: a sub-set of a population  Parameter: an unknown “fixed” value of population characteristic

7. University Of Malakand | Department of Computer Science | UoMIPS | Dr. Engr. Sami ur Rahman | 7 Basic Concepts (contd.)  Randomness: Many things occur by pure chances…. rainfall, disease, birth, death,..  Variability: Stochastic processes bring in them various different dimensions, characteristics, properties, features, etc., in the population  Statistical analysis: Methods have been developed to deal with these very nature of real world.

8. University Of Malakand | Department of Computer Science | UoMIPS | Dr. Engr. Sami ur Rahman | 8 Central Tendency Central tendency: The way in which quantitative data tend to cluster around some value. A measure of central tendency is any of a number of ways of specifying this "central value" MedianMode Central Tendency Average (Mean)

9. University Of Malakand | Department of Computer Science | UoMIPS | Dr. Engr. Sami ur Rahman | 9 Mean Mean (arithmetic mean) of data values

10. University Of Malakand | Department of Computer Science | UoMIPS | Dr. Engr. Sami ur Rahman | 10 Mean  The most common measure of central tendency  Affected by extreme values (outliers) 0 1 2 3 4 5 6 7 8 9 100 1 2 3 4 5 6 7 8 9 10 12 14 Mean = 5Mean = 6

11. University Of Malakand | Department of Computer Science | UoMIPS | Dr. Engr. Sami ur Rahman | 11 Median Median: The “middle” number Not affected by extreme values 0 1 2 3 4 5 6 7 8 9 10 Median = 5 0 1 2 3 4 5 6 7 8 9 10 12 14 Median = 5

12. University Of Malakand | Department of Computer Science | UoMIPS | Dr. Engr. Sami ur Rahman | 12 Mode Mode: Value that occurs most often  Not affected by extreme values  There may be no mode  There may be several modes Mode = 9 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 0 1 2 3 4 5 6 No Mode

13. Which measure of Central Tendency should be used? Measures of Central Tendency University Of Malakand | Department of Computer Science | UoMIPS | Dr. Engr. Sami ur Rahman | 13 The measure you choose should give you a good indication of the typical score in the sample or population.

14. Measures of Central Tendency Mean … the most frequently used but is sensitive to extreme scores e.g. 1 2 3 4 5 6 7 8 9 10 Mean = 5.5 (median = 5.5) e.g. 1 2 3 4 5 6 7 8 9 20 Mean = 6.5 (median = 5.5) e.g. 1 2 3 4 5 6 7 8 9 100 Mean = 14.5 (median = 5.5) University Of Malakand | Department of Computer Science | UoMIPS | Dr. Engr. Sami ur Rahman | 14

15. Measures of Central Tendency Median … is not sensitive to extreme scores … use it when you are unable to use the mean because of extreme scores University Of Malakand | Department of Computer Science | UoMIPS | Dr. Engr. Sami ur Rahman | 15

16. Measures of Central Tendency Mode … does not involve any calculation or ordering of data … use it when you have categories (e.g. occupation) University Of Malakand | Department of Computer Science | UoMIPS | Dr. Engr. Sami ur Rahman | 16

17. University Of Malakand | Department of Computer Science | UoMIPS | Dr. Engr. Sami ur Rahman | 17 Thanks for your attention