Introduction to Statistics .pdf
- 1. ALLPPT.com _ Free PowerPoint Templates, Diagrams and Charts Presented By Ms. A. DALLY MARIA EVANGELINE ASSISTANT PROFESSOR DEPARTMENT OF MATHEMATICS NUMERICAL ANALYSIS & STATISTICS
- 2. OBJECTIVE
- 3. To learn basic concepts of statistics To learn the basic ideas of numerical analysis
- 4. Statistics • Numerical statement of facts in any department • Classified facts representing the conditions of the people in a state….. Specially those facts which can be stated in number or in tables of numbers
- 5. Statistics • Branch of scientific methods which deals with the data obtained by counting or measuring the properties of population of natural phenomenon • Deals with the method of collecting, classifying, presenting comparing and interpreting numerical da ta collected to throw some light on any sphere of inquiry
- 6. Importance and Scope • Statistics and planning • Statistics and mathematics • Statistics and economics • Statistics and biology
- 7. Statistical data • Data are individual pieces of factual information recorded and used for the purpose of analysis • Raw information from which statistics are created • Statistics deals with collection, analysis and inter - pretation of numerical data
- 8. Types of data • Primary Data – first hand data gathered by the researcher himself • Secondary Data – data collected by someone else earlier – data already available in library, internet • Grouped and ungrouped data
- 9. Data collection methods • Interviews • Surveys • Questionnaires • Observations
- 10. Frequency Distribution A classification according to the number possessing the same values of the variables. It is simply a table in which the data are grouped into classes and the number of cases which fall in each class is recorded
- 11. Frequency Distribution Frequency distribution can be of two kinds: ➢ Univariate Frequency Distribution ➢ Bivariate Frequency Distribution
- 12. Frequency Distribution Frequency distribution can be of two kinds: ➢ Univariate Frequency Distribution ➢ Bivariate Frequency Distribution
- 13. Frequency Distribution Representation of data as above is called frequency distribution
- 14. Frequency distribution • Prepare the frequency distribution table for the given set of scores: 39, 16, 30, 37, 53, 15, 16, 60, 58, 26, 28, 19, 20, 12, 14, 24, 59, 21, 57, 38, 25, 36, 24, 15, 25, 41, 52, 45, 60, 63, 18, 26, 43, 36, 18, 27, 59, 63, 46, 42, 48, 35, 64, 24.
- 15. Frequency Distribution Class interval Frequency 10-20 9 20-30 12 30-40 8 40-50 7 50-60 6 60-70 5
- 16. Classification & Tabulation Classification is the process of arranging things in groups or classes according to their resemblances and affinities, and giving expression to the unity of attribute that may subsist amongst a diversity of individuals
- 17. Chief Characteristics of Classification • All the facts are classified into homogeneous group by the process of classification • The basis of classification is unity in diversity • It should be flexible to accommodate adjustments
- 18. Types of Classification • Geographical • Chronological or Historical • Qualitative by character or by attributes • Quantitative or numerical or by magnitudes
- 19. Graphical Representation of Data
- 20. General Characteristics of Quantitative Data • Measure of Central Tendency • Measure of Dispersion • Skewness and Kurtosis
- 21. Averages or Measure of Central Tendency • Arithmetic Mean • Median • Mode • Geometric Mean • Harmonic Mean
- 22. Arithmetic Mean • Average is a value which is typical or representative of a set of data • Arithmetic mean of series is the figure obtained by dividing the total value of the various item by their number
- 23. Arithmetic Mean Arithmetic Mean is given by ത 𝑋 = σ 𝑋 𝑛 Where, n is the number of observations σ 𝑋 is the sum of variables
- 24. Arithmetic Mean Arithmetic Mean is given by ത 𝑋 = σ 𝑋 𝑛 Where, n is the number of observations σ 𝑋 is the sum of variables
- 25. Merits & Demerits of Arithmetic Mean It is widely used because: • It is easy to understand • It is rigidly defined The demerits are: • The mean is unduly affected by the extreme items. • It cannot be accurately determined even if one of the values is not known
- 26. Median Median is the value of item that goes to divide the series into equal parts. It maybe defined as the value of that item which divides the series into two equal parts, one half containing the values greater than it and the other half containing values less than it
- 27. Median Median is given by Median = 𝑆𝑖𝑧𝑒 𝑜𝑓 𝑁+1 2 𝑡ℎ 𝑖𝑡𝑒𝑚 Where, n is the number of observation
- 28. Merits & Demerits of Median Merits: • It is easy to understand and easy to compute • It is quite rigidly defined Demerits: • It cannot be computed if the distribution is irregular • It ignores extreme items
- 29. Mode Mode is the most common items of a series. It is the value which occurs the greater number of frequency in a series.
- 30. Merits & Demerits of Mode Merits: • It is easy to understand and it can be easily compute d by inspection • It is not affected by the extreme values Demerits: • It cannot be computed if the distribution is irregular • It ignores extreme items