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STATISTICS IN METEOROLOGY

STATISTICS IN METEOROLOGY. COVERAGE. Introduction Statistics and its applications in Meteorology Raw data, array, grouped data Cumulative frequency Ogives Summary. STATISTICS. An imposing form of Mathematics Suggests tables, charts and figures

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STATISTICS IN METEOROLOGY

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  1. STATISTICS IN METEOROLOGY

  2. COVERAGE • Introduction • Statistics and its applications in Meteorology • Raw data, array, grouped data • Cumulative frequency • Ogives • Summary

  3. STATISTICS • An imposing form of Mathematics • Suggests tables, charts and figures • Numbers play essential role:- • Provide raw material • Must be processed further, to be useful

  4. STATISTICS • Statistics is concerned with scientific methods for:- • Collection of Data • Organisation of Data • Summarising and Presentation of Data • Analysis of Data • Drawing valid Conclusions and making reasonable Decisions based on analysis

  5. STATISTICS • Involves methods of refining numerical and non-numerical information into useful forms • When numbers are collected and compiled, they become Statistics • Synonymous with ways and means of presenting and handling Data, making inferences logically and drawing relevant conclusions

  6. CHARACTERISTICS • Numerical data must possess the following characteristics to be called as statistics. • Aggregate of Facts: Single and isolated figures are not statistics – they are unrelated and cannot be compared.Ex - Monthly Income of Mr X is Rs 50000/-. It would not constitute statistics although it is a numerical statement of fact

  7. CHARACTERISTICS • Affected by multiplicity of causes • Facts and figures are affected by number of forces operating together.Ex- Statistics of production of rice are affected by the rainfall, quality of soil,seeds and manure ,methods of cultivation,etc It is difficult to study separately the effect of each of these forces separately on the production of rice. • Numerically expressed • All stats are numerical statements of facts i.e. expressed in numbers.Qualitative statements such as the population of india is rapidly increasing is not statistics

  8. CHARACTERISTICS • Accuracy • Facts and figures about any phenomenon can be derived in two ways: • By actual counting and measurement. • By estimate. • Collected in systematic manner • Before collecting data a suitable plan should be made and worked out in systematic manner. • Data collected in haphazard manner would very likely lead to fallacious conclusions.

  9. CHARACTERISTICS • Collected for pre-determined purpose • Purpose must be decided in advance • It should be specific and well defined • Should be placed in relation to each other • They should be comparable

  10. FUNCTIONS • Presents facts in definite form. • Simplifies mass of data. • Facilitates comparison. • Helps in formulating and testing hypothesis. • Helps in prediction. • Helps in formulation of suitable policies.

  11. LIMITATIONS • Does not deal with individual measurements. • Deals only with quantitative characteristics. • Only one of the methods to study a problem.

  12. LIMITATIONS • Does not always yield best results. • Can be misused. • Anybody (without knowledge) can not deal with it. • Requires skills and experience. • No qualitative inferences.

  13. DISTRUST OF STATISTICS • Statistics can prove almost anything : figures are convincing; hence, people are easily led to believe them. • Data can be manipulated : to establish foregone conclusions. • Even with correct figures, misled presentation can be made.

  14. STATISTICS • Descriptive Statistics. Collection, Presentation and Description of numerical data (e.g., Means, Medians, Counts, Variance, Deviations, etc.). • Inferential Statistics. Process of interpreting what the values of your statistical tests mean and making decisions from those.

  15. BASIC DEFINITIONS • It is often impossible or impractical to observe the entire group of data collected, especially if it is large. • Population. A collection, or set of individuals, objects, or measurements whose properties are to be analysed. • A population can be finite or infinite .

  16. BASIC DEFINITIONS • Instead of examining the entire group, called population or universe, one examine a small part of group called sample. • Sample (a subset of the population). It consists of the individuals, objects or measurements selected by the sample collector from the Population.

  17. BASIC DEFINITIONS • Variables.A variable is a symbol X ,Y A etc which can assume any of a prescribed set of values called the domain of the variable. • Constant. If the variable can assume only one value it is called a constant • Data.The set of values collected for the variable from each of the elements belonging to the sample.

  18. VARIABLES • Discrete : Result of counting (counts), usually Integers. • Counting give rise to discrete data. • Example : No. of children in each house of a village. • Continuous : A measurement of quantity, can assume any value between two given values. • Measurement give rise to continous data. • Example : Rainfall amount, Temperature, etc.

  19. BASIC DEFINITIONS FUNCTION • If to each value which a variable X can assume there corresponds one or more values of a variable Y, we say that Y is a function of X. • Y = F (X) • Variable X is independent variable • Variable Y is dependent variable • Single valued function • Multiple valued function

  20. BASIC DEFINITIONS GRAPHS • A graph is a pictorial presentation of the relationship between variables. • Many types of graphs are used in stats depending on • Nature of data involved. • Purpose for which graph is intended. • Ex – Bar graphs,Pie graph, Picto-graphs etc. • Graphs also referred as charts / diagrams

  21. TABULATION OF DATA : FREQUENCY DISTRIBUTION

  22. BASIC DEFINITIONS • Raw Data : Collected data, which has not been numerically organized. • Arrays : An arrangement of raw data in ascending / descending order of magnitude. • Frequency Distribution : A tabular arrangement of data by classes, together with the corresponding Class Frequencies.

  23. CLASSIFICATION OF DATA • After collection and editing of data the next step is classification • Classification is grouping of related facts into classes • Sorting of facts • Ex: • Post Office • School

  24. CLASSIFICATION OF DATA • Objectives • To condense the mass of data in such a manner that similarities and dissimilarities can be readily apprehended • To Facilitate comparison • To pin point the most significant features of data at a glance • To give prominence to the important information gathered and dropping out the unnecessary elements • To enable statistical treatment of data

  25. TYPES OF CLASSIFICATION • Geographical – Area wise ,cities, districts etc.(State wise production of food grains) • Chronological – on basis of time( Population of india from 1951-2011) • Qualitative - According to attributes or qualities (On basis of literacy, religion etc) • Dichotomous or two fold classification • Manifold classification • Quantitative – In terms of magnitudes(Students of college on the basis of weight)

  26. FORMATION OF DISCRETE FREQUENCY DISTRIBUTION • Very simple method. • Count the number of times, a particular value is repeated • Table represents frequency of that particular class • Example

  27. RAW DATA No. of Children per family at Air Force Station, XYZ is:-

  28. FREQUENCY DISTRIBUTION

  29. FORMATION OF FREQUENCY DISTRIBUTION • Determine the largest and smallest numbers in the raw data and thus find the range • Divide the range into a convenient number of class intervals having the same size • Determine the number of observations falling into each class interval i.e find the class frequencies. This is best done by using a tally or score sheet

  30. FORMATION OF CONTINUOUS FREQUENCY DISTRIBUTION • More popular and widely used • Class Limits : LCL & UCL • Class Interval : UCL – LCL • Class Frequency • Class Mid-points / Class Marks :- • Mid-point = (UCL + LCL) / 2

  31. CLASSIFICATION OF DATA ACCORDING TO CLASS INTERVALS • Exclusive Method - Upper limit of one class is the lower limit of the next class • It ensures continuity of data • It is always assumed that the upper limit is exclusive.i.e the item of that value is not included in that class.( Ex- 10-20,20-30,30-40) • Inclusive Method – The upper limit of one class is included in that class itself.(10-19,20-29)

  32. RAW DATA Marks obtained by students in Maths are:-

  33. FORMATION OF CONTINUOUS FREQUENCY DISTRIBUTION EXCLUSIVE & INCLUSIVE METHODS

  34. TABULATION OF DATA • A Table is a systematic arrangement of statistical data in columns and rows • Rows are horizontal arrangements • Columns are vertical arrangements • Purpose: The purpose of a table is to simplify the presentation and to facilitate comparisons

  35. TABULATION OF DATA • ONE OF THE SIMPLEST AND MOST REVEALING DEVICES FOR SUMMARISING DATA. • ROLE OF TABULATION • IT SIMPLIFIES COMPLEX DATA • IT FACILITATES COMPARISON • IT GIVES IDENTITY TO THE DATA • IT REVEALS PATTERNS • PARTS OF TABLE • TABLE NUMBER,TITLE OF TABLE,CAPTION, STUB,BODY OF THE TABLE,HEADNOTE,FOOTNOTE.

  36. DIAGRAMMATIC & GRAPHIC PRESENTATION • One of the most convincing and appealing ways in which statistical results may be presented • Significance of Diagrams and Graph • They give bird’s eye view of the entire data ,information presented is easily understood. “A picture is worth 10,000 words”. • They are attractive to the eye • They facilitate comparison

  37. DIAGRAMMATIC & GRAPHIC PRESENTATION • Comparison of Tabular and Diagrammatic Presentation • Tables contain precise figures whereas diagrams give only an appx data • More information can be presented in one table than either in one graph • Table more difficult to interpret than diagrams • Graphs and Diagrams have a visual appeal thus more impressive

  38. DIAGRAMMATIC & GRAPHIC PRESENTATION • Types of Diagrams • ONE-D Diagrams e.g., Bar diagrams • TWO-D Diagrams e.g., Rectangular, Squares ,Circles • Three-D Diagrams e.g., Cubes, Cylinders and spheres • Pictograms & Cartograms • Types of Graphs • Graphs of time series • Graphs of frequency distributions

  39. DIAGRAMMATIC & GRAPHIC PRESENTATION • Difference between Diagrams & Graphs • Graphs are generally constructed on a graph paper whereas diagram is constructed on a plain paper. A graph represents mathematical relationship between variables whereas diagram does not • Diagrams are more attractive to eyes thus better suited for publicity and propaganda. They do not add anything to the meaning of the data thus not helpful to statisticians and researchers • For representing frequency distribution and time series, graphs are more appropriate than diagrams. In fact for presenting frequency distribution diagrams are rarely used

  40. GRAPHICAL PRESENTATION

  41. GRAPHS OF FREQUENCY DISTRIBUTION • Histogram. • Frequency Polygon • Smoothed Frequency Curve • Cumulative Frequency Curve, i.e., ‘Ogive’

  42. HISTOGRAM • Most popular and widely used • Set of Vertical Bars, whose areas are proportional to frequency represented • Variables always on X-axis and frequency on Y-axis • Bases on horizontal axis (X-axis) with centers at the class marks and lengths equal to class interval sizes • Areas proportional to class frequencies

  43. CONSTRUCTION OF HISTOGRAM • For Distributions having Equal Class-Intervals • Take frequency on Y-axis • Variable on X-axis • Construct adjacent rectangles • Height of the rectangles will be proportional to the frequencies

  44. CONSTRUCTION OF HISTOGRAM • For Distributions having Unequal Class-Intervals. • A correction for unequal class intervals must be made • Finding frequency density or relative frequency density • The frequency density is the frequency for that class divided by the width of that class • Areas proportional to class frequencies

  45. FORMATION OF CONTINUOUS FREQUENCY DISTRIBUTION EXCLUSIVE & INCLUSIVE METHODS

  46. HISTOGRAM

  47. FREQUENCY POLYGON • Graph for Frequency Distribution • Draw Histogram, join mid-points of upper side of each bar with straight line

  48. FREQUENCY POLYGON • By constructing a frequency polygon the value of mode can be easily ascertained • It facilitate comparison of two or more frequency distribution on the same graph

  49. ADVANTAGES OF FREQUENCY POLYGON OVER HISTOGRAM • Several distributions can be plotted on same axis • Much simpler • Sketches outline of data pattern more clearly • Becomes increasingly smooth as observations increase

  50. Instead of straight line, curved line is used for smoothening. SMOOTHED FREQUENCY CURVE

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