STATIA-STICAL ANALYSIS of grain size data.ppt
- 2. The study of sediments are largely The study of sediments are largely statistical in nature statistical in nature Collection and classification of Collection and classification of data(mechanical analysis) data(mechanical analysis) Preservation of data in the form of Preservation of data in the form of tables and graphs tables and graphs Statistical analysis of data and inference Statistical analysis of data and inference about the sediments about the sediments
- 3. Ways of statistical analysis Ways of statistical analysis 1.Frequency distribution ----if it involves 1.Frequency distribution ----if it involves magnitude such as size of grains and magnitude such as size of grains and percentage of heavy minerals percentage of heavy minerals 2.Time series ----if time is an important 2.Time series ----if time is an important factor factor
- 4. Frequency distribution Frequency distribution It include size frequency distribution It include size frequency distribution It has two principle variances-----size It has two principle variances-----size and frequency and frequency
- 5. Histograms Histograms Common graphic device –readily under Common graphic device –readily under stood stood Clarity and simplicity Clarity and simplicity Class which has gradient frequency can Class which has gradient frequency can be recognised at first site be recognised at first site Modal class Modal class
- 6. Draw backs Draw backs Hidstograms are influenced by the class Hidstograms are influenced by the class intervals used in the analysis intervals used in the analysis Its shape varies according to a Its shape varies according to a particular class limits chosen particular class limits chosen If same distribution analysed in two If same distribution analysed in two different stereograms one may be different stereograms one may be symmetrical or the other may symmetrical or the other may assymmetrical assymmetrical
- 7. Cumulative curves Cumulative curves The original frequency data is The original frequency data is cumulated cumulated It converts finite class intervals into a It converts finite class intervals into a continuous function continuous function
- 8. Statistical parameters Statistical parameters 1. measuring central tendency 1. measuring central tendency The value about which all other values The value about which all other values cluster cluster This correspond to the value which is This correspond to the value which is most frequent most frequent Called averages –arithmatic mean Called averages –arithmatic mean size ,median size and model size size ,median size and model size
- 9. 2.measuring the degree of scatter 2.measuring the degree of scatter The average value does not indicate the The average value does not indicate the spread of data on either side spread of data on either side Hence a second measure is needed Hence a second measure is needed It is a measure of degree of spread or It is a measure of degree of spread or dispersion of data around the central dispersion of data around the central tendency tendency The measuring may be the mean The measuring may be the mean deviation or std deviation deviation or std deviation
- 10. 3.measuring the degree of asymmetries 3.measuring the degree of asymmetries The average size and degree of spread The average size and degree of spread of two curves may be the same but one of two curves may be the same but one may not be symmetrical may not be symmetrical
- 11. Hence it is necessary to have a measure Hence it is necessary to have a measure of the tendency of the data to spread on of the tendency of the data to spread on one side or the other side of the one side or the other side of the average average Such asymmetry is called skewness Such asymmetry is called skewness Skewness may be left to right /positive Skewness may be left to right /positive or negative or negative
- 12. 4 4 measuring of degree of peakedness measuring of degree of peakedness Frequency curves which are alike in Frequency curves which are alike in their degree eithre of symmetry or their degree eithre of symmetry or asymmetry may vary in the degree of asymmetry may vary in the degree of peakedness peakedness It is the measure of kurtosis It is the measure of kurtosis
- 13. Trask’s method Trask’s method Graph between values of cumulative wt Graph between values of cumulative wt % and diameters(grain size) of % and diameters(grain size) of sediments sediments From the graph find out the diameters From the graph find out the diameters corresponding to the following corresponding to the following parameters parameters Q1=75% Q2 =50% Q3=25% Q1=75% Q2 =50% Q3=25%
- 14. Folk and Ward method Folk and Ward method Graph – cumulatve wt% are plotted Graph – cumulatve wt% are plotted against grain size (mm & against grain size (mm &Ф Ф) ) Percentile values are deduced from the Percentile values are deduced from the graph graph P16,P50,P84 P16,P50,P84