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# Statisticsix

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### Statisticsix

1. 1. STATISTICS MRS.P.NAYAK,P.G.T K.V.F.W
2. 2. STATISTICS Statistics, branch of mathematics that deals with the collection, organization, and analysis of numerical decision-making.
3. 3. HISTORY Simple forms of statistics have been used since the beginning of civilization, when pictorial representations or other symbols were used to record numbers of people, animals, and inanimate objects on skins, slabs, sticks of wood, or the walls of caves.
4. 4. Before 3000 bc the Babylonians used small clay tablets to record tabulations of agricultural yields and of commodities bartered or sold.
5. 5. The Egyptians analysed the population and material wealth of their country before beginning to build the pyramids in the 31st century bc.
6. 6. The Roman Empire was the first government to gather extensive data about the population, area, and wealth of the territories that it controlled.
7. 7. Registration of deaths and births was begun in England in the early 16th century, and in 1662 the first noteworthy statistical study of population.
8. 8. At present, statistics is a reliable means of describing accurately the values of economic, political, social, psychological, biological, and physical data and serves as a tool to correlate and analyse such data. The work of the statistician is no longer confined to gathering and tabulating data, but is chiefly a process of interpreting the information.
9. 9. STATISTICAL METHODS STEPS • COLLECTION OF DATA • TABULATION AND PRESENTATION OF DATA • INTERPRETATION OF DATA.
10. 10. COLLECTION OF DATA: Primary Data – When Data are collected directly it is called Primary Data. Secondary Data. If they are collected through others than it is called Secondary Data.
11. 11. TABULATION AND PRESENTATION OF DATA The collected data are called RAW DATA
12. 12. TABULATION AND PRESENTATION OF DATA 1. They must be arranged either ascending order or descending order. 2. They are grouped. 3. They are tabulated. 4. Construction of frequency distribution table.(Grouped / Ungrouped)
13. 13. INTERPRETATION OF DATA. (a) From graph (b) Measures Of Central Tendency (c) Measures Of Variability (d) Measures Of Variability (e) Co-relation (f) Mathematical Models
14. 14. GRAPHICAL REPRESENTATION OF DATA (i) Pictorial graph (ii) Bar Graph (iii) Histogram (iv) Frequency polygon
15. 15. GRAPHS Graphs are used to display number information, or data, in a visual way that is easy to understand and interpret. They are usually drawn with two lines, called axes, which meet at a right angle like this. The line going across the page is the horizontal axis, and the line going up the page is the vertical axis. The axes are labelled to show the type of data and the value of the data being shown
16. 16. A BAR-LINE GRAPH
17. 17. BLOCK GRAPHS se have a block or square to show one unit value of
18. 18. BAR GRAPH
19. 19. LINE GRAPHS Line graphs can be used to show a relationship  between the data on one axis and the data on the other.
20. 20. PIE CHARTS These have a circle divi ded into parts, or sectors, of different sizes to show different amounts of data. They are called pie charts because they look like pies cut into slices.
21. 21. MEASURES OF CENTRAL TENDENCY After data have been collected and tabulated, analysis begins with the calculation of a single number, which will summarize or represent all the data. Because data often exhibit a cluster or central point, this number is called a measure of central tendency. Mean Median Mode
22. 22. MEASURES OF CENTRAL TENDENCY Let x, x2, ..., xn be the numbers of some statistic. The most frequently used measure is the simple arithmetic average, or mean, written, which is the sum of the numbers divided by n:
23. 23. MEASURES OF CENTRAL TENDENCY After data have been collected and tabulated, analysis begins with the calculation of a single number, which will summarize or represent all the data. Because data often exhibit a cluster or central point, this number is called a measure of central tendency. Let x1, x2, ..., xn be the numbers of some statistic. The most frequently used measure is the simple arithmetic average, or mean, written , which is the sum of the numbers divided by n: The symbol Σ denotes the sum of all values. If the xs are grouped into k intervals, with midpoints m1, m2, ..., mk and frequencies f1, f2, ..., fk, respectively, the simple arithmetic average is given by with i = 1, 2, ..., k.
24. 24. MEASURES OF CENTRAL TENDENCY The median and the mode are two other measures of  central tendency. Let the xs be arranged in numerical  order; if n is odd, the median is the middle x; if n is  even, the median is the average of the two middle xs.  The mode is the x that occurs most frequently. If two or  more distinct xs occur with equal frequencies, but none  with greater frequency, the set of xs may be said not to  have a mode or to be bimodal, with modes at the two  most frequent xs, or trimodal, with modes at the three  most frequent
25. 25. VARIABILITY OF THE DISTRIBUTION The investigator is frequently concerned with the variability of the distribution, that is, whether the measurements are clustered tightly around the mean or spread over the range. One measure of this variability is the difference between two percentiles, usually the 25th and the 75th percentiles. The pth percentile is a number such that p per cent of the measurements are less than or equal to it; in particular, the 25th and the 75th percentiles are called the lower and upper quartiles, respectively.
26. 26. VARIABILITY OF THE DISTRIBUTION The standard deviation is a measure of variability that is more convenient to use than percentile differences as it is defined via basic arithmetic terms as follows. The simple deviation of a number in a set is defined as the difference between that number and the mean of the set. For example, in the series x1, x2, ..., xn, the deviation of x1 is x1 - , and the square of the deviation is (x1 - )2. The variance of the set is the mean of the square deviations. Finally, the standard deviation, denoted by σ (the lower-case Greek letter sigma), is the square root of the variance, and is calculated as follows,
27. 27. CORRELATION When two social, physical, or biological phenomena increase or decrease proportionately and simultaneously because of identical external factors, the phenomena are positively correlated; if one increases in the same proportion that the other decreases, the two phenomena are negatively correlated. Investigators calculate the degree of correlation by applying a coefficient of correlation to data concerning the two phenomena. The most common correlation coefficient is expressed as
28. 28. CORRELATION in which x is the deviation of one variable from its mean, y is the deviation of the other variable from its mean, and N is the total number of cases in the series. A perfect positive correlation between the two variables results in a coefficient of +1, a perfect negative correlation in a coefficient of -1, and a total absence of correlation in a coefficient of 0. Thus, .89 indicates high positive correlation, -.76 high negative correlation, and . 13 low positive correlation.
29. 29. A MATHEMATICAL MODEL In a related but more involved example of a mathematical model, many sets of measurements have been found to have the same type of frequency distribution—for example, the number of 6s cast in runs of n tosses of a die; the weights of N beans chosen haphazardly from a bag; the barometric pressures recorded by different students, reading the same barometer.