Tabular and Graphical Representation of Data

This slideshow describes about type of data, its tabular and graphical representation by various ways. It is slideshow is useful for bio statisticians and students.

1. Tabular and Graphical representation of Data Dr. A.V. Dusane Sir Parashurambhau College Pune, India [email protected] 1

2. Collection and representation of data Classification of data: Data is a set of values of recorded for an event is called data. Data can be stored and presented in various ways so as to draw some inference. Data classification: Primary data Secondary data. Qualitative data Quantitative data. 2

3. N eed of data classification A data presented without any orderliness does not allow deriving any inference from it. So it is essential to organize the data. This is accomplished by summarizing data into a frequency distribution table. Main Objectives of data classification: 1. To make a proper use of raw data. 2. To study the data and make comparisons easier. 3. To use the collected material to statistical treatment. 4. To simplify the complexities of raw. 5. To draw the statistical inferences from data. 5. To keep unnecessary information aside. 3

4. Frequency distribution A frequency distribution or frequency table is the tabular arrangement of data by classes together with the corresponding class frequencies. The main purpose of frequency distribution is to organize the data into a more compact form without obscuring essential information contained in the values. 4

5. Example of frequency distribution Class Frequency Relative frequency Cumulative frequency 48-50 2 2/15 2 50-52 2 2/15 4 52-54 5 5/15 9 54-56 3 3/15 12 56-58 3 3/15 15 5 Eg. Height of 15 plants measured in inches is recorded as follows: 53 48 55 51 50 57 56 54 56 54 53 53 52 53 49 .

6. Construction grouped frequency distribution table Important points to be considered at the time of construction of frequency distribution table 1. Number of classes: The number of classes or range of class interval is an important factor for preparing frequency table. There is no fixed rule for how many classes to be taken. Generally depends on the observation of available data, minimum 3 classes and maximum 20 classes are formed. The size of class interval also depends on the range of data and the number of classes, it is equal to the difference between the highest and lowest value divided by the number of classes. 6

7. Construction grouped frequency distribution table Class interval: It depends on the range (The range is the difference in the highest and the lowest value of the variable) of the data and the number of classes. Following formula should be used to estimate class interval. i = (L –S ) / C i = class interval L = largest value S = smallest value C = number of classes However for simplicity under root of number of observations is taken. Class limit: These are the lowest and highest values, which are included in the class e.g. in the class 10-20, lowest value is 10 and the highest is 20. 7

8. Construction grouped frequency distribution table Mid value or mid point: The central point of a class interval is mid point\ mid value. It can be calculated by adding the upper and lower limits of a class and dividing the sum by 2. Mid point of a class = (L1 +L2)/ 2 L1 =lower limit of the class, L2 = upper limit of the class. I=H-L/K where I- interval, H= highest value, L= lowest value K= number of classes 8

9. Types of frequency distribution tables No. of pods in class interval No. of plants in frequency 15-17 3 17-19 4 19-21 4 21-23 5 23-25 3 9 There are two types: Overlapping frequency distribution table Non-overlapping frequency distribution table Overlapping frequency distribution table: Values of variables are grouped in such a fashion that the upper limit of one class interval is represented in next class interval. In a table number of pods ranges from 15-25 the classes may be 15-17,17-19, etc .

10. Non-overlapping frequency distribution table No. of pods in class interval No. of plants in frequency 15-17 3 18-20 4 21-23 4 24-26 5 27-28 3 10 Values of variable are grouped in such a fashion that the upper levels of one class interval do not overlap the preceding class interval. In the above example, number of pods ranges from 15-28, the classes may be 15-17,18-20, etc

11. Methods of representation of statistical data There are two main methods of statistical data presentation i ) Table method and ii) graph method. Essential features of tabular presentation: Tabulation is a process of orderly arrangement of data into series or rows or columns were they can be read at a glance. This process is also called summarization of data in an orderly manner within a limited space. 11

12. Types of table Length of plant (cm) 6-10 11-15 16-20 21-25 No of plants 5 10 11 9 12 Length of plant (cm) Infected male Healthy male Infected female Healthy female 6-10 2 1 1 1 11-15 2 4 2 2 16-20 1 4 2 4 21-25 1 2 2 4 Simple table: In this typ e of table only one parameter is considered e.g. Length of Papaya plant in field. Complex table: In this more than one parameter is considered e.g. Length, sex of plant, disease, incidence, etc.

13. Advantages of tabular presentation   It helps in simplifying the raw data. Comparisons can be done easily made. It reveals the pattern of distribution of any attribute, defects, omissions and errors. Accurate figures are given. It is having a great value to the expert. 13

14. Graphical representation of data Graph: A graph is a pictorial presentation of relationship between variables especially to express the change in some quantity over a period of time. Graph is a visual form of the representation of statistical data. Graphical method enables statistician to present quantitative data in a simple, clear and effective manner. Comparisons can be easily made between two or more phenomena with the help of graph. To obtain clearer picture we can represent the frequency table pictorially. Such a visual pictorial representation can be done through graphs. 14

15. Purpose of Graphs To compare two or more numbers: The comparison is often by bars of different lengths. To express the distribution of individual objects of measurements into different categories: The frequency distribution of numerical categories is usually represented by histogram. The distribution of individuals into non-numerical categories can be shown as a bar-diagram. The length of bar represents the number of observations (or frequency) in each category. If the frequencies are expressed as percentages, totaling 100%, a convenient way is a pie chart. 15

16. Types of Graphs Types of graphs: Line graph, Bar graph, Pie chart, Histogram, frequency polygon, frequency curve, are main types of graphs. Histograms: This is one of the most popular methods for displaying the frequency distribution. In this type of representation, the given data is plotted in the form of a series of rectangles. The height of rectangle is proportional to the respective frequency and width represents the class interval. The class intervals are marked along the X-axis and the frequencies along the Y-axis. Any blank spaces between the rectangles would mean that the category is empty and there are no values in that class interval. A histogram is two-dimensional in which both the length and the width are important. 16

17. Histogram 17 Height of the plant (in inches)

18. Histogram Merits of histograms: It gives the idea about the amount of variability present in the data. It is useful to find out mode. Demerits of histograms: Histogram can not be drawn for frequency distribution with open-end class. Histogram is not a convenient method for comparisons especially the super-imposed histograms are usually confusing. 18

19. Histogram Major steps involved in construction of histogram: Arrange the data in ascending order Find out class interval Prepare the frequency distribution diagram Draw the histogram by taking class value on X- axis and frequency on Y-axis. 19

20. Frequency polygon It is a line chart of frequency distribution in which midpoints of class intervals are plotted are joined by straight lines. It is the variation of histogram in which instead of rectangles erect over the intervals, the points are plotted at the mid points of the tops of the corresponding rectangles in a histogram, and the successive points are joined by straight lines. Frequency polygon is used in cases of time series, that is when the distribution of the variate is given as a function of time E.g . Growth of plant over a period of time, trends in food production, etc. 20

21. Frequency polygon 21

22. Frequency polygon Merits: It can be constructed quickly than histograms. It enables to understand the pattern on the data more clearly than histogram. Demerit: It can not give an accurate picture as that given by histogram because in frequency polygon the areas above the various intervals are not exactly proportional to the frequencies. 22

23. Frequency curve When the total frequency is large, and the class intervals are narrow so the frequency polygon or histogram will approach more and more towards the form of a smooth curve. Such a smooth curve is called frequency curve . Frequency curve is also called as ‘ Smoothed frequency polygon ’. In this, total area under the curve is equal to the area under the original histogram or polygon. This usually has single hump or mode (value with highest frequency) 23

24. Scatter or Dot diagram T his is the simplest method for confirming whether there is any relationship between two variables by plotting values on graph. It is nothing but a visual representation of two variables by points (dots) on a graph. In a scatter diagram one variable is taken on the X-axis and other on the Y-axis and the data is represented in the form of points. It is called as a scatter diagram because it indicates scatter of various points (variables). The scatter diagram gives a general idea about existence of correlation between two variables and type of correlation . It does not give correct numerical value of the correlation as given by correlation coefficient. 24

25. Scatter diagram Merits of scatter diagram: It is a simple method to find out the nature of correlation between two variables. It is not influenced by extreme limits It is easy to understand. Demerits of Scatter diagram: It doesn’t give correct numerical value of correlation. It is unable to give the exact degree of correlation between two variables. It is a subjective method. It cannot be applied to qualitative data. Scatter is the first step in finding out the strength of correlation-ship. 25

26. Scatter diagram 26

27. Line diagram Line diagram: It is a simplest type of diagram. It is used for presenting the frequencies of discrete variables. In this there are two variables under considerations. Frequencies are taken on X – axis and independent variables on Y – axis and the line segments join the points. 27

28. Line graph 28 Moisture contents

29. Bar diagram This one-dimensional diagram where bars of equal width are drawn either horizontally or vertically which represents the frequency of the variable. The width of bars should be uniform throughout the diagram. In this diagram, bars are simply vertical lines where the lengths of the bars proportional to the corresponding numerical values. In bar diagram, length is important and nor the width. The bars should be equally spaced. The bars may be horizontal or vertical. There are four type of bar diagram. i ) Simple bar diagram ii) D ivided bar diagram iii) Percentage bar diagram and iv) M ultiple bar diagram. 29

30. Simple Bar D iagram This type of bar diagram is used to represent only one variable by one figure. 30

31. Divided bar diagram When frequency is divided into different components then diagrammatic representation is called divided bar diagram . 31

32. Percentage bar diagram The total length of bar corresponds to 100 and the division of the bar corresponds to percentage of different components. 32

33. Multiple bar diagram When comparisons between two or more related variables has to be made then this type diagram is essential. 33

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35. Pie diagram T his type of diagram enables us to show the partitioning to a total into its component parts. It is in the form of a circle divided by radial lines into sections (components). It is called, as a pie because the entire diagram looks like a pie and the components resembles slices cut from it. The area of each section is proportional to the size of the figures. It is used to present discrete data such as age group, total expenditure, total area under cultivation for different crops etc. 35

36. Pie diagram 36

37. Merits of the graphic representation It is more attractive representation as compared to figures. It simplifies the numerical complexity. It facilitates easy comparison of data. It is easy to understand even to the common man. Graphs have long lasting impression on the mind. It reveals hidden facts, which normally cannot be detected from tabular presentation. Quick conclusions can be drawn. 37

38. Limitations of Graphic representation It can not be used for detailed studies but only for comparative studies. Tables shows the exact figures while graph shows overall position. The figures are approximately correct but not exact. It can give only a limited amount of information because it shows approximate values. It can not be analyzed further. It’s utility to an expert is limited A table can be used to give data on three or more characteristics/parameters but this is not possible in case of graph. 38

39. Significance of graphs In biometry diagrams and graphs have a lot of significance as these are useful for showing the comparisons. Two or more graphs can be drawn on the same graph paper (having the same scale) to show the trend variability occurring in the data. 39