Data presentation.pptx

Data organization & presentation

1. Data organization & presentation

2. Once data has been collected, it has to be organized and classified in such a way that it becomes easily readable and interpretable. Measurements that have not been organized, summarized or otherwise manipulated are called raw data. First step in organizing data is the preparation of an ordered array. An ordered array is listing the values in order of magnitude from the smallest value to the largest value. Summarizing qualitative data is very straight forward, the main task is being to count the number of observation in each category. These counts are called frequencies.

3. Data can be presented in one of the three ways As text: It is the main method of conveying information and it is used to explain results and trends and provide contextual information. In tabular form: It conveys information by converting words and numbers into rows and columns. It is easier to see patterns and relationship. In graphical form: Graphs simplify complex information by using images and emphasizing data patterns or trends and are useful for summarizing, explaining or exploring quantitative data.

4. Tabular forms Array: An array is a matrix or rows and columns of numbers which have been arranged in some orders. Simple tables: A table needs a heading and names of variables involved.

5. Compound tables: It is an extension of simple table where more than one variable is used. We may also refer a compound table as a cross-tabulation or contingency table depending on the context in which it is used. Bivariate table: When two variables are presented in one table. Multivariate table: When more than two variables are used in one table. Age group yr Male Female Illiterate Literate Illiterate literate <40 Total Age group yr Male Female Illiterate Literate Illiterate literate <40 Total

6. Frequency distribution of grouped data: To group a set of observations first to select a set contiguous, non overlapping intervals such that each value in the set of observations can be placed in one and only one of the interval. These intervals are known as class interval. Width of class interval should be of same width. This width may be determined by dividing the range R by k, the number of class interval.

7. Rule of thumb: Class interval width of 5 units, 10 units. Following points should be kept in mind for classification The classes should be clearly defined and should not lead to any ambiguity The classes should be exhaustive and each of the given values should be included in one of the classes The classes should be mutually exclusive and non overlapping The classes preferably of equal width The number of classes should neither be too large or too small There should no gaps between groups

8. Inclusive & Exclusive Class Interval When the lower and upper class limit is included, then it is an Inclusive Class Interval. For example 21- 25, 26-30. Usually in discrete variable, this type of class interval is used. When the lower limit is included, but the upper limit is excluded, then it is an Exclusive Class Interval. For example, 20 - 25, 25- 30. In case of continuous variable, exclusive class interval is used.

9. Drawing/ Graphical presentation For quantitative data, common graphs are 1. Histogram 2. Frequency polygon 3. Frequency curve 4. Line chart/graph 5. Cumulative frequency polygon or Ogive 6. Scatter plot 7. Stem and leaf 8. Box and Whiskers diagram

10. The common diagrams for qualitative variable are: Bar diagram i . Simple Bar diagram ii. Multiple bar iii. Proportional/ component bar Pie chart Pictogram Spot map

11. Simple bar diagram Only one variable is presented in a simple bar diagram. Steps of drawing a bar diagram Construct scale by a horizontal line which is known as x-axis and a vertical line which is y – axis. Place categories of the variable on the x-axis and y-axis represents the frequency or percentage of the categories. Width of the bars should be equal. Gap between the bars should also be equal.

12. Component bar diagram Categories of a variable forms a bar which constitutes 100%. Scale the y-axis from 0% to 100%. A bar on x-axis should be as tall as 100%. The bar is constituted as per proportion of the categories.

13. Pie diagram A pie diagram is similar to component bar diagram. In pie diagram all the components adds up to 360 degree as a circle consists of 360 . Steps Multiply percentage of a category by 3.6 and get the angle for that category Draw a circle. Place the categories in the circle according to the calculated angles.

14. Pictogram Spot map

15. Histogram A histogram is used to display the continuous variable. A histogram is a set of vertical bars whose areas are proportional to the frequencies of the classes that they represent. In a histogram the variables are taken on x-axis and the frequencies are repented on y-axis. Each class is then represented by a distance on the scale that is proportional to the class interval. Unlike the bar charts, there are no gaps between successive rectangles of a histogram. A histogram is two-dimensional, here both length and width are important.

16. Histogram with unequal class interval In this situation, correction must be made and it can be done by finding the frequency density of each class. The frequency density will be the actual heights of the rectangles since the areas of the rectangles should be proportional to the frequencies. Frequency density =  

17. Frequency polygon

18. Line chart/graph A line chart shows the frequencies for different values of a variable. Successive points are joined by means of line segments so that a glance at the graph tells the distribution of the variable. Simple line chart: When values of one variable is presented. Trends can be determined. Multiple line chart: More than one variables are presented here. Comparison between variables and also trends can be understood.

19. Simple line graph Multiple line graph

20. Cumulative frequency polygons or Ogives It is generated when cumulative frequencies are plotted on real limits of classes of a distribution. Cumulative frequency means that the frequencies of classes are accumulated over the entire distribution. Two types of cumulative frequency ‘Less than’ cumulative frequency: It is the total number of observations in the entire distribution, which is less than or equal to the real upper limit of the class. ‘More than’ cumulative frequency: It is the total number of observations in the entire distribution, which is more than or equal to the real lower limit of the class.

21. Scatter plot This type of diagram is used to investigate the relationship between two continuous variables. In such a relationship, there is usually an independent variable and a dependent variable. It is a prerequisite diagram in correlation and regression analysis.

22. Stem and leaf Stem and leaf is also known as stemplot used to represent raw data, that is individual observation without loss of information. The leaves of the diagram are the last digits of the observation while the stems are the remaining part of the value. Suppose, the value 117, here ‘11’ is the stem and ‘7’ is the leaf.

23. Raw data

24. Box and Whiskers diagram Box and whiskers diagram is usually known as boxplots, specially designed to display the dispersion and skewness of the distribution. The figure consists of a box in the middle from which two lines ( whiskers) extends toward minimum and maximum values of the distribution. A box plot is drawn according to 5 descriptive statistics Minimum value Upper quartile Median Lower quartile Maximum value

25. Exercise 65 91 85 76 85 87 79 93 82 75 100 70 88 78 83 59 87 69 89 54 74 89 83 80 94 67 77 92 82 70 94 84 96 98 46 70 90 96 88 72 Construct a frequency distribution Construct a corresponding histogram