1. Presentation Of Data

2. Data Presentation All business decisions are based on evaluation of some data All business decisions are based on evaluation of some data The large amount of data generally generated from various business sources makes it highly cumbersome for the management to use the entire data collected The large amount of data generally generated from various business sources makes it highly cumbersome for the management to use the entire data collected All this voluminous data must be presented in a condensed form to the management without any loss of information contained in it All this voluminous data must be presented in a condensed form to the management without any loss of information contained in it Hence the collected data must be organized, carefully summarized and presented either in the form of tables or graphs that can be easily interpreted Hence the collected data must be organized, carefully summarized and presented either in the form of tables or graphs that can be easily interpreted

3. Frequency Distribution When the raw data has been collected and edited, it should be put into an ordered array in ascending or descending order so that it can be looked at more objectively When the raw data has been collected and edited, it should be put into an ordered array in ascending or descending order so that it can be looked at more objectively Then this data must be organized into a “frequency distribution”, which simply lists the value and the frequency of its occurrence in a tabular form Then this data must be organized into a “frequency distribution”, which simply lists the value and the frequency of its occurrence in a tabular form A frequency distribution can then be defined as “the list of all the values obtained in the data and the frequency with these values occur in the data” A frequency distribution can then be defined as “the list of all the values obtained in the data and the frequency with these values occur in the data”

4. Ex. 20 families were surveyed to find out how many children they had. The raw data obtained from the survey is as follows: 0, 2, 3, 1, 1, 3, 4, 2, 0, 3, 4, 2, 2, 1, 0, 4, 1, 2, 2, 3. The number of children becomes our variable (x), for which we can list the frequency of occurrence (f) in a tabular form as follows Number of children (x) Frequency (f) 0 3 1 4 2 6 3 4 4 3 ____ Total 20 This is known as discrete frequency distribution

5. If the data is very large, with mostly repeated values of variables, it is necessary to condense the data into a suitable number of groups or classes of variable values and then assigning the combined frequencies of these values to their respective classes If the data is very large, with mostly repeated values of variables, it is necessary to condense the data into a suitable number of groups or classes of variable values and then assigning the combined frequencies of these values to their respective classes Ex. 100 employees were surveyed in a factory to find out their ages. The youngest person was 20 years old and the oldest was 50 years old. Ex. 100 employees were surveyed in a factory to find out their ages. The youngest person was 20 years old and the oldest was 50 years old. We can construct a grouped frequency distribution for this data so that instead of listing frequency according to every age, we can list frequency according to an age group. We can construct a grouped frequency distribution for this data so that instead of listing frequency according to every age, we can list frequency according to an age group.

6. Since age is a continuous variable, a frequency distribution would be as follows Age group Frequency (f) Age group Frequency (f) 20 to less than 25 5 20 to less than 25 5 25 to less than 30 15 25 to less than 30 15 30 to less than 35 25 30 to less than 35 25 35 to less than 40 30 35 to less than 40 30 40 to less than 45 15 40 to less than 45 15 45 to less than 50 10 45 to less than 50 10

7. Constructing a Frequency Distribution Guidelines for constructing frequency distribution 1) The classes should be clearly defined and each of the observations should be included in only one of the class intervals 2) The number of classes should be neither too large nor too small. Normally between 6 and 15 classes are considered to be adequate. 3) All intervals should be of the same width Range Range The width of interval = ------------------------- The width of interval = ------------------------- Number of classes Number of classes

8. 4) Open end classes, where there is no lower limit of the first group or no upper limit of the last group, should be avoided since this creates difficulty in analysis and interpretation. 5) Intervals would be continuous throughout the distribution. For example for factory workers, we could group them in groups of 20 to 24. then 25 to 29 and then 30 to 34 and so on But it would be highly misleading because it does not accurately represent a person who is between 24 and 25 years of age But it would be highly misleading because it does not accurately represent a person who is between 24 and 25 years of age 6) The lower limit of the class intervals should be simple multiples of the interval width. This is primarily for the purpose of simplicity in construction and interpretation.

9. Example A sample of 30 persons showed their ages as follows: A sample of 30 persons showed their ages as follows: 20, 18, 25, 68, 23, 25, 16, 22, 29, 37 20, 18, 25, 68, 23, 25, 16, 22, 29, 37 35, 49, 42, 65, 37, 42, 63, 65, 49, 42 35, 49, 42, 65, 37, 42, 63, 65, 49, 42 53, 48, 65, 72, 69, 57, 48, 39, 58, 67 53, 48, 65, 72, 69, 57, 48, 39, 58, 67 Construct a frequency distribution for this data.

10. Solution Follow the steps as given below 1. Find the range of the data by subtracting the lowest score from the highest score. The lowest value is 16 and the highest is 72. Hence the range of data is 72 – 16 = 56 2. Assume that we shall have 6 classes, since the number of values is not too large 3. Now we divide the range 56 by 6 in order to get the width of the class interval. 4. The width is 56 / 6 = 9.33 take it as 10 5. Start the first class boundary with 15 so that the interval would be 15 and up to 25. the second interval would be 25 and up to 25

11. 6) Combine all the frequencies that belong to each class interval and assign this total frequency to the corresponding class interval as follows Class Interval (C.I.) Frequency (f) Class Interval (C.I.) Frequency (f) 15 to less than 25 5 15 to less than 25 5 25 to less than 35 3 25 to less than 35 3 35 to less than 45 7 35 to less than 45 7 45 to less than 55 5 45 to less than 55 5 55 to less than 65 3 55 to less than 65 3 65 to less than 75 7 65 to less than 75 7 ------- ------- Total 30 Total 30

12. Cumulative Frequency Distribution Previous table tells us the number of units in each class interval., it does not tell us directly the number of units that lie below or above the specified values of the class intervals. This can be determined from a cumulative frequency distribution Previous table tells us the number of units in each class interval., it does not tell us directly the number of units that lie below or above the specified values of the class intervals. This can be determined from a cumulative frequency distribution Class Interval (C.I.) Frequency (f) Cum Freq. Class Interval (C.I.) Frequency (f) Cum Freq. 15 to less than 25 5 5 25 to less than 35 3 8 35 to less than 45 7 15 35 to less than 45 7 15 45 to less than 55 5 20 45 to less than 55 5 20 55 to less than 65 3 23 55 to less than 65 3 23 65 to less than 75 7 30 65 to less than 75 7 30 In the above less than cumulative frequency distribution, there are 5 persons less than 25, 8 persons less than 35 and 15 persons less than 45 and so on In the above less than cumulative frequency distribution, there are 5 persons less than 25, 8 persons less than 35 and 15 persons less than 45 and so on

13. Greater than Cumulative frequency Class Interval (C.I.) Frequency (f) Cum Freq. Greater Than Greater Than Greater Than Greater Than 15 to less than 25 5 30 25 to less than 35 3 25 35 to less than 45 7 22 45 to less than 55 5 15 55 to less than 65 3 10 65 to less than 75 7 7 In above greater than cumulative frequency distribution, 30 persons are older than 15, 25 persons are older than 25, 22 persons are over 35 and so on In above greater than cumulative frequency distribution, 30 persons are older than 15, 25 persons are older than 25, 22 persons are over 35 and so on

14. Relative Frequency Distribution If researcher would like to know the proportion or the percentage of cases in each group, instead of simply the number of cases in each group, he can do so by constructing a relative frequency distribution table If researcher would like to know the proportion or the percentage of cases in each group, instead of simply the number of cases in each group, he can do so by constructing a relative frequency distribution table Class Interval (C.I.) Frequency (f) Rel.freq. % freq. 15 to less than 25 5 5 / 30 16.7 % 25 to less than 35 3 3 / 30 10.0 % 35 to less than 45 7 7 / 30 23.3 % 45 to less than 55 5 5 / 30 16.70 % 55 to less than 65 3 3 / 30 10.0 % 65 to less than 75 7 7 / 30 23.3 % ----- --------- ----- --------- Total 30 Total 100 % Total 30 Total 100 %

15. Distribution developed from less than cumulative frequency distribution (C.I.) (f) Cum. Cum. Rel. Freq. (C.I.) (f) Cum. Cum. Rel. Freq. freq (less than) freq (less than) (less than) (less than) 15 to less than 25 5 5 5/30 or 16.7% 25 to less than 35 3 8 8/30 or 26.7 % 35 to less than 45 7 15 15/30 or 50.0 % 45 to less than 55 5 20 20/30 or 66.7 % 55 to less than 65 3 23 23/30 or 76.7 % 65 to less than 75 7 30 30/30 or 100 %

16. Distribution developed from less than cumulative frequency distribution (C.I.) (f) Cum. Cum. Rel. Freq. (C.I.) (f) Cum. Cum. Rel. Freq. freq (greater than) freq (greater than) (greater than) (greater than) 15 to less than 25 5 30 30/30 or 100 % 25 to less than 35 3 25 25/30 or 83.3 % 35 to less than 45 7 22 22/30 or 73.3 % 45 to less than 55 5 15 15/30 or 50.0 % 55 to less than 65 3 10 10/30 or 33.3 % 65 to less than 75 7 7 7/30 or 23.3 %

17. Graphic Presentation The data we collect can often be more easily understood for interpretation, if it is presented graphically or pictorially. The data we collect can often be more easily understood for interpretation, if it is presented graphically or pictorially. Diagrams and graphs give visual indications of magnitudes, groupings, trends and pattern in the data Diagrams and graphs give visual indications of magnitudes, groupings, trends and pattern in the data The diagrams should be clear and easy to read and understand The diagrams should be clear and easy to read and understand Each diagram should include a brief and self explanatory title dealing with the subject matter Each diagram should include a brief and self explanatory title dealing with the subject matter The scale of the presentation should be chosen in such a way that the resulting diagram is of appropriate size The scale of the presentation should be chosen in such a way that the resulting diagram is of appropriate size

18. The following are the diagrammatic and graphic representations that are commonly used The following are the diagrammatic and graphic representations that are commonly used A) Diagrammatic Representation a) Bar Diagrams a) Bar Diagrams b) Pie Diagrams b) Pie Diagrams c) Pictograms c) Pictograms B) Graphic Representation a) Histogram a) Histogram b) Frequency Polygon b) Frequency Polygon c) Cumulative Frequency Curve c) Cumulative Frequency Curve

19. A) Diagrammatic Representation

20. A Bar Diagram Example Suppose that the following were the gross revenues (in $ 100,000.00s) for a company XYZ for the years 1980, 1981 and 1982 Suppose that the following were the gross revenues (in $ 100,000.00s) for a company XYZ for the years 1980, 1981 and 1982 S.N. Year Revenues S.N. Year Revenues 1. 1980 120 1. 1980 120 2. 1981 100 2. 1981 100 3. 1982 60 3. 1982 60 The bar diagram for this data can be constructed as follows, with the revenue represented by the vertical axis and the year represented by the horizontal axis. The bar diagram for this data can be constructed as follows, with the revenue represented by the vertical axis and the year represented by the horizontal axis.

21. A Bar Diagram

22. A sub-Divided Bar Chart Example Construct a sub-divided bar chart for the 3 types of expenditure in dollars of a family of four for the years 1982, 1983, 1984 and 1985 Construct a sub-divided bar chart for the 3 types of expenditure in dollars of a family of four for the years 1982, 1983, 1984 and 1985 Year Expenditure Food Education Other Total Food Education Other Total 1982 3000 2000 3000 8000 1983 3500 3000 4000 10,500 1984 4000 3500 5000 12,500 1985 5000 5000 6000 16, 000

23. Series 1 – Food Series 2 – Education Series 3- Other

24. Pie Diagrams This type of diagram enables us to show the partitioning of a total into its component parts. This type of diagram enables us to show the partitioning of a total into its component parts. The diagram is in the form of a circle and is also called a “Pie” because the entire graph looks like a pie and the components resembles slices cut from it. The diagram is in the form of a circle and is also called a “Pie” because the entire graph looks like a pie and the components resembles slices cut from it. The size of the slice represents the proportion of the component out of the total. The size of the slice represents the proportion of the component out of the total.

25. Pie Diagram Example: The following figures relate to the cost of the construction of the house, for various components that go into it represented as percentages of the total costs The following figures relate to the cost of the construction of the house, for various components that go into it represented as percentages of the total costs Item % expenditure Item % expenditure Labour 25 % Labour 25 % Cement, bricks 30 % Cement, bricks 30 % Steel 15 % Steel 15 % Timber, glass 20 % Timber, glass 20 % Misc. 10 % Misc. 10 %

26. Pie Chart

27. Pictograms Pictograms means presentation of data in the form of pictures Pictograms means presentation of data in the form of pictures It is quite a popular method used by governments and other organization for informational exhibition It is quite a popular method used by governments and other organization for informational exhibition Its main advantage is its attraction value. Its main advantage is its attraction value. They stimulate interest in the information being presented They stimulate interest in the information being presented News magazines are very find of presenting data in this form News magazines are very find of presenting data in this form

30. B) Graphic Presentation

31. Histogram In this type of representation the given data are plotted in the form of a rectangles In this type of representation the given data are plotted in the form of a rectangles Class intervals are marked along the x-axis and the frequencies along the y-axis according to a suitable scale Class intervals are marked along the x-axis and the frequencies along the y-axis according to a suitable scale Unlike the bar chart, which is one-dimensional meaning that only the length of the bar is material and not the width but histogram is two- dimensional in which the length and the width are both important Unlike the bar chart, which is one-dimensional meaning that only the length of the bar is material and not the width but histogram is two- dimensional in which the length and the width are both important A histogram is constructed from a frequency distribution of grouped data, where the height of the rectangle is proportional to the respective frequency and the width represents the class interval A histogram is constructed from a frequency distribution of grouped data, where the height of the rectangle is proportional to the respective frequency and the width represents the class interval

32. Histogram Example: C. I. (f) (Mid-Point) C. I. (f) (Mid-Point) 15-25 5 20 15-25 5 20 25-35 3 30 25-35 3 30 35-45 7 40 35-45 7 40 45-55 5 50 45-55 5 50 55-65 3 60 55-65 3 60 65-75 7 70 65-75 7 70

34. Frequency Polygon A frequency polygon is a line chart of frequency distribution in which either the values of discrete variables or the mid points are joined together by straight lines A frequency polygon is a line chart of frequency distribution in which either the values of discrete variables or the mid points are joined together by straight lines Since the frequencies do not start at zero or end at zero, this diagram as such would not touch the horizontal axis Since the frequencies do not start at zero or end at zero, this diagram as such would not touch the horizontal axis The curve is enclosed. The beginning of the curve touches the horizontal axis and the last mid-point is joined with the fictitious succeeding mid point, whose value is also zero. The curve is enclosed. The beginning of the curve touches the horizontal axis and the last mid-point is joined with the fictitious succeeding mid point, whose value is also zero.