Presentation Of DataPresentation Of Data

Data PresentationData Presentation All business decisions are based on evaluation of All business decisions are based on evaluation of

some datasome data The large amount of data generally generated The large amount of data generally generated

from various business sources makes it highly from various business sources makes it highly cumbersome for the management to use the entire cumbersome for the management to use the entire data collecteddata collected

All this voluminous data must be presented in a All this voluminous data must be presented in a condensed form to the management without any condensed form to the management without any loss of information contained in itloss of information contained in it

Hence the collected data must be organized, Hence the collected data must be organized, carefully summarized and presented either in the carefully summarized and presented either in the form of tables or graphs that can be easily form of tables or graphs that can be easily interpretedinterpreted

Frequency DistributionFrequency Distribution

When the raw data has been collected and When the raw data has been collected and edited, it should be put into an ordered array in edited, it should be put into an ordered array in ascending or descending order so that it can be ascending or descending order so that it can be looked at more objectivelylooked at more objectively

Then this data must be organized into a Then this data must be organized into a “frequency distribution”, which simply lists the “frequency distribution”, which simply lists the value and the frequency of its occurrence in a value and the frequency of its occurrence in a tabular formtabular form

A frequency distribution can then be defined as A frequency distribution can then be defined as “the list of all the values obtained in the data and “the list of all the values obtained in the data and the frequency with these values occur in the the frequency with these values occur in the data” data”

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 20This is known as discrete frequency distribution

If the data is very large, with mostly repeated If the data is very large, with mostly repeated values of variables, it is necessary to condense values of variables, it is necessary to condense the data into a suitable number of groups or the data into a suitable number of groups or classes of variable values and then assigning classes of variable values and then assigning the combined frequencies of these values to the combined frequencies of these values to their respective classes their respective classes

Ex. 100 employees were surveyed in a factory to Ex. 100 employees were surveyed in a factory to find out their ages. The youngest person was 20 find out their ages. The youngest person was 20 years old and the oldest was 50 years old. years old and the oldest was 50 years old.

We can construct a grouped frequency We can construct a grouped frequency distribution for this data so that instead of listing distribution for this data so that instead of listing frequency according to every age, we can list frequency according to every age, we can list frequency according to an age group. frequency according to an age group.

Since age is a continuous variable, a frequency distribution would be as follows

Age groupAge group Frequency (f)Frequency (f)

20 to less than 25 520 to less than 25 5

25 to less than 30 1525 to less than 30 15

30 to less than 35 2530 to less than 35 25

35 to less than 40 3035 to less than 40 30

40 to less than 45 1540 to less than 45 15

45 to less than 50 1045 to less than 50 10

Constructing a Frequency Constructing a Frequency DistributionDistribution

Guidelines for constructing frequency distribution1) 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 RangeRange The width of interval = -------------------------The width of interval = ------------------------- Number of classesNumber of classes

4) 4) Open end classes, where there is no lower limit Open end classes, where there is no lower limit of the first group or no upper limit of the last of the first group or no upper limit of the last group, should be avoided since this creates group, should be avoided since this creates difficulty in analysis and interpretation.difficulty in analysis and interpretation.

5) Intervals would be continuous throughout the 5) Intervals would be continuous throughout the distribution. For example for factory workers, we distribution. For example for factory workers, we could group them in groups of 20 to 24. then 25 could group them in groups of 20 to 24. then 25 to 29 and then 30 to 34 and so onto 29 and then 30 to 34 and so on

But it would be highly misleading because it But it would be highly misleading because it does not accurately represent a person who is does not accurately represent a person who is between 24 and 25 years of age between 24 and 25 years of age

6) The lower limit of the class intervals should be 6) The lower limit of the class intervals should be simple multiples of the interval width. This is simple multiples of the interval width. This is primarily for the purpose of simplicity in primarily for the purpose of simplicity in construction and interpretation. construction and interpretation.

ExampleExample

AA sample of 30 persons showed their ages as sample of 30 persons showed their ages as follows:follows:

20, 18, 25, 68, 23, 25, 16, 22, 29, 3720, 18, 25, 68, 23, 25, 16, 22, 29, 37

35, 49, 42, 65, 37, 42, 63, 65, 49, 4235, 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.Construct a frequency distribution for this data.

SolutionSolution

Follow the steps as given belowFollow the steps as given below1.1. Find the range of the data by subtracting the Find the range of the data by subtracting the

lowest score from the highest score. The lowest lowest score from the highest score. The lowest value is 16 and the highest is 72. Hence the range value is 16 and the highest is 72. Hence the range of data is 72 – 16 = 56of data is 72 – 16 = 56

2.2. Assume that we shall have 6 classes, since the Assume that we shall have 6 classes, since the number of values is not too largenumber of values is not too large

3.3. Now we divide the range 56 by 6 in order to get Now we divide the range 56 by 6 in order to get the width of the class interval.the width of the class interval.

4.4. The width is 56 / 6 = 9.33 take it as 10The width is 56 / 6 = 9.33 take it as 105.5. Start the first class boundary with 15 so that the Start the first class boundary with 15 so that the

interval would be 15 and up to 25. the second interval would be 15 and up to 25. the second interval would be 25 and up to 25interval would be 25 and up to 25

6) Combine all the frequencies that belong to each 6) Combine all the frequencies that belong to each class interval and assign this total frequency to class interval and assign this total frequency to the corresponding class interval as follows the corresponding class interval as follows

Class Interval (C.I.)Class Interval (C.I.) Frequency (f)Frequency (f) 15 to less than 25 515 to less than 25 5 25 to less than 35 325 to less than 35 3 35 to less than 45 735 to less than 45 7 45 to less than 55 545 to less than 55 5 55 to less than 65 355 to less than 65 3 65 to less than 75 765 to less than 75 7 -------------- Total 30Total 30

Cumulative Frequency Cumulative Frequency DistributionDistribution Previous table tells us the number of units in each class Previous table tells us the number of units in each class

interval., it does not tell us directly the number of units that lie interval., it does not tell us directly the number of units that lie below or above the specified values of the class intervals. This below or above the specified values of the class intervals. This can be determined from a cumulative frequency distributioncan be determined from a cumulative frequency distribution

Class Interval (C.I.)Class Interval (C.I.) Frequency (f)Frequency (f) Cum Freq. Cum Freq.

15 to less than 25 5 5 15 to less than 25 5 5 25 to less than 35 3 825 to less than 35 3 8 35 to less than 45 7 1535 to less than 45 7 15 45 to less than 55 5 2045 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 3065 to less than 75 7 30

In the above less than cumulative frequency distribution, there In the above less than cumulative frequency distribution, there are 5 persons less than 25, 8 persons less than 35 and 15 are 5 persons less than 25, 8 persons less than 35 and 15 persons less than 45 and so onpersons less than 45 and so on

Greater than Cumulative frequencyGreater than Cumulative frequency

Class Interval (C.I.)Class Interval (C.I.) Frequency (f)Frequency (f) Cum Freq.Cum Freq. Greater ThanGreater Than Greater ThanGreater Than 15 to less than 25 5 3015 to less than 25 5 3025 to less than 35 3 25 25 to less than 35 3 25 35 to less than 45 7 2235 to less than 45 7 2245 to less than 55 5 1545 to less than 55 5 1555 to less than 65 3 10 55 to less than 65 3 10 65 to less than 75 7 765 to less than 75 7 7

In above greater than cumulative frequency In above greater than cumulative frequency distribution, 30 persons are older than 15, 25 distribution, 30 persons are older than 15, 25 persons are older than 25, 22 persons are over 35 persons are older than 25, 22 persons are over 35 and so onand so on

Relative Frequency DistributionRelative Frequency Distribution If researcher would like to know the proportion or the If researcher would like to know the proportion or the

percentage of cases in each group, instead of simply the percentage of cases in each group, instead of simply the number of cases in each group, he can do so by number of cases in each group, he can do so by constructing a relative frequency distribution tableconstructing a relative frequency distribution table

Class Interval (C.I.)Class Interval (C.I.) Frequency (f)Frequency (f) Rel.freq. % freq. Rel.freq. % freq. 15 to less than 25 5 5 / 30 16.7 %15 to less than 25 5 5 / 30 16.7 %25 to less than 35 3 3 / 30 10.0 %25 to less than 35 3 3 / 30 10.0 %35 to less than 45 7 7 / 30 23.3 % 35 to less than 45 7 7 / 30 23.3 % 45 to less than 55 5 5 / 30 16.70 %45 to less than 55 5 5 / 30 16.70 %55 to less than 65 3 3 / 30 10.0 %55 to less than 65 3 3 / 30 10.0 %65 to less than 75 7 7 / 30 23.3 %65 to less than 75 7 7 / 30 23.3 % ----- -------------- --------- Total 30 Total 100 % Total 30 Total 100 %

Distribution developed from less than Distribution developed from less than cumulative frequency distributioncumulative frequency distribution

(C.I.)(C.I.) (f)(f) Cum. Cum. Rel. FreqCum. Cum. Rel. Freq. .

freq (less thanfreq (less than))

(less than)(less than)

15 to less than 25 5 5 5/30 or 16.7%15 to less than 25 5 5 5/30 or 16.7%

25 to less than 35 3 8 8/30 or 26.7 %25 to less than 35 3 8 8/30 or 26.7 %

35 to less than 45 7 15 15/30 or 50.0 % 35 to less than 45 7 15 15/30 or 50.0 %

45 to less than 55 5 20 20/30 or 66.7 %45 to less than 55 5 20 20/30 or 66.7 %

55 to less than 65 3 23 23/30 or 76.7 %55 to less than 65 3 23 23/30 or 76.7 %

65 to less than 75 7 30 30/30 65 to less than 75 7 30 30/30 or 100 %or 100 %

Distribution developed from less than cumulative Distribution developed from less than cumulative frequency distributionfrequency distribution

(C.I.)(C.I.) (f)(f) Cum. Cum. Rel. FreqCum. Cum. Rel. Freq. .

freq (greater than)freq (greater than)

((greater than)greater than)

15 to less than 25 5 30 30/30 or 100 %15 to less than 25 5 30 30/30 or 100 %

25 to less than 35 3 25 25/30 or 83.3 %25 to less than 35 3 25 25/30 or 83.3 %

35 to less than 45 7 22 22/30 or 73.3 % 35 to less than 45 7 22 22/30 or 73.3 %

45 to less than 55 5 15 15/30 or 50.0 %45 to less than 55 5 15 15/30 or 50.0 %

55 to less than 65 3 10 10/30 or 33.3 %55 to less than 65 3 10 10/30 or 33.3 %

65 to less than 75 7 7 7/30 or 23.3 %65 to less than 75 7 7 7/30 or 23.3 %

Graphic PresentationGraphic Presentation The data we collect can often be more easily The data we collect can often be more easily

understood for interpretation, if it is presented understood for interpretation, if it is presented graphically or pictorially.graphically or pictorially.

Diagrams and graphs give visual indications of Diagrams and graphs give visual indications of magnitudes, groupings, trends and pattern in the magnitudes, groupings, trends and pattern in the datadata

The diagrams should be clear and easy to read The diagrams should be clear and easy to read and understandand understand

Each diagram should include a brief and self Each diagram should include a brief and self explanatory title dealing with the subject matterexplanatory title dealing with the subject matter

The scale of the presentation should be chosen The scale of the presentation should be chosen in such a way that thein such a way that the resulting diagram is of resulting diagram is of appropriate sizeappropriate size

The following are the diagrammatic and graphic The following are the diagrammatic and graphic representations that are commonly usedrepresentations that are commonly used

A) Diagrammatic RepresentationA) Diagrammatic Representation

a) Bar Diagramsa) Bar Diagrams

b) Pie Diagramsb) Pie Diagrams

c) Pictogramsc) Pictograms

B) Graphic RepresentationB) Graphic Representation

a) Histograma) Histogram

b) Frequency Polygonb) Frequency Polygon

c) Cumulative Frequency Curve c) Cumulative Frequency Curve

A) Diagrammatic A) Diagrammatic RepresentationRepresentation

A Bar DiagramA Bar DiagramExampleExample Suppose that the following were the gross Suppose that the following were the gross

revenues (in $ 100,000.00s) for a company XYZ revenues (in $ 100,000.00s) for a company XYZ for the years 1980, 1981 and 1982for the years 1980, 1981 and 1982

S.N. S.N. Year Year RevenuesRevenues 1. 1980 1201. 1980 120 2. 1981 1002. 1981 100 3. 1982 603. 1982 60 The bar diagram for this data can be constructed The bar diagram for this data can be constructed

as follows, with the revenue represented by the as follows, with the revenue represented by the vertical axis and the year represented by the vertical axis and the year represented by the horizontal axis. horizontal axis.

A Bar Diagram

020406080

100120140

1 2 3 4

Year

Rev

enu

e

Series1

A Bar DiagramA Bar Diagram

A sub-Divided Bar ChartA sub-Divided Bar Chart

ExampleExample

Construct a sub-divided bar chart for the 3 types Construct a sub-divided bar chart for the 3 types of expenditure in dollars of a family of four for of expenditure in dollars of a family of four for the years 1982, 1983, 1984 and 1985the years 1982, 1983, 1984 and 1985

YearYear ExpenditureExpenditure

Food Education Other TotalFood Education Other Total

1982 3000 2000 3000 80001982 3000 2000 3000 8000

1983 3500 3000 4000 10,5001983 3500 3000 4000 10,500

1984 4000 3500 5000 12,5001984 4000 3500 5000 12,500

1985 5000 5000 6000 16, 000 1985 5000 5000 6000 16, 000

A Sub-Divided Bar Chart

02000400060008000

1000012000140001600018000

1 2 3 4

Year

Exp

en

dit

ure

Series1 Series2 Series3

Series 1 – Food Series 2 – Education Series 3- Series 1 – Food Series 2 – Education Series 3- OtherOther

Pie DiagramsPie Diagrams This type of diagram enables us to show the This type of diagram enables us to show the

partitioning of a total into its component parts. partitioning of a total into its component parts. The diagram is in the form of a circle and is The diagram is in the form of a circle and is

also called a “Pie” because the entire graph also called a “Pie” because the entire graph looks like a pie and the components resembles looks like a pie and the components resembles slices cut from it. slices cut from it.

The size of the slice represents the proportion The size of the slice represents the proportion of the component out of the totalof the component out of the total..

Pie DiagramPie DiagramExample:Example: The following figures relate to the cost of the The following figures relate to the cost of the

construction of the house, for various construction of the house, for various components that go into it represented as components that go into it represented as percentages of the total costspercentages of the total costs

ItemItem % expenditure% 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 %

Pie ChartPie Chart

Labour25%

Misc10%

Timber, glass20%

Steel15% Cement,

Bricks30%

PictogramsPictograms Pictograms means presentation of data in Pictograms means presentation of data in

the form of picturesthe form of pictures It is quite a popular method used by It is quite a popular method used by

governments and other organization for governments and other organization for informational exhibitioninformational exhibition

Its main advantage is its attraction value.Its main advantage is its attraction value. They stimulate interest in the information They stimulate interest in the information

being presentedbeing presented News magazines are very find of presenting News magazines are very find of presenting

data in this formdata in this form

B) Graphic PresentationB) Graphic Presentation

HistogramHistogram In this type of representation the given data are In this type of representation the given data are

plotted in the form of a rectanglesplotted in the form of a rectangles Class intervals are marked along the x-axis and Class intervals are marked along the x-axis and

the frequencies along the y-axis according to a the frequencies along the y-axis according to a suitable scalesuitable scale

Unlike the bar chart, which is one-dimensional Unlike the bar chart, which is one-dimensional meaning that only the length of the bar is meaning that only the length of the bar is material and not the width but histogram is two-material and not the width but histogram is two-dimensional in which the length and the width dimensional in which the length and the width are both importantare both important

A histogram is constructed from a frequency A histogram is constructed from a frequency distribution of grouped data, where the height of distribution of grouped data, where the height of the rectangle is proportional to the respective the rectangle is proportional to the respective frequency and the width represents the class frequency and the width represents the class intervalinterval

HistogramHistogram

Example:Example:

C. IC. I. . (f(f) () (Mid-PointMid-Point))

15-25 5 2015-25 5 20

25-35 3 3025-35 3 30

35-45 7 4035-45 7 40

45-55 5 5045-55 5 50

55-65 3 6055-65 3 60

65-75 7 7065-75 7 70

Frequency PolygonFrequency Polygon A frequency polygon is a line chart of frequency A frequency polygon is a line chart of frequency

distribution in which either the values of discrete distribution in which either the values of discrete variables or the mid points are joined together by variables or the mid points are joined together by straight linesstraight lines

Since the frequencies do not start at zero or end Since the frequencies do not start at zero or end at zero, this diagram as such would not touch the at zero, this diagram as such would not touch the horizontal axishorizontal axis

The curve is enclosed. The beginning of the curve The curve is enclosed. The beginning of the curve touches the horizontal axis and the last mid-point touches the horizontal axis and the last mid-point is joined with the fictitious succeeding mid point, is joined with the fictitious succeeding mid point, whose value is alsowhose value is also zero. zero.