PRESENTATION OF DATA

There are generally three forms of presentation of data:

Textual or Descriptive presentation: In textual presentation, data are described within the text.

• Example 1: The workers union called for a nationwide strike on November 23, 2017, protesting the unjust laws passed during the winter session of the Parliament. In Kerala, 13 factories were closed, and two were found open. Even the schools supported the strike of the workers in the town. Out of 7 schools, five were found to be shut on the day of the protest. 

• Example 2: According to the 2011 Census of India, the country’s population is 130 billion, out of which 57 crores were females and 73 crores were men. 71% of the population lived in rural areas, and 19% lived in cities. There were 84 crores quick lurkers in the entire country, against 46 crores workers. 

Tabular presentation: In a tabular presentation, data are presented in rows (read horizontally) and columns (read vertically).

For example, given below is a 3 x 3 table presenting information about the literacy rates in  Indian 

Literacy in India by sex and location (per cent)

 

Sex                 Location

                                Rural       Urban        Total

Male                       79                 90             82

Female                    59                 80             65

Total                        68                 84             74

Source: Census of India 2011

Classification used in tabulation is of four kinds: –

• Qualitative - When classification is done according to attributes, such as social status, physical status, nationality, etc., it is called qualitative classification.

• Quantitative - In quantitative classification, the data are classified on the basis of characteristics which are quantitative in nature, age, height, production, income, etc are quantitative characteristics.

• Temporal - In Temporal classification time becomes the classifying variable and data are categorized according to time. Time may be in hours, days, weeks, months, years, etc.

• Spatial - When classification is done on the basis of place, it is called spatial classification. The place may be a village/town, block, district, state, country, etc.

TABULATION OF DATA AND PARTS OF A TABLE

A good table should essentially have the following components:-

(i) Table number - A table should always be numbered for identification and reference in the future. A table must be numbered 1, 2, 3 etc.

(ii) Title - There must be a title on the top of the table. The title must be appealing and attractive. A good title must contain – the topic of study, the time period of study, place of study and criteria of classification of data 

(iii) Captions or Column Headings - It is the title given to the columns of a table.

A caption refers to information contained in the column of the table.

It may have sub-heads when information is divided in more than one category

For example – employees may have male and female as sub-heads

(iv)Stubs or Row Headings - Stubs are headings of horizontal rows.

These titles indicate information contained in the row of the table.

Each  row in the table should be given a heading

(v)Body of the Table -Body of a table contain numerical information which has fixed location in the table.

It indicates numerical data from top to bottom in columns and from left to right in rows.

Each item in the body is called cell.

 (vi) Unit of Measurement

(vii)Source - When tables are using secondary data, source of the data must be given.

(viii) Note

DIAGRAMMATIC PRESENTATION OF DATA

This is the third method of presenting data. There are various kinds of diagrams in common use. Amongst them the important ones are the following:

(i) Geometric diagram 

Bar diagram

Bar diagrams are rectangular and placed on the same base. Their heights represent the magnitude/value of the variable. The width of all the bars and the gaps between the two bars are kept the same.

The following are the types of one-dimensional diagram.

(1) Simple bar diagram

Simple bar diagram consists of a group of rectangular bars of equal width for each class or category of data.

Question - The following table shows the interest of students in a school in different games.

Games	Table Tennis	Volleyball	Hockey	Basketball	Cricket
Number of Students	500	300	350	400	550

Solution

(2) Multiple bar diagram

This diagram is used when we have to make a comparison between two or more variables like income and expenditure, import and export for different years, marks obtained in different subjects in different classes, etc.

Question 1. Make a multiple bar diagram of the following data:

Faculty	Number of Students
	2014-15	2015-16	2016-17
Arts Science Commerce	600 400 200	550 500 250	500 600 300

(3) Subdivided bar diagram

This diagram is constructed by subdividing the bars in the ratio of various components.

Question 

The following table shows the monthly expenditure of different families on different items.

Items of expenditure	Education	Clothing	Food	Rent	Other	Total expenditure
Family A	1,500	1,000	1,250	750	500	5,000
Family B	1,700	850	1,200	850	600	5,200
Family C	1,600	700	1,500	800	600	5,200

Represent the data in the form of a sub-divided bar diagram.

Solution

Pie-Diagram Question 3

Following are the data about the market share of four brands of TV sets sold in Panipat and Ambala. Present the data in the pie chart.

Brand of Sets	Units sold in Panipat	Units sold in Ambala
Samsung	480	625
Akai	360	500
Onida	240	438
Sony	120	312

Solution Total sets sold in Place A and Place B are 1,200 and 1,875 respectively. Data are to be represented by two circles whose radii are in the ratio of square roots of total TV sets sold in each city in the ratio of 1:1. The calculations regarding the construction of the pie diagram are as follows.

Brands of Sets	Place A			Place B
	Sets sold	Sales(₹) %	Sales in terms of components of 360°	Sets sold	Sales %	Sales in terms of components of 360°
Samsung	480	40	$\begin{array}{l}\frac{40}{100}\times {360}^{\circ }={144}^{\circ }\end{array}$	625	33.3	$\begin{array}{l}\frac{33.3}{100}\times {360}^{\circ }={119.88}^{\circ }\end{array}$
Akai	360	30	$\begin{array}{l}\frac{30}{100}\times {360}^{\circ }={108}^{\circ }\end{array}$	500	26.7	$\begin{array}{l}\frac{26.7}{100}\times {360}^{\circ }={96.12}^{\circ }\end{array}$
Onida	240	20	$\begin{array}{l}\frac{20}{100}\times {360}^{\circ }={72}^{\circ }\end{array}$	438		$\begin{array}{l}\frac{23.4}{100}\times {360}^{\circ }={84.24}^{\circ }\end{array}$
Sony	120	10	$\begin{array}{l}\frac{10}{100}\times {360}^{\circ }={36}^{\circ }\end{array}$	312	16.6	$\begin{array}{l}\frac{16.6}{100}\times {360}^{\circ }={59.76}^{\circ }\end{array}$
Total	1,200		360°	1,875		360°

(ii) Frequency diagram - Frequency diagrams are a diagrammatic or graphical representation of data, enabling a quick and clear understanding of complex data sets. Frequency diagrams are created to avoid mistakes and provide a bird’s eye view of large data sets. The large data sets are first grouped under various frequencies and then diagrammatically represented on a paper. Besides giving an accurate picture of data, the frequency diagrams reflect a definite pattern. 

The advantages of frequency diagrams are:

• It simplifies complex data sets.
• Helps represent data using appropriate diagrams.
• Saves time.
• Makes data more meaningful.
• Helps in planning, extrapolating, interpolating, and decision making with the given data.

Types of Frequency Diagrams 

Histogram- A histogram is a graphical representation of a frequency distribution of a continuous series. It is a two-dimensional diagram that looks like a bar chart. 

Present the following information in the form of a Histogram:

Marks 0-10 10-20 20-30 30-40 40-50

Number of Students 16 36 70 50 28

Solution

It is visible that the set of data given is of the equal class interval; i.e., the difference between the upper limit and the lower limit of each class interval is 10. So, drawing a Histogram is feasible.

The X-axis represents the marks (class intervals), and Y-axis represents the number of students (frequency distribution).

Histogram of Unequal Class Intervals

When histograms are drawn based on the data with unequal class intervals, they are known as Histograms of unequal class intervals. Histogram of unequal class intervals includes rectangles of different width sizes. Histogram also gives value of mode of the frequency distribution 

Present the following information in the form of a Histogram:

Present the following information in the form of a Histogram:

Wages	Number of Workers
10-15	14
15-20	20
20-25	54
25-30	30
30-40	24
40-60	24
60-80	16

Solution

1. It can be seen clearly that the given class interval is unequal. So, before plotting the histogram, frequencies have to be adjusted.

2. Determine the class of the smallest interval, i.e., 10-15. Thus, the lowest class interval in the given frequency distribution is 5.

3. Formulate the Adjusted Table as shown below:

Wages	Number of Workers	Adjustment Factor	Frequency Density (Adjusted Frequency)
10-15	14	5 ÷ 5 = 1	14 ÷ 1 = 14
15-20	20	5 ÷ 5 = 1	20 ÷ 1 = 20
20-25	54	5 ÷ 5 = 1	54 ÷ 1 = 54
25-30	30	5 ÷ 5 = 1	30 ÷ 1 = 30
30-40	24	10 ÷ 5 = 2	24 ÷ 2 = 12
40-60	24	20 ÷ 5 = 4	24 ÷ 4 = 6
60-80	16	20 ÷ 5 = 4	16 ÷ 4 = 4

• Ogive – Ogive is also known as cumulative frequency curve. Since there are two categories of cumulative frequencies – “less than” and “more than,” ogives for any grouped frequency data are also drawn in two types. While for the ‘less than’ ogives, the cumulative frequencies are plotted against upper limits of the class interval, for ‘more than’ ogives, they are plotted against the lower limits of class intervals. The shape of ‘less than’ ogive rises upward, whereas the shape of ‘more than’ ogive falls downwards. Interestingly, the intersection point of two ogives gives the median. Draw the ‘less than’ and ‘more than’ ogives on the same graph paper from the given data:

  Weekly wages (₹)	No. of workers
  0-20 20-40 40-60 60-80 80-100	10 20 40 20 10

  Solution

  (i) ‘Less than’ method

  Weekly wages (₹)	C.F
  Less 20 Less 40 Less 60 Less 80 Less 100	10 30 70 90 100

  (ii) ‘More than’ method

  Weekly wages (₹)	C.F
  More than 0 – 100 More than 20 – 90 More than 40 – 70 More than 60 – 30 More than 0 – 10	10 30 70 90 100

  Both ‘less than’ and ‘more than’ ogives based on the above data are presented in the following graph.

  

  
  

Frequency Polygon

A frequency polygon is a plane bounded by straight lines, usually four or more lines. Frequency polygon is an alternative to histogram and is also derived from histogram itself. 

A Make a frequency curve of the following data:

Age (Years)	0-10	10-20	20-30	30-40	40-50	50-60	60-70	70-80
No of Residents	150	300	500	800	1,000	900	400	100

Solution

The given data set is first converted into a histogram. The mid-points are marked on the top of the rectangles of the histogram. These points are joined through a freehand smoothed curve as shown in the figure

Frequency Curve

The frequency curve is obtained by drawing a smooth freehand curve passing through the points of the frequency polygon as closely as possible. It may not necessarily pass through all the points of the frequency polygon but it passes through them as closely as possible

Draw a frequency curve for the following distribution.

$\begin{array}{ccccccc}\text{Class-interval}& 0-10& 10-20& 20-30& 30-40& 40-50& 50-60\\ \text{Frequency}& 4& 10& 15& 18& 20& 16\end{array}$

The frequency distribution is continuous with equal class-intervals. We will first prepare a histogram and then the frequency curve. The class-intervals are shown along the X-axis and frequency on the Y-axis. 

(iii) Arithmetic line graph - An arithmetic line graph is also called time series graph. In this graph, time (hour, day/date, week, month, year, etc.) is plotted along x-axis and the value of the variable (time series data) along y-axis. A line graph by joining these plotted points, thus, obtained is called arithmetic line graph (time series graph). It helps in understanding the trend, periodicity, etc., in a long term time series data.

Draw the graph of interest on deposit for a year.

Deposits (in ₹)	10,000	20,000	30,000	40,000	50,000
Interest (in ₹)	750	1,500	2,350	3,300	4,400

Solution

Q. Statement I An arithmetic line graph is also called time series graph

(a) Both the statements are true.

Statement I is true. Statements II is false

Both the statements are false

(d) Statement Il is true, Statement 1 in fabe

Q.Statement Is Diagrammatic presentation of data translate quite effectively the highly abstract sinas contained in numbers in

Statement II: Height or length of a bar diagram can be visually compared by their relative height and accordingly dam comprehended quickly. Bars of the bar reads the magnitude of data.

(a) Both the statements are true.

(h) Both the statements are false.

(c) Statement I is true. Statement II is false.

(d) Statement Il is true, Statement I is false.

Q. Statement 1: To construct a component bar diagram, first of all, a bar is constructed on the X-axis with its height equivalent to th total value of the bar and for per cent data the bar height is of 100 units.

Statement II: A circle in a pie chart, irrespective of its value of radius, is thought of having 100 equal parts of 3.6 degre cach

(a) Both the statements are true.

(b) Both the statements are false.

(c) Statement I is true, Statement II is false.

(d) Statement Il is true, Statement I is false.

Q. Statement I: A histogram is never drawn for a continuous variable. Statement II: While constructing a histogram, if bases vary in their width, the heights of rectangles are to be adjusted no y comparable measurements. The answer in such a situation is frequency density instead of absolute frequency.

(a) Both the statements are truc.

(b) Both the statements are false.

(d) Statement II is true, Statement I is false.

(c) Statement I is true, Statement Il is false.

Q.64 Statement I: In Histogram no space is left between two rectangles, but in a Bar Diagram some space must be left berw consecutive bars.

Statement II: We can have a Bar diagram both for discrete and continuous variables.

(a) Both the statements are true.

(b) Both the statements are false.

(c) Statement I is true, Statement II is false.

(d) Statement II is true. Statement I is false.

Q. Statement I: Histogram also gives value of mode of the frequency distribution graphically. Statement II: A frequency polygon is a plane bounded by straight lines, usually four or more lines.

(a) Both the statements are true.

(b) Both the statements are false.

(c) Statement 1 is true, Statement II is false.

(d) Statement II is true, Statement I is false.

Q Statement I: Frequency polygon is an alternative to and is also derived from histogram itself.

Statement II: The simplest method of drawing a frequency polygon is to join the midpoints of the topside of the conse

rectangles of the histogram.

(a) Both the statements are true.

(b) Both the statements are false.

(c) Statement I is true, Statement Il is false.

d) Statement II is true, Statement I is false.

Q. Statement I: When comparing two or more distributions plotted on the same axes, frequency curve is likely to be more use histogram since the vertical and horizontal lines of two or more distributions may coincide in a histogram. Statement Ili The frequency polygon is obtained by drawing a smooth freehand curve passing through the points of the fr

polygon as closely as possible.

(a) Both the statements are true.

(c) Statement I is true, Statement II is false.

(b) Both the statements are false.

(d) Statement 11 is true. Statement I is false.