Covers T.R. Jain & V.K. Ohri (2026-27) ch 5-8. Based on NCERT Statistics for Economics, Chapter 4 (Reprint 2026-27) and the CBSE 2026-27 curriculum (Unit 2). The UP, Bihar, Rajasthan and MP boards teach the same chapter in Class 11.
- present data in textual, tabular and diagrammatic form
- identify qualitative, quantitative, temporal and spatial classification and write all eight parts of a table
- draw simple, multiple and component bar diagrams, and a pie diagram with computed angles
- draw a histogram with equal and unequal class widths, a frequency polygon, a frequency curve and both ogives
- find the mode from a histogram and the median from ogives graphically, and draw an arithmetic line graph
1 Why and how data are presented
- Collected data are generally voluminous; they must be put in a compact and presentable form so that they can be used readily and understood easily
- According to the book, there are generally three forms of presentation of data
Textual or descriptive
Data described within the text; for small quantities of data
Tabular
Data in rows and columns; for any volume of data
Diagrammatic
Data as bars, circles, rectangles, lines; the quickest understanding
2 Textual presentation of data
In textual (descriptive) presentation, data are described within the text. When the quantity of data is not too large, this form of presentation is more suitable.
In a bandh call given on 08 September 2005 protesting the hike in prices of petrol and diesel, 5 petrol pumps were found open and 17 were closed, whereas 2 schools were closed and the remaining 9 schools were found open in a town of Bihar.
- Indian population had risen to 102 crore: 49 crore females and 53 crore males
- 74 crore people lived in rural India and only 28 crore in towns or cities
- There were 62 crore non-workers against 40 crore workers in the entire country
- Urban India had an even higher share of non-workers: 19 crore non-workers against 9 crore workers; rural India had 31 crore workers out of 74 crore
Merit and drawback of textual presentation
Merit
- Simplest for a small amount of data
- Certain points of the presentation can be emphasised (e.g. “only 28 crore lived in towns”)
Serious drawback
- One has to go through the complete text to understand it
- Comparison becomes hard when there are many figures
3 Tabular presentation of data
In tabular presentation, data are presented in rows (read horizontally) and columns (read vertically).
| Sex | Rural | Urban | Total |
|---|---|---|---|
| Male | 79 | 90 | 82 |
| Female | 59 | 80 | 65 |
| Total | 68 | 84 | 74 |
Source: Census of India 2011 (literacy rates relate to the population aged 7 years and above)
- It has 3 rows (male, female, total) and 3 columns (rural, urban, total), so it is a 3 × 3 table giving 9 items of information in 9 boxes
- A brief description of the row headings may also be given at the left-hand top of the table
- Each box is a cell of the table; each cell relates an attribute (male, female or total) with a number (a literacy percentage)
- The most important advantage of tabulation: it organises data for further statistical treatment and decision-making
3.1 The four kinds of classification used in tabulation
Qualitative classification: classification done according to attributes, such as social status, physical status or nationality. In Table 4.1 the attributes for classification, sex and location, are qualitative.
Quantitative classification: data are classified on the basis of characteristics that can be measured quantitatively (age, height, production, income). Classes are formed by assigning limits called class limits.
| Age group (yrs) | No. of respondents | Per cent |
|---|---|---|
| 20-30 | 3 | 0.55 |
| 30-40 | 61 | 11.25 |
| 40-50 | 132 | 24.35 |
| 50-60 | 153 | 28.24 |
| 60-70 | 140 | 25.83 |
| 70-80 | 51 | 9.41 |
| 80-90 | 2 | 0.37 |
| All | 542 | 100.00 |
Source: Assembly election Patna central constituency 2005, A.N. Sinha Institute of Social Studies, Patna. The book prints the 60-70 row and the “All” count as “?” and asks you to calculate them; 542 comes from the title.
Given
Total respondents = 542; the other six classes have 3, 61, 132, 153, 51, 2
To find
The missing number and its per cent
Formula: missing number = total − sum of the known numbers; per cent = (class number ÷ total) × 100
Substitution: 3 + 61 + 132 + 153 + 51 + 2 = 402; missing number = 542 − 402 = 140
Result: per cent = (140 ÷ 542) × 100 = 25.83%
Interpretation: about a quarter of the respondents were aged 60-70; the largest group (153) was aged 50-60.
Temporal classification: time becomes the classifying variable, and data are categorised according to time (hours, days, weeks, months, years etc.).
| Years | 1995 | 1996 | 1997 | 1998 | 1999 | 2000 |
|---|---|---|---|---|---|---|
| Sale (Rs in lakhs) | 79.2 | 81.3 | 82.4 | 80.5 | 100.2 | 91.2 |
Data source: Unpublished data
Spatial classification: classification on the basis of place. The place may be a village/town, block, district, state, country etc.
| Destination | Export share | Destination | Export share |
|---|---|---|---|
| USA | 12.5 | Russia | 0.7 |
| Germany | 2.4 | China | 4.7 |
| Other EU | 10.9 | West Asia-Gulf Coop. Council | 15.3 |
| UK | 3.1 | Other Asia | 29.4 |
| Japan | 2.2 | Others | 18.8 |
| All | 100.0 (Total exports: US $ 314.40 billion) | ||
| Classification | Basis | Book’s table | Other examples |
|---|---|---|---|
| Qualitative | Attributes (cannot be measured) | 4.1 (sex, location) | Religion, caste, nationality |
| Quantitative | Measurable characteristic, with class limits | 4.2 (age) | Height (cm), weight (kg), income |
| Temporal | Time | 4.3 (years) | Monthly rainfall, daily sales |
| Spatial | Place | 4.4 (destinations) | State-wise output, district-wise literacy |
- Calling “age” qualitative is wrong; age can be measured, so classification by age is quantitative
- Mixing up temporal and spatial: years/months = temporal; states/countries/districts = spatial
4 Tabulation of data and parts of a table
- The simplest way to conceptualise a table: data presented in rows and columns along with some explanatory notes
- Depending on the number of characteristics involved, tabulation can be one-way (one characteristic), two-way (two) or three-way (three). Table 4.5 is three-way: location, gender and working status
(i) Table number
for identification
(ii) Title
narrates the contents
(iii) Captions
column headings
(iv) Stubs
row headings
(v) Body
the actual data
(vi) Unit of measurement
stated with the title
(vii) Source
where the data came from
(viii) Note
last part, explanation
(i) Table number is assigned for identification; when there is more than one table, it distinguishes one from another. It is given at the top or at the beginning of the title. Numbers are whole numbers in ascending order; subscripted numbers like 1.2, 3.1 identify the location: Table 4.5 is the fifth table of the fourth chapter.
(ii) Title narrates the contents of the table. It must be clear, brief and carefully worded so that interpretations are free from ambiguity. It is placed at the head of the table, after the table number or just below it.
(iii) Caption or column heading: the designation at the top of each column that explains the figures of that column.
(iv) Stubs or row headings: the heading given to each row. The designations of the rows are called stubs or stub items, and the complete left column is the stub column.
(v) Body of the table is the main part and contains the actual data. The location of any figure is fixed by its row and column.
(vi) Unit of measurement should always be stated along with the title. If rows or columns have different units, they are stated with the stubs or captions. Large figures are rounded and the method of rounding is indicated.
(vii) Source is a brief statement or phrase indicating the source of the data. If there is more than one source, all are written. It is generally written at the bottom of the table.
(viii) Note is the last part of the table. It explains a specific feature of the data that is not self-explanatory and has not been explained earlier.
| Location | Gender | Workers | Non-worker | Total | ||
|---|---|---|---|---|---|---|
| Main | Marginal | Total | ||||
| Rural | Male | 17 | 3 | 20 | 18 | 38 |
| Female | 6 | 5 | 11 | 25 | 36 | |
| Total | 23 | 8 | 31 | 43 | 74 | |
| Urban | Male | 7 | 1 | 8 | 7 | 15 |
| Female | 1 | 0 | 1 | 12 | 13 | |
| Total | 8 | 1 | 9 | 19 | 28 | |
| All | Male | 24 | 4 | 28 | 25 | 53 |
| Female | 7 | 5 | 12 | 37 | 49 | |
| Total | 31 | 9 | 40 | 62 | 102 | |
Source: Census of India 2001 · Note: Figures are rounded to the nearest crore. (Table 4.5 presents in tabular form the same data given in Case 2 of textual presentation.)
| Part, in Table 4.5 | Where / what |
|---|---|
| Table number | “Table 4.5”, at the top |
| Title | “Population of India according to workers and non-workers by gender and location, 2001” |
| Captions | Workers (main, marginal, total), non-worker, total |
| Stubs | Location (rural, urban, all) and gender (male, female, total), in the left columns |
| Body | All the figures; e.g. the second row and fourth column (rural female, non-worker): 25 crore rural females were non-workers |
| Unit | “(Crore)”, with the title |
| Source | Census of India 2001, at the bottom |
| Note | Figures rounded to the nearest crore |
For “describe the parts of a good table”, write all eight parts in order, each with a one-line meaning, and if possible draw a small skeleton table with the parts labelled.
5 Diagrammatic presentation of data
- This is the third method; it gives the quickest understanding of the actual situation compared with textual or tabular presentation
- Diagrams translate the highly abstract ideas contained in numbers into a more concrete and easily understood form
- Diagrams may be less accurate but are much more effective than tables in presenting data
Geometric diagram
Bar diagram (simple, multiple, component) and pie diagram
Frequency diagram
Histogram, frequency polygon, frequency curve, ogive
Arithmetic line graph
Also called a time series graph
5.1 Bar diagram
A simple bar diagram comprises a group of equispaced and equiwidth rectangular bars, one for each class or category. The height or length of a bar reads the magnitude of the data; the lower end touches the base line so that the height starts from the zero unit.
- Bars are compared by their relative heights, so data are understood quickly; a longer bar (literacy of Kerala) has more of the characteristic than a shorter one (literacy of West Bengal)
- Bar diagrams suit both frequency and non-frequency data; discrete variables (family size, spots on a dice, grades) and attributes (gender, religion, caste, country)
- They are more convenient for non-frequency data such as income-expenditure profiles and exports/imports over the years; bars (columns) are usually used for time series data (food grain produced between 1980 and 2000, decadal variation in work participation rate, registered unemployed over the years, literacy rates)
- The values of the characteristics (measured or counted) retain the identity of each value
| State | 2001 | 2011 | ||
|---|---|---|---|---|
| Male | Female | Male | Female | |
| Andhra Pradesh (AP) | 70.3 | 50.4 | 75.6 | 59.7 |
| Assam (AS) | 71.3 | 54.6 | 78.8 | 67.3 |
| Bihar (BR) | 59.7 | 33.1 | 73.4 | 53.3 |
| Jharkhand (JH) | 67.3 | 38.9 | 78.4 | 56.2 |
| Gujarat (GJ) | 79.7 | 57.8 | 87.2 | 70.7 |
| Haryana (HR) | 78.5 | 55.7 | 85.3 | 66.8 |
| Karnataka (KA) | 76.1 | 56.9 | 82.9 | 68.1 |
| Kerala (KE) | 94.2 | 87.7 | 96.0 | 92.0 |
| Madhya Pradesh (MP) | 76.1 | 50.3 | 80.5 | 60.0 |
| Chhattisgarh (CH) | 77.4 | 51.9 | 81.5 | 60.6 |
| Maharashtra (MR) | 86.0 | 67.0 | 89.8 | 75.5 |
| Odisha (OD) | 75.3 | 50.5 | 82.4 | 64.4 |
| Punjab (PB) | 75.2 | 63.4 | 81.5 | 71.3 |
| Rajasthan (RJ) | 75.7 | 43.9 | 80.5 | 52.7 |
| Tamil Nadu (TN) | 82.4 | 64.4 | 86.8 | 73.9 |
| Uttar Pradesh (UP) | 68.8 | 42.2 | 79.2 | 59.3 |
| Uttarakhand (UK) | 83.3 | 59.6 | 88.3 | 70.7 |
| West Bengal (WB) | 77.0 | 59.6 | 82.7 | 71.2 |
| India | 75.3 | 53.7 | 82.1 | 65.5 |
- Categories (states) on the X-axis, values (literacy %) on the Y-axis; start the Y scale at zero
- Keep all bars of equal width with equal gaps between them
- Make each bar’s height equal to its value (e.g. Kerala 96.0) and write the value on top
- Add the title, axis labels, unit and source
Multiple bar diagrams are used for comparing two or more sets of data, for example income and expenditure or imports and exports over years, or marks in different subjects in different classes. Two or more bars stand side by side for each category, with different shades shown in a legend.
- Female literacy rose across the country between 2001 and 2011; every state’s 2011 bar is taller than its 2001 bar
- The sharpest rise was in Bihar (33.1 to 53.3, i.e. 20.2 points), Jharkhand (17.3 points) and Uttar Pradesh (17.1 points)
- In 2011, 10 states (AS, GJ, HR, KA, KE, MR, PB, TN, UK, WB) had female literacy above the national average of 65.5
- The gap between the highest and lowest female literacy fell from 87.7 − 33.1 = 54.6 points in 2001 (Kerala − Bihar) to 92.0 − 52.7 = 39.3 points in 2011 (Kerala − Rajasthan)
Component bar diagrams (also called sub-diagrams) divide a bar into its components (the elements or parts that a thing is made of). They compare the sizes of components and show the relationship among them, e.g. sales proceeds from different products, the expenditure pattern of a typical Indian family (food, rent, medicine, education, power), budget receipts and expenditures, components of the labour force.
| Gender | Enrolled (per cent) | Out of school (per cent) |
|---|---|---|
| Boy | 91.5 | 8.5 |
| Girl | 58.6 | 41.4 |
| All | 78.0 | 22.0 |
Data source: Unpublished data
- Draw a bar on the X-axis whose height equals the total value; for per cent data every bar is 100 units tall
- Otherwise, equate the height to the total and work out the components’ proportional heights by the unitary method
- Smaller components are given priority in parting the bar
- Shade or colour the components and add a legend
5.2 Pie diagram
A pie diagram (pie chart) is also a component diagram, but instead of a bar it is a circle whose area is proportionally divided among the components. The circle is divided into as many parts as there are components by straight lines from the centre to the circumference.
- Pie charts are usually not drawn with absolute values; each category is first expressed as a percentage of the total
- Whatever its radius, the circle is thought of as having 100 equal parts of 3.6° (360°/100) each
- Angle at the centre for a component = its percentage × 3.6°
- Data shown by a component bar diagram can be shown equally well by a pie chart; the only requirement is converting absolute values into percentages
| Status | Population | Per cent | Angular component |
|---|---|---|---|
| Marginal worker | 12 | 9.9 | 36° |
| Main worker | 36 | 29.8 | 107° |
| Non-worker | 73 | 60.3 | 217° |
| All | 121 | 100.0 | 360° |
The book prints the total as 102; the three parts add to 121, and the book’s per cents and angles are worked on 121.
Given
Marginal workers 12, main workers 36, non-workers 73 crore; total 121 crore
To find
The angle of each component at the centre
Formula: angle = (value ÷ total) × 100 × 3.6°
Substitution: 12 ÷ 121 × 100 = 9.9%, 9.9 × 3.6 = 35.64° ≈ 36°; 36 ÷ 121 × 100 = 29.8%, 29.8 × 3.6 = 107.28° ≈ 107°; 73 ÷ 121 × 100 = 60.3%, 60.3 × 3.6 = 217.08° ≈ 217°
Check: 36° + 107° + 217° = 360° (the full circle)
Interpretation: in 2011 about 60% of India’s population were non-workers, the largest slice of the pie.
- Taking the per cent as the angle (writing 60.3°) is wrong; multiply the per cent by 3.6
- After rounding, check that the angles add up to 360°
- The size (area) of the pie does not show the total value; whatever the radius, the total is always 100% = 360°
5.3 Frequency diagrams
Data in the form of grouped frequency distributions are generally represented by frequency diagrams: histogram, frequency polygon, frequency curve and ogive.
5.4 Histogram
A histogram is a two-dimensional diagram. It is a set of rectangles with bases as the intervals between class boundaries (along the X-axis) and with areas proportional to the class frequency.
- If the class intervals are of equal width (as they generally are), the areas are proportional to the frequencies, so height = frequency
- A histogram is never drawn for a discrete variable. For a continuous variable the lower boundary of a class fuses with the upper boundary of the previous one, so all rectangles are adjacent, with no open space between them
- If the classes are not continuous (45-49, 50-54), they are first converted into continuous classes (44.5-49.5, 49.5-54.5), as in Chapter 3
- Sometimes the common portion between adjacent rectangles is omitted to give a better impression of continuity; the figure then looks like a double staircase
| Daily earning (Rs) | Continuous class | Wage earners (f) | Daily earning (Rs) | Continuous class | Wage earners (f) |
|---|---|---|---|---|---|
| 45-49 | 44.5-49.5 | 2 | 85-89 | 84.5-89.5 | 9 |
| 50-54 | 49.5-54.5 | 3 | 90-94 | 89.5-94.5 | 7 |
| 55-59 | 54.5-59.5 | 5 | 95-99 | 94.5-99.5 | 6 |
| 60-64 | 59.5-64.5 | 3 | 100-104 | 99.5-104.5 | 4 |
| 65-69 | 64.5-69.5 | 6 | 105-109 | 104.5-109.5 | 2 |
| 70-74 | 69.5-74.5 | 7 | 110-114 | 109.5-114.5 | 3 |
| 75-79 | 74.5-79.5 | 12 | 115-119 | 114.5-119.5 | 3 |
| 80-84 | 79.5-84.5 | 13 | Total | 85 | |
Source: Unpublished data. To make the classes continuous, 0.5 was subtracted from each lower limit and added to each upper limit (half of 50 − 49 = 1).
- The tallest rectangle is the modal class: 79.5-84.5 (f = 13)
- Join the top-left corner of the modal rectangle to the top-left corner of the next rectangle, and its top-right corner to the top-right corner of the previous rectangle; the two lines cross
- Drop a perpendicular from the crossing to the X-axis; its foot is the mode
- Here mode = 79.5 + (13 − 12) ÷ [(13 − 12) + (13 − 9)] × 5 = 79.5 + 1 = Rs 80.5 (the book’s figure reads about 80.6)
Interpretation: the most common daily earning in this locality is about Rs 80-81.
5.5 Histogram with unequal class intervals: frequency density
- Some data need classes of varying width. The book’s example: when tabulating deaths by age at death, very short age intervals (0, 1, 2, … yrs / 0, 7, 28, … days) are meaningful at the beginning, because death rates are very high at those ages
- Height of a rectangle = area ÷ base = frequency ÷ class width
- When bases vary, heights must be adjusted; the answer is frequency density instead of absolute frequency
Frequency density = class frequency ÷ width of the class interval. In a histogram with unequal class intervals, this is the height of each rectangle.
Given
Weekly pocket money (₹) of 60 students: 0-10: 5, 10-20: 8, 20-40: 20, 40-50: 12, 50-80: 15
To find
Heights of the rectangles
Formula: frequency density = f ÷ class width
| Class | f | Width | Frequency density (height) | Adjusted frequency (width 10) |
|---|---|---|---|---|
| 0-10 | 5 | 10 | 5 ÷ 10 = 0.5 | 5 |
| 10-20 | 8 | 10 | 8 ÷ 10 = 0.8 | 8 |
| 20-40 | 20 | 20 | 20 ÷ 20 = 1.0 | 20 × 10 ÷ 20 = 10 |
| 40-50 | 12 | 10 | 12 ÷ 10 = 1.2 | 12 |
| 50-80 | 15 | 30 | 15 ÷ 30 = 0.5 | 15 × 10 ÷ 30 = 5 |
Result: heights 0.5, 0.8, 1.0, 1.2, 0.5; total area = 5 + 8 + 20 + 12 + 15 = 60 = total frequency
Interpretation: 20-40 holds 20 students, but the class is twice as wide; its density (1.0) is lower than that of 40-50 (1.2). Without adjustment the 20-40 rectangle would look misleadingly the biggest.
An equivalent method uses adjusted frequency = (smallest class width ÷ class width) × f. It equals frequency density multiplied by the smallest width, so the shape of the histogram is the same. Write the book’s method (frequency density); you may mention this alternative.
5.6 Histogram vs bar diagram
| Basis | Bar diagram | Histogram |
|---|---|---|
| Dimension | One-dimensional: only the height matters | Two-dimensional: height and width (area) |
| Width | All bars equal, but width is unimportant for comparison; a single vertical line could serve the same purpose | Width = class width; as important as the height |
| Spacing | Some space must be left between consecutive bars (except multiple and component bars) | Rectangles adjacent, no space |
| Variable | Discrete and continuous variables, and attributes | Only a continuous variable |
| Graphical measure | None | Mode, graphically |
5.7 Frequency polygon
A frequency polygon is a plane bounded by straight lines, usually four or more. It is an alternative to the histogram and is derived from the histogram itself.
- Join the mid-points of the topsides of consecutive rectangles of the histogram by straight lines
- This leaves the two ends away from the base line, so the area under the curve cannot be calculated
- The solution: join the two end-points to the base line at the mid-values of the two classes with zero frequency at each end (here 42 and 122), using broken lines or dots
- Now the total area under the polygon, like the area of the histogram, represents the total frequency (sample size)
- It is the most common method of presenting a grouped frequency distribution
- Class boundaries or class marks may be used along the X-axis, but frequencies (ordinates) are always plotted against the mid-points of class intervals
- A frequency polygon can be fitted to a histogram for studying the shape of the curve; it can also be drawn directly by plotting (mid-point, frequency) points without a histogram
- For comparing two or more distributions on the same axes the polygon is more useful, since the vertical and horizontal lines of two histograms may coincide
5.8 Frequency curve
A frequency curve is a smooth freehand curve drawn through the points of the frequency polygon as closely as possible. It need not pass through all the points, but passes as close to them as possible.
5.9 Ogive
An ogive is also called a cumulative frequency curve. Instead of simple frequencies, cumulative frequencies are plotted along the Y-axis against class limits. As there are two types of cumulative frequency, any grouped distribution has two ogives: the ‘less than’ ogive and the ‘more than’ ogive.
| Marks | No. of students | Marks | ‘Less than’ c.f. | Marks | ‘More than’ c.f. |
|---|---|---|---|---|---|
| 0-20 | 6 | Less than 20 | 6 | More than 0 | 64 |
| 20-40 | 5 | Less than 40 | 6 + 5 = 11 | More than 20 | 64 − 6 = 58 |
| 40-60 | 33 | Less than 60 | 11 + 33 = 44 | More than 40 | 58 − 5 = 53 |
| 60-80 | 14 | Less than 80 | 44 + 14 = 58 | More than 60 | 53 − 33 = 20 |
| 80-100 | 6 | Less than 100 | 58 + 6 = 64 | More than 80 | 20 − 14 = 6 |
| Total | 64 | ||||
‘Less than’ ogive
- Cumulative frequencies plotted against the upper limits
- Points: (20, 6), (40, 11), (60, 44), (80, 58), (100, 64); start (0, 0)
- Never decreasing (rises from left to right)
‘More than’ ogive
- Cumulative frequencies plotted against the lower limits
- Points: (0, 64), (20, 58), (40, 53), (60, 20), (80, 6); end (100, 0)
- Never increasing (falls from left to right)
Given
N = 64, so N/2 = 32; the 32nd value lies in 40-60 (cumulative frequency 11 to 44)
To find
The median
Graphical method: drop a perpendicular to the X-axis from the point where the two ogives cross. The crossing is at a height of N/2 = 32
Formula (detailed in Chapter 5): median = L + [(N/2 − c.f.) ÷ f] × h
Substitution: 40 + [(32 − 11) ÷ 33] × 20 = 40 + 12.73 = 52.73 marks
Interpretation: half the students (32) scored below 52.73 and half above. The crossing point and the formula give the same answer. The ‘less than’ ogive alone also gives the median: draw a horizontal line from N/2 = 32 on the Y-axis to the ogive, then a perpendicular to the X-axis.
- Plotting ‘less than’ cumulative frequency against the lower limit is wrong; ‘less than’ → upper limit, ‘more than’ → lower limit
- Plotting an ogive at mid-points (as in a polygon) is wrong; ogives use class limits
- The median is the X-coordinate of the crossing, not the Y-coordinate (32)
- The median needs the data arranged (cumulated) first
5.10 Arithmetic line graph
An arithmetic line graph is also called a time series graph. Time (hour, day/date, week, month, year etc.) is plotted along the X-axis and the value of the variable (time series data) along the Y-axis; joining the plotted points gives the line graph. It helps in understanding the trend, periodicity etc. in long-term time series data.
| Year | Exports | Imports | Year | Exports | Imports |
|---|---|---|---|---|---|
| 1993-94 | 698 | 731 | 2004-05 | 3753 | 5011 |
| 1994-95 | 827 | 900 | 2005-06 | 4564 | 6604 |
| 1995-96 | 1064 | 1227 | 2006-07 | 5718 | 8815 |
| 1996-97 | 1188 | 1389 | 2007-08 | 6559 | 10123 |
| 1997-98 | 1301 | 1542 | 2008-09 | 8408 | 13744 |
| 1998-99 | 1398 | 1783 | 2009-10 | 8455 | 13637 |
| 1999-2000 | 1591 | 2155 | 2010-11 | 11370 | 16835 |
| 2000-01 | 2036 | 2309 | 2011-12 | 14660 | 23455 |
| 2001-02 | 2090 | 2452 | 2012-13 | 16343 | 26692 |
| 2002-03 | 2549 | 2964 | 2013-14 | 19050 | 27154 |
| 2003-04 | 2934 | 3591 |
Source: DGCI&S, Kolkata
- For the period 1993-94 to 2013-14, imports were more than exports all through the period: the import line lies above the export line every year
- Both exports and imports rose rapidly after 2001-02
- The gap between the two widened after 2001-02: 2452 − 2090 = 362 in 2001-02, 27154 − 19050 = 8104 in 2013-14 (Rs in 100 crores)
- How many rows and columns are essentially required to form a table? One row of captions and at least one row of data, and one stub column and at least one column of data; i.e. at least 2 rows and 2 columns
- Can the column/row headings of a table be quantitative? Yes; in quantitative classification the headings are class limits (age groups 20-30, 30-40 in Table 4.2)
- How are the totals arrived at in Table 4.1? The total rate is not a simple average but a weighted average by the size of the male and female (or rural and urban) populations; so male 82 and female 65 give a total of 74, not 73.5
- Rounding Tables 4.2 and 4.3: e.g. per cents 0.55, 11.25, 24.35, 28.24, 25.83, 9.41, 0.37 become 0.6, 11.3, 24.4, 28.2, 25.8, 9.4, 0.4 (one decimal), and sales 79.2, 81.3, 82.4, 80.5, 100.2, 91.2 become 79, 81, 82, 81, 100, 91 (Rs lakh); state the method of rounding in a note
- Table of students’ liking for Star News, Zee News, BBC World, CNN, Aaj Tak and DD News: first column the channels (stubs), second the number of students, third the per cent; it is a qualitative classification
- Present the first two sentences of Case 2 as a table: rows male/female/total, columns rural/urban/total (male 38, 15, 53; female 36, 13, 49; total 74, 28, 102 crore, from Table 4.5)
- Represent Fig 4.4 by a component bar diagram: one bar 100 units tall divided into 9.9 (marginal), 29.8 (main) and 60.3 (non-worker), smaller components first
- Does the area of a pie have any bearing on the total value? No; whatever the radius, the total is always treated as 100% = 360°
6 Which diagram when? (one table)
| Kind of data | Suitable diagram | Example |
|---|---|---|
| Values of one variable across categories/years | Simple bar diagram | Male literacy by state, monthly rainfall |
| Comparison of two or more sets, category by category | Multiple bar diagram | Female literacy 2001 vs 2011, exports and imports |
| Parts of a total, for several groups | Component bar diagram | Enrolled and out-of-school boys/girls |
| Parts of a total, in per cent | Pie diagram | Population by working status, cost components |
| Grouped frequency distribution of a continuous variable | Histogram, polygon, curve | Daily earnings, marks |
| Cumulative frequencies, median | Ogive | ‘Less than’ and ‘more than’ marks |
| Values changing over time (trend) | Arithmetic line graph | Exports and imports by year, GDP growth rates |
- Drawing bars touching each other in a bar diagram (gaps needed) and leaving gaps between histogram rectangles (none allowed)
- Drawing a histogram for discrete data (family size); use a bar diagram
- Using frequency as the height when class widths are unequal; find frequency density first
- Leaving the polygon’s ends in the air; take them to the base line at the mid-points of the zero-frequency classes
- Not starting the Y-axis at zero; a bar’s height starts from the zero unit
7 Conclusion (book)
- You have learnt how data can be presented in textual, tabular and diagrammatic form
- You can choose the appropriate form of presentation and the type of diagram for a given set of data (see the “Which diagram when?” table)
- Thus presentation of data can be made meaningful, comprehensive and purposeful
- Data (even voluminous data) speak meaningfully through presentation
- For small data, textual presentation serves better; for large data, tables
- Tabulated data can be presented through diagrams for quicker understanding
- Classification: qualitative (attributes), quantitative (measurement), temporal (time), spatial (place)
- 8 parts of a table: number, title, captions, stubs, body, unit, source, note
- Bar diagram is one-dimensional; histogram is two-dimensional
- Pie: angle = per cent × 3.6°; book’s Table 4.8: 36°, 107°, 217°
- Unequal classes: height = frequency density
- Histogram → mode (80.5 for Table 4.9); ogives → median (52.73 for Table 4.10)
- ‘Less than’ → upper limits, never decreasing; ‘more than’ → lower limits, never increasing
- Line graph: trend; imports exceeded exports every year from 1993-94 to 2013-14
- Can I write all eight parts of a table in order and show them on a sample table?
- Can I get 36°, 107°, 217° from 12, 36, 73 crore?
- Can I make a frequency density table for unequal classes?
- Can I draw the two slanting lines on a histogram and show the mode?
- Can I draw both ogives on one graph and read the median 52.73?
- Can I write four differences between a bar diagram and a histogram without looking?