Bar diagrams, the line-and-bar graph and the histogram

Detail

1. The bar diagram (columnar diagram): basic rules

• A bar diagram (also called a columnar diagram) shows data as rectangular bars.
• Rules for drawing one:
• All bars have the same width.
• Bars stand at equal spacing (the same gap between each pair).
• Bar length (height) is proportional to the value. A bar twice as tall means a value twice as large.

• Bars are shaded or coloured so they are easy to tell apart.

• Only the length carries meaning. The width is fixed, so the width tells you nothing.

• Bars can stand upright (vertical) or lie flat (horizontal). Upright bars are used most often for time series such as months or census years.
• There are three types: simple, multiple and compound.

2. Simple bar diagram

• Definition: one bar for each item. Only one variable is shown. It is used for quick comparison.
• How to arrange the bars:
• Normally put them in ascending or descending order, so the ranking is clear at a glance.

• Exception: keep a time series (months, years) in time order. If you sorted the months by value, the seasonal rhythm would be lost.

• NCERT example: monthly rainfall of Thiruvananthapuram (Table 3.3, Fig. 3.4).

• Thiruvananthapuram is the capital of Kerala, on the south-west coast of India, at about 8.5°N.
• There are 12 bars, January to December, kept in month order.
• The peak is in June, at 35.6 cm. This is when the south-west monsoon first reaches the Kerala coast.

• A second rise in Oct–Nov shows the retreating (north-east) monsoon rain on the southern tip.

• Steps to draw it:

• Choose a scale for the Y-axis (for example, 1 cm = 5 cm of rain).
• Mark the months on the X-axis with equal gaps.
• Draw each bar to its value and shade them all the same way, since there is only one variable.

3. Multiple bar diagram

• Definition: for each item, two or more bars stand next to each other, one for each variable. Each variable has its own shade, and a key (legend) explains the shades.
• It is used to compare variables within each item and across items.
• NCERT example: literacy in India by census (Table 3.5, Fig. 3.6). Each census year has three adjoining bars: total, male and female.

Census	Total (%)	Male (%)	Female (%)
1951	18.33	27.16	8.86
2011	73.0	80.9	64.6

• What the diagram shows:
• All three bars grow over time.

• The gap between the male and female bars gets smaller in relative terms. In 1951 male literacy was about 3 times female literacy. In 2011 the gap was 16.3 percentage points.

• Other official figures for the same census:

• MOSPI's Women and Men in India 2014 gives Census 2011 literacy as 74.04% (persons), 82.14% (male) and 65.46% (female) [2] (NCERT: 73.0, 80.9, 64.6).

• Different publications use different figure sets, so always note which table a question uses.

• Watch the age base when you compare years:

• Literacy rates for 1951, 1961 and 1971 are for people aged 5 years and above.
• Rates from 1981 onwards are for people aged 7 years and above [2].

• The 1951 figures for persons, male and female are effective literacy rates (literates as a share of the population of the stated age, not of all people) [2].

• State extremes for Census 2011: Kerala was highest at about 94%, and Bihar was lowest at 63.82% [2]. A simple bar diagram of states, sorted in descending order, would start with Kerala and end with Bihar.

• Another dataset suited to a multiple bar diagram: adult literacy (age 15+).
• Male adult literacy rose from 73.4% to 78.8% between 2001 and 2011.
• Female adult literacy rose from 47.8% to 59.3% over the same period [2].

4. Compound bar diagram

• Definition: one bar per item shows the total, and the bar is split into rectangles, one for each part. It is also called a sub-divided or component bar diagram.
• It shows two things at once:
• the size of the total (the full bar length), and

• the share of each part (the length of each segment).

• NCERT example: gross electricity generation in India (Economic Survey 2011-12; Table 3.6, Fig. 3.7).

• Each year has one bar, divided into thermal, hydro and nuclear.
• The total grew from 741.2 billion kWh in 2008-09 to 844.8 billion kWh in 2010-11.

• The thermal segment is by far the largest in every year, which shows how much India depends on coal-based power.

• Steps to draw it:

• Draw the full bar to the total value.
• Mark off each part in turn, cumulatively, starting from the base.
• Use the same order of parts in every bar (for example, thermal at the bottom, then hydro, then nuclear).
• Give each part its own shade and add a key.

5. Exercise trap: multiple vs compound

Feature	Multiple bar diagram	Compound bar diagram
Bars per item	2 or more, side by side	1, split into segments
Variables are	separate, and can overlap (total, male, female)	parts that add up to a whole
Best for	comparing variables with each other	showing the total and its make-up
NCERT example	literacy 1951–2011	electricity generation 2008-09 to 2010-11

• Test question: do the parts add up to a total?
• Yes → compound.

• No → multiple.

• Literacy cannot go in a compound bar. Male % + female % ≠ total %, because these are rates, not counts.

• Electricity can. Thermal + hydro + nuclear = total generation.

6. Line and bar graph

• Definition: a single graph that uses both a line and bars over a shared X-axis (usually the 12 months).
• It has two Y-axes, one on each side, each with its own unit and scale.
• Rainfall is drawn as bars against one Y-axis (cm).

• Temperature is drawn as a line against the other Y-axis (°C).

• Why each variable gets its shape:

• Rainfall is a total collected over the month. Each month's amount is separate, so bars fit it.

• Temperature is a continuous average that changes smoothly from month to month, so a line fits it.

• NCERT example: Delhi (Table 3.4, Fig. 3.5). Delhi is at about 28.6°N, on the Yamuna, in the north-western plains.

• Temperature rises from 14.4°C in January to 33.3°C in May–June, the hot dry pre-monsoon season.
• Rainfall bars stay low until the monsoon arrives. They peak at 19.3 cm in July.

• Temperature drops slightly in July–August even though the sun is high. This is because cloud cover and rain cool the air.

• Use: this is the standard way to show a weather station's climate. Such a graph is often called a climograph or climatic graph. NCERT's exercise asks you to draw one for Kolkata, a humid station in eastern India on the Hugli.

• Steps to draw it:
• Mark the months on the X-axis.
• Draw the left and right Y-axes with suitable scales.
• Draw the rainfall bars first.
• Plot each temperature at the middle of its month's bar, then join the points with a smooth line.
• Add a key and the station's name.

7. Histogram

• Definition: a histogram is a graph of a frequency distribution.

• A frequency distribution is a table that shows how many observations fall in each class interval. A class interval is a range of values such as 0–10 or 10–20.

• How it is built:

• Bars touch each other, with no gaps, because one class ends exactly where the next one begins.
• Bar width = the class interval.

• Bar height shows the frequency. Strictly, it is the area of the bar that is proportional to frequency. This matters when class intervals are unequal: a class twice as wide must have its height halved for the same frequency.

• What it shows: continuous data, meaning values that can take any value along a scale, such as rainfall amounts, heights or temperatures.

• How it differs from a bar diagram:

Feature	Bar diagram	Histogram
Gaps between bars	Yes, equal gaps	No gaps
Bar width	Fixed, carries no meaning	= class interval, carries meaning
Data type	Separate (discrete) categories: months, states, years	Continuous classes: 0–10, 10–20 …
Value shown by	Length	Area (height if classes are equal)
Order of bars	Can be rearranged (ascending or descending)	Fixed by the order of the classes

• Frequency polygon: mark the midpoint of the top of each bar and join the points with straight lines. The result is a frequency polygon, which shows the shape of the distribution (see geographical-data-processing).
• Geography uses:
• the number of districts in each population-density class,
• the number of years in each annual-rainfall class at a station,
• the number of villages in each altitude class.

Prelims Hooks

• Bar diagram: equal width and equal spacing; only length is proportional to value.
• Simple bar diagram: sort in ascending or descending order, except time series, which stay in time order. NCERT example: Thiruvananthapuram rainfall, June peak of 35.6 cm.
• Parts adding to a whole → compound bar. Separate variables side by side → multiple bar. Literacy (total, male, female) → multiple. Electricity (thermal, hydro, nuclear) → compound.
• NCERT literacy: 18.33% (1951) → 73.0% (2011); female literacy 8.86% → 64.6%.
• MOSPI gives Census 2011 literacy as 74.04 / 82.14 / 65.46 (persons, male, female). The highest state is Kerala (~94%) and the lowest is Bihar (63.82%) [2].
• Trap: literacy rates for 1951–1971 are for people aged 5+; from 1981 onwards they are for people aged 7+ [2].
• Line and bar graph: rainfall as bars, temperature as a line, two Y-axes, shared months. Delhi: 14.4°C (January) → 33.3°C (May–June); rainfall peaks at 19.3 cm in July.
• Histogram: no gaps, width = class interval, area ∝ frequency, continuous data. Joining the midpoints of the bar tops → frequency polygon.
• "Which diagram shows continuous data?" → histogram, not a bar diagram.

Mains Points

• Choosing the right diagram is part of a geography answer.
• A climograph (line and bar graph) of Thiruvananthapuram vs Delhi vs Kolkata shows the monsoon's arrival time and how much rain it brings at each station.

• Kerala gets its peak rain in June, while Delhi gets a smaller peak in July → the monsoon advances from south-west to north-west.

• Bar diagrams show regional and gender gaps in development (GS-I, Society).

• A multiple bar diagram of male and female literacy from 1951 to 2011 shows that the gender gap narrowed but did not close.
• A state-wise simple bar diagram shows how unequal states are, from Kerala (~94%) to Bihar (63.82%) in Census 2011 [2].

• Adult female literacy reached only 59.3% in 2011 [2].

• Compound bars show the energy mix (GS-III, Infrastructure).

• The thermal-dominated bars for 2008-09 to 2010-11 (total 741.2 → 844.8 billion kWh) show how much India depends on coal.

• The same diagram can track the energy transition as the hydro, nuclear and renewable segments grow.

• Comparability of data: before drawing any time-series bar diagram, check that the definitions match across years. Examples are the 5+ vs 7+ age base for literacy [2] and equal vs unequal class intervals in a histogram. A mismatch can mislead the reader.