Data Interpretation: Chart Methods and Speed Plan

SSC · Banking · Railways · State exams — method by method

4 Part14 worked examples18 practice questions

This is part 2. Part 1 (Data Interpretation: Methods and Shortcuts) had reading a chart, fractions and percents, estimation, comparing, change, ratio, average and growth rate. Here every chart gets its own move: angle ↔ percent ↔ quantity in a pie; several series in a bar chart; slope in a line graph; then cumulative and missing values, joining two tables or two charts, caselets, and finally a plan to solve 5 questions in 4 minutes.

Type of chart	Open this for more practice
Table	Data Table
Pie chart	Pie Chart
Bar chart	Bar Chart
Line graph	Line Graph
Two charts together	Mixed Graph
“Is it enough?”	Data Sufficiency

PracticeTheir questions are not repeated in this chapter: learn the method here, practise there.

Pie, bar and line charts

Three charts, three moves

Angle-percent-quantity in a pie, several series and stacks in a bar chart, slope in a line graph.

Pie chart: angle, percent and quantity

Full circle = 360° = 100% = total

Angle ↔ percent ↔ quantity, a missing sector and the trap of two pies.

The idea

In a pie chart the whole circle is the total. There are $36 0^{\circ}$ around the circle, so each sector’s angle gives its share: $9 0^{\circ}$ is a quarter, $3 6^{\circ}$ a tenth. There are three languages (angle, percent, real quantity) and you must move between them. If one sector’s value is given you get the total, and if the total is given you get any sector, by the same ladder.

◭ Diagram

Angles are given; the angle of “Others” is missing:

360 - (108 + 72 + 54 + 36) = 9 0^{\circ}

∑ Formula

p = \frac{θ}{3.6} θ = 3.6 p Q = \frac{θ}{360} \times T = \frac{p}{100} \times T

Angle to percent, percent to angle, and angle or percent to quantity

$θ$: central angle of the sector (degrees)
$p$: percent of the sector
$Q$: real quantity of the sector
$T$: the total
$3.6$: $\frac{360}{100}$ : the angle of 1%

Angle	$1 8^{\circ}$	$3 6^{\circ}$	$4 5^{\circ}$	$7 2^{\circ}$	$9 0^{\circ}$	$12 0^{\circ}$	$18 0^{\circ}$
Percent	5%	10%	12.5%	20%	25%	$33 \frac{1}{3} %$	50%

Steps

See whether sectors are given in angles or percents (they must add up to 360 or 100).
If a sector is missing, take $360 -$ (sum of the rest).
Unless a real quantity is asked, you need no total: the ratio of sectors is the ratio of the angles.
For a quantity use $\frac{θ}{360} \times T$ , or first turn the angle into a fraction ( $7 2^{\circ} = \frac{1}{5}$ ).

TrapTwo pie charts: a bigger percent is not always a bigger quantity. 20% of 600 = 120 and 25% of 480 = 120 are equal.

Worked questions

Example 1 · Basic

The area of the “Others” sector in hectares?

Solution, step by step

1Sectors add to $36 0^{\circ}$ : Others $= 360 - (108 + 72 + 54 + 36) = 360 - 270 = 9 0^{\circ}$ .
2 $9 0^{\circ} = \frac{1}{4}$ of $36 0^{\circ}$ , so the area $= \frac{7200}{4} = 1800$ ha.

Answer 1,800 ha

Example 2 · Basic

What percent of the area is wheat, and what is its area?

Solution, step by step

1Percent $= \frac{108}{3.6} = 30%$ ( $10 8^{\circ} = \frac{3}{10}$ of $36 0^{\circ}$ ).
2Area $= 30%$ of $7200 = 2160$ ha.

Answer 30%; 2,160 ha

Example 3 · Standard

By how much is the wheat area more than the mustard area?

Solution, step by step

1Both are parts of the same total, so first the gap of angles: $108 - 72 = 3 6^{\circ}$ .
2 $3 6^{\circ} = \frac{1}{10}$ : gap $= \frac{7200}{10} = 720$ ha.

Answer 720 ha

Finding each and subtracting is right but longer.

Example 4 · Standard

The ratio of the areas of barley and others?

Solution, step by step

1The total is the same, so the ratio = the ratio of angles: $36 : 90$ .
2HCF $= 18$ ⟹ $2 : 5$ .

Answer 2 : 5

Example 5 · Advanced

In two pie charts the same item is 20% (total 600) and 25% (total 480). Where is its quantity larger?

Solution, step by step

1Find quantities, not percents: $20%$ of $600 = 120$ .
2 $25%$ of $480 = 120$ .

Answer Equal in both (120)

Try yourself

◭ Diagram

Electricity use of the town (in percent)

BasicTry it yourself first

The central angle of the Industry sector?

BasicTry it yourself first

How many units are used for domestic purposes?

StandardTry it yourself first

By how many units is industry use more than agriculture use?

StandardTry it yourself first

The ratio of commercial to other use?

StandardTry it yourself first

If next year the total rises 10% to 19,800 and the domestic share stays 30%, what is domestic use?

AdvancedTry it yourself first

The sum of industry and agriculture is what percent of the sum of domestic and commercial?

Bar charts: several series and stacks

First copy all bars into a mini-table

Differences and ratios from clustered bars, and reading the segments of a stacked bar from the differences of tops.

The idea

A clustered bar chart has several coloured bars at each category (year), one colour per series. Questions compare series in one year or follow one series over years. The safest way: first copy all the bars into a mini-table, then answer from the table: looking back at the bars again and again costs time and causes slips. In a stacked bar the segments sit on top of each other; a segment’s value is the difference of its top and bottom edge, not the number read at its top edge.

◭ Diagram

Exports and imports; both 2024 bars are marked

Year	2019	2020	2021	2022	2023	2024
Exports	42	48	45	54	60	66
Imports	36	44	50	48	57	55
Exports − imports	+6	+4	−5	+6	+3	+11

Here: “exports − imports” = trade balance; positive = surplus, negative = deficit. The third row is the extra row built from the mini-table.

Steps

Identify the series from the legend; write each bar’s value (from its label or the scale) into a mini-table.
Add one extra row for the difference, sum or ratio the questions use.
In a stack: total = top edge; segment = top edge − bottom edge.
Read the answer off the row; do not go back to the chart.

CautionIf the bars carry labels, use those; estimate from the scale only when no values are written.

Worked questions

Example 6 · Basic

The trade balance of 2021 (₹ hundred crore)?

Solution, step by step

12021: exports $= 45$ , imports $= 50$ .
2Balance $= 45 - 50 = - 5$ : negative, i.e. a deficit of ₹ 500 crore.

Answer −5 (a deficit)

Keep the sign: a deficit is not a surplus.

Example 7 · Standard

In which year was the surplus the highest, and what was exports : imports that year?

Solution, step by step

1The third row: $6, 4, - 5, 6, 3, 11$ ⟹ the highest is 11, in 2024.
2Exports : imports $= 66 : 55$ ; HCF 11 ⟹ $6 : 5$ .

Answer 2024; 6 : 5

Example 8 · Standard

By what percent are 2024 exports more than 2019 exports?

Solution, step by step

1Rise $= 66 - 42 = 24$ ; base 2019’s $42$ .
2 $\frac{24}{42} \times 100 = \frac{4}{7} \times 100 = 57.1%$ ( $57 \frac{1}{7} %$ ).

Answer 57.1%

◭ Diagram

A stacked bar: three segments in each bar; the total on top

Example 9 · Standard

By what percent did Science enrolment rise from 2022 to 2024, and what share of the 2024 total is Commerce?

Solution, step by step

1The Science segments are labelled: $24 \to 36$ ; rise $= 12$ , $\frac{12}{24} = 50%$ .
2The 2024 total $= 32 + 36 + 28 = 96$ (on top of the bar). Commerce $= \frac{28}{96} \times 100 = 29.17%$ ( $\frac{7}{24}$ ).

Answer 50%; 29.17%

Example 10 · Advanced

In the 2023 stack the Science segment has its bottom edge at 28 and its top at 58. What is the Science value?

Solution, step by step

1A segment’s value = top − bottom edge.
2 $58 - 28 = 30$ (the 58 at the top is not the value: it includes Arts’ 28).

Answer 30

Try yourself

◭ Diagram

Wheat procured in five cities, 2023 and 2024

BasicTry it yourself first

In which city did procurement rise the most (in quantity)?

BasicTry it yourself first

Total procurement of the five cities in 2023 (thousand tonnes)?

StandardTry it yourself first

Which city has the highest percent rise?

StandardTry it yourself first

In how many cities did 2024 procurement fall below 2023, and what is their total fall?

StandardTry it yourself first

The ratio of 2024 procurement of Jaipur to Bikaner?

AdvancedTry it yourself first

The percent rise in the total procurement of the five cities from 2023 to 2024 (to one decimal)?

Line graphs and reading the slope

Steepest climb = biggest change

A point is a value, a segment is a change; the steepest climb, percent rise and unequal gaps.

The idea

In a line graph a point gives a value and the segment joining two points gives the change. The steeper a segment climbs, the bigger the rise in that interval; going down means a fall; flat means no change. If the x-axis gaps are equal (every day, every year) then the steepest climb = the biggest difference $y_{2} - y_{1}$ . Two traps: (1) “steepest” (amount) and “highest percent rise” can differ; (2) with unequal gaps you must use the slope $\frac{rise}{time}$ .

◭ Diagram

Green segment: the steepest climb (Thu → Fri, +12); rose segment: the fall (−6)

∑ Formula

slope = \frac{y _{2} - y _{1}}{x _{2} - x _{1}} rise % = \frac{y _{2} - y _{1}}{y _{1}} \times 100

First: change per unit time; second: percent rise

$y_{1}, y_{2}$: values at the two points
$x_{2} - x_{1}$: the time between the two points

Steps

Check scale and unit; read every point (from the axis if there are no labels).
Write the difference ( $y_{2} - y_{1}$ ) for each interval: that is the mini-table.
For “steepest climb” take the largest positive difference; for “sharpest fall” the largest negative.
Two lines: where they meet the values are equal; the gap = the vertical distance.

TrapThe highest point (peak) is the biggest value, not the biggest rise.

Worked questions

Example 11 · Basic

Between which days is the climb steepest?

Solution, step by step

1Interval differences: +6, -3, +9, +12, -6, +3.
2The gaps are equal, so the largest positive difference $+ 12$ : Thu → Fri.

Answer Thu → Fri (+12 thousand)

Example 12 · Standard

In which interval is the percent rise the highest?

Solution, step by step

1Tue: $\frac{6}{12} = 50%$ ; Thu: $\frac{9}{15} = 60%$ ; Fri: $\frac{12}{24} = 50%$ ; Sun: $\frac{3}{30} = 10%$ .
2The highest is 60%: Wed → Thu, though the biggest amount of rise is Thu → Fri.

Answer Wed → Thu (60%)

The smaller the starting value, the bigger the percent.

Example 13 · Standard

The average daily visitors in the week?

Solution, step by step

1Total of seven days $= 12 + 18 + 15 + 24 + 36 + 30 + 33 = 168$ thousand.
2Average $= \frac{168}{7} = 24$ thousand.

Answer 24 thousand

Table (unequal gaps): water level of a reservoir.

Date	1 Jan	1 Mar	1 Apr	1 Aug
Level (cm)	40	52	61	85

Example 14 · Advanced

In which period did the level rise fastest (per month)?

Solution, step by step

1The periods are unequal, so use slopes: Jan–Mar $\frac{12}{2} = 6$ ; Mar–Apr $\frac{9}{1} = 9$ ; Apr–Aug $\frac{24}{4} = 6$ cm/month.
2Fastest: Mar–Apr (9 cm/month), though the biggest total rise is Apr–Aug (24 cm).

Answer Mar–Apr

Try yourself

◭ Diagram

Output of two factories, 2018–2023

BasicTry it yourself first

In which year was the output of both factories equal?

StandardTry it yourself first

In which year was the gap between the outputs the largest, and how much?

StandardTry it yourself first

Between which years is Factory 1’s climb steepest?

StandardTry it yourself first

Between which years is Factory 2’s climb steepest?

StandardTry it yourself first

In how many years was Factory 1’s output higher than Factory 2’s?

AdvancedTry it yourself first

The total percent rise in Factory 1’s output from 2018 to 2023 (to one decimal)?

Adding up, filling in, joining

More than one source, or incomplete data

Cumulative and combined data, missing values, two tables, two charts and caselets.

Cumulative and combined data

“up to”, “between”, “both together”

Running totals, counting the period, and percent of a combined total.

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Missing values from totals

Start where only one cell is empty

Filling empty cells from row and column totals, averages and percents.

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Joining two tables

Join by name, not by position

Quantity in one table and a rate in the other: multiply on the common name to build a new column.

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Double-chart questions

One chart gives the total, the other the share

Bar + pie or bar + line: multiplying on the shared year or category to get quantities.

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Caselets: from words to a table

Build the table first, then the questions

Putting the figures of a paragraph into a table or a tree before answering.

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Speed: eliminating and the time plan

Which calculation to skip, and how to split 4 minutes

Tricks to cut options and the time plan for a 5-question set.

Which calculation can be skipped: eliminating options

Hunt the wrong options, not the answer

Choosing the answer without the full calculation by last digit, direction, range, divisibility and estimate.

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A 5-question set in 4 minutes

Read first, then easy to hard

The time plan for a DI set, the order of questions and the skipping rule.

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Summary, mixed practice, revision

All methods in one place

A table of all methods, a mixed set and revision.

Summary of all methods

Pick the method as you read

Every method: when to use it and the key move.

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Mixed practice: a stacked bar

Reading, segments, growth, ratio

Mixed questions on one stacked bar chart.

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Revision: the commonest slips

Once before the exam

One slip per method.

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Data Interpretation: Chart Methods and Speed Plan

Pie, bar and line charts

Pie chart: angle, percent and quantity

The idea

Steps

Worked questions

Try yourself

Bar charts: several series and stacks

The idea

Steps

Worked questions

Try yourself

Line graphs and reading the slope

The idea

Steps

Worked questions

Try yourself

Adding up, filling in, joining

Cumulative and combined data

Missing values from totals

Joining two tables

Double-chart questions

Caselets: from words to a table

Speed: eliminating and the time plan

Which calculation can be skipped: eliminating options

A 5-question set in 4 minutes

Summary, mixed practice, revision

Summary of all methods

Mixed practice: a stacked bar

Revision: the commonest slips

Free All Access Passevery mind map · Hindi + English · 12 months

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