Week 17: Data Interpretation I — Tables, Bar & Line Graphs

1. Read Before You Solve

The single most common DI mistake isn't a calculation error — it's answering the wrong question because the chart's structure (units, time period, what each axis or column actually represents) wasn't fully read before diving into the first question.

a 30-second reading pass, before question 1

1. TITLE -- what is this data actually about?
2. UNITS -- are values in absolute numbers, thousands,
   percentages, or something else?
3. TIME PERIOD -- what years/months/categories are covered?
4. AXES/COLUMNS -- what does each one represent, precisely?
5. FOOTNOTES -- often contain a critical qualifier (e.g.
   "figures in lakhs," "excludes returns") that changes
   every answer if missed

This 30 seconds is never wasted time — a misread unit or time period doesn't just cost one question, it silently corrupts every question that follows, since DI questions on the same chart usually build on the same base numbers.

2. Table-Based Questions

A table's questions are almost always Week 3's percentage or Week 6's ratio machinery, applied directly to two or more cells.

a sample table — company revenue (in crores)

Year      | Product A | Product B | Product C
2021      |    120    |    80     |    60
2022      |    150    |    90     |    75
2023      |    180    |    100    |    90

Q: What is the percentage increase in Product A's revenue
from 2021 to 2023?

  = (180-120)/120 x 100
  = 60/120 x 100
  = 50%   (Week 3's percentage-change formula, directly)

Q: In 2023, what is the ratio of Product A's revenue to the
TOTAL revenue that year?

  Total 2023 = 180+100+90 = 370
  Ratio = 180:370 = 18:37   (Week 6's ratio simplification)

Every DI table question is really "which earlier chapter's formula does this question want, and which two (or more) cells does it want applied to" — the table itself is just a fast way to present many related numbers at once.

3. Bar & Line Graph Questions

A bar graph is the same underlying data as a table, drawn as heights instead of numbers — a line graph adds the visual sense of a trend across a continuous axis (usually time). The questions asked are identical in kind to Section 2's; only the extraction step (reading a bar's height, or a line's y-value at a given x) differs.

a sample line graph, described in text — monthly sales (units)

Jan: 200   Feb: 250   Mar: 220   Apr: 300   May: 280   Jun: 350

Q: In which month was the percentage increase over the
PREVIOUS month the highest?

  Feb: (250-200)/200 = 25%
  Mar: (220-250)/250 = -12%  (a decrease)
  Apr: (300-220)/220 ≈ 36.4%   <-- highest so far
  May: (280-300)/300 ≈ -6.7%  (a decrease)
  Jun: (350-280)/280 = 25%

  Answer: April, with ≈36.4% increase

This question type — "find the month/year/category with the highest percentage change" — requires computing the change for EVERY consecutive pair, not just eyeing the graph for the steepest-looking segment; a large absolute jump on a large base can have a smaller percentage change than a smaller jump on a small base, which the eye alone won't reliably catch.

4. When to Approximate

DI sections are timed tightly, and many questions (especially "which is largest/smallest," or a rough comparison) don't need an exact calculation at all — recognizing this is a real speed advantage.

approximation vs. exact calculation

Q: Which product had the highest percentage growth from
2021 to 2023 -- A (120 to 180), B (80 to 100), or C (60 to 90)?

APPROXIMATE first (rough mental math):
  A: roughly +50% (obvious: 120 -> 180 is 1.5x)
  B: roughly +25% (80 -> 100 is a 1/4 increase)
  C: roughly +50% (60 -> 90 is also 1.5x)

A and C are CLOSE (both ~50%) -- THIS is where you'd switch
to exact calculation to break the tie:
  A: 60/120 = 50.0% exactly
  C: 30/60  = 50.0% exactly
  -- genuinely tied; B is clearly not the answer without
     needing its exact value at all

The discipline: approximate first, and only reach for exact arithmetic when the approximate values are close enough that the answer genuinely depends on the precise figure — spending 45 seconds computing an exact percentage when a 5-second glance already ruled out two of three options is time a timed test doesn't have to spare.

"Find the exact value" questions still deserve exact arithmetic

Approximation is a tool for comparison and elimination questions, not for questions that explicitly ask for a specific numeric answer (like "what was the exact revenue in 2022?"). Misapplying the approximate-first habit to a question that wants precision is its own kind of error — know which question type you're facing before deciding how much rigor it needs.

5. Practice Problems

Practice

30 problems, no calculator — Easy, Medium & Tough

Easy and Medium reuse this course's revenue table: Product A/B/C revenue (crores) for 2021/2022/2023 — A: 120, 150, 180; B: 80, 90, 100; C: 60, 75, 90. Tough uses a new quarterly-sales dataset introduced below. Easy problems should take under 30 seconds each; Medium under 60 seconds; Tough under 90 seconds.

Easy (1–10) — using the Product A/B/C table above

Find Product A's revenue in 2022.
Find Product B's revenue in 2023.
Find Product C's revenue in 2021.
Find the total revenue of all three products in 2021.
Find the total revenue of all three products in 2023.
Which product had the highest revenue in 2022?
Which product had the lowest revenue in 2021?
Find Product A's revenue increase (in crores) from 2021 to 2022.
Find Product B's revenue increase (in crores) from 2022 to 2023.
Find the combined 2022 revenue of Products B and C.

Easy — Answers

1) 150 crores. 2) 100 crores. 3) 60 crores. 4) 120+80+60=260 crores. 5) 180+100+90=370 crores. 6) Product A (150). 7) Product C (60). 8) 150-120=30 crores. 9) 100-90=10 crores. 10) 90+75=165 crores.

Medium (11–20) — using the same table

Find the percentage increase in Product A's revenue from 2021 to 2023.
Find the percentage increase in Product C's revenue from 2021 to 2023.
Find the ratio of Product A's 2021 revenue to Product C's 2021 revenue.
Find the average revenue of Product B across the three years.
Find the percentage of total 2023 revenue contributed by Product B.
Find the total combined revenue growth (all three products) from 2021 to 2023, in crores.
Find the percentage growth in total combined revenue from 2021 to 2023.
Which product had the largest year-on-year absolute increase, repeated identically both years?
Find the difference between Product A's and Product C's revenue in 2023.
If Product A's 2024 revenue is projected to grow by the same percentage as its 2022→2023 growth, find the projected 2024 revenue.

Medium — Answers

11) (180-120)/120×100=50%. 12) (90-60)/60×100=50%. 13) 120:60=2:1. 14) (80+90+100)/3=90 crores. 15) 100/370×100≈27.03%. 16) 370-260=110 crores. 17) 110/260×100≈42.31%. 18) Product A (+30 crores each year, the largest consistent increase). 19) 180-90=90 crores. 20) 2022→2023 growth=(180-150)/150=20%; 2024 projected=180×1.2=216 crores.

Tough (21–30)

new dataset — quarterly sales (Rs. lakhs)

Q1: 45   Q2: 60   Q3: 55   Q4: 80

Find the total annual sales.
Find the percentage of annual sales contributed by Q4.
Find the percentage increase in sales from Q1 to Q2.
Find the percentage decrease in sales from Q2 to Q3.
Find the average quarterly sales.
By approximation only, is the percentage increase from Q3 to Q4 closer to 30%, 45%, or 60%?
If Q4 sales grow by 25% next year while other quarters stay the same, find the new annual total.
Find the ratio of (Q1+Q2) sales to (Q3+Q4) sales.
If total costs were 70% of total annual sales, find total profit for the year.
Find which quarter-on-quarter transition (Q1→Q2, Q2→Q3, or Q3→Q4) had the largest percentage change in magnitude.

Tough — Answers

21) 45+60+55+80=240 lakhs. 22) 80/240×100≈33.33%. 23) (60-45)/45×100≈33.33%. 24) (60-55)/60×100≈8.33%. 25) 240/4=60 lakhs. 26) (80-55)/55×100≈45.45% → closer to 45%. 27) New Q4=80×1.25=100; new total=45+60+55+100=260 lakhs. 28) (45+60):(55+80)=105:135=7:9. 29) Profit=30% of 240=72 lakhs. 30) Q1→Q2≈+33.33%, Q2→Q3≈-8.33%, Q3→Q4≈+45.45% → Q3→Q4 is largest in magnitude.

6. Knowledge Check

Four quick questions. Expand each to check your answer.

Why can a misread footnote (like "figures in lakhs") corrupt every subsequent answer, not just the first question?

DI questions on the same chart typically reuse the same underlying data, so a wrong assumption about units gets baked into every calculation drawn from that chart, not just the one question where it was first needed. A single missed qualifier can silently produce a wrong answer on every remaining question in that set.

Why is finding "the month with the highest percentage increase" not the same as finding "the month with the largest visual jump" on a line graph?

Percentage change depends on both the size of the jump AND the base value it's measured against — a large absolute jump starting from a large base can be a smaller percentage change than a smaller jump starting from a small base. The eye reads absolute height differences well, but percentage change requires actually computing the ratio, not just the visual gap.

When is approximation the wrong tool to reach for on a DI question?

Approximation is appropriate for comparison or elimination questions where a rough estimate can already distinguish the answer from the alternatives. It's the wrong tool when a question explicitly asks for a specific, exact numeric value, or when the approximate values for competing options are too close together to distinguish without precise calculation.

Why are DI table and graph questions described as "no new concepts" compared to the rest of this course?

Every calculation a DI question asks for — percentage change, ratio, average — is one of the formulas already built in earlier weeks; the chart is simply a different, denser way of presenting the input numbers than a word-problem paragraph. The genuinely new skill this week adds is reading the chart's structure correctly and choosing when precision is actually needed, not new arithmetic.