Data Interpretation

medium importance~2 Q in Tier 116 formulas⚡ 10 shortcuts5 subtopics

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Subtopic 1 of 5·Percentage change and comparisons →

Reading tables: totals, differences, ratios

DI starts with reading discipline: note what rows and columns are (units! years!), and only then look at the question. Most Tier-1 table questions ask for a total, a difference of two cells, or a simple ratio — the data hunting is the question.

Work cell-by-cell with running subtotals rather than reading values one by one for every sub-question.

📖 Notes 🧩 5 question types ⚡ Formulas 🎯 13 practice Q

Detailed notes

What a DI table is

A table is data arranged in rows (going across) and columns (going down). Think of a school marks register: each row is a student, each column is a subject. In competitive exams a table usually shows years down the side and companies, states or products across the top. Every question is a small calculation on a few cells, so the real skill is reading the right cells quickly and correctly.

Step 1: read the frame before the numbers

Before touching any question, spend 15 seconds on the frame:

Title and units. "Production (in thousand tonnes)" means a cell showing 45 is really 45,000 tonnes. Options are often written in the same unit, but sometimes they convert — check.
Row and column labels. Is the year down the side or across the top? Mixing up a row and a column is the most common silly error.
Totals row or column. If the table already has a total, use it instead of adding again.

Step 2: the five things tables ask

Total and difference. Add a row or a column; or find the gap between two cells or two totals. Add in friendly pairs: $120 + 150 + 135 + 165 + 140$ becomes $(120+150+140) + (135+165) = 410 + 300 = 710$ .
Ratio. "Ratio of A to B" means $\frac{A}{B}$ reduced to lowest terms. Cancel the common factor first: $255 : 230$ , both divide by 5, gives $51 : 46$ . Keep the order the question uses — $A : B$ is not $B : A$ .
Maximum / minimum. "In which year was the gap between R and S the least?" Write the small list of gaps (70, 50, 60, 60, 55) in the margin and pick. Do not compute more than the question needs.
Counting years that satisfy a condition. "In how many years was P above its own average?" Find the average once, then tick cells. Watch "more than" versus "at least": a cell equal to the average is not more than it.
Missing value. If a total or an average is given, the missing cell is $\text{total} - \text{sum of the known cells}$ ; with an average, first make the total $= \text{average} \times \text{count}$ .

Worked example

A table shows sales (in ₹ lakh) of four shops: A 240, B ?, C 310, D 185, with a total of 990. Missing B $= 990 - (240 + 310 + 185) = 990 - 735 = 255$ .

Speed habits that save marks

Round only at the end. DI tables are built with friendly numbers, so exact answers usually come out whole.
Use the options. If the options are 540, 550, 560, 570 and your unit digits add to 0, only 550 and 570 survive. The last digit of a sum is a free check.
One table, many questions. In Tier-2 style sets, 4 or 5 questions use one table. Write column totals once in the margin and reuse them.
Equal is a trap. In "more than" counting questions, the setter often places one cell exactly equal to the benchmark.

Common mistakes

Reading 2021's row when the question says 2020.
Reporting the ratio upside down.
Forgetting the unit (thousands, lakh, crore) when options are in full numbers.
Adding every cell when only two were needed.

Quick revision

Ask	Method
Total	Add in friendly pairs; check the last digit
Difference	Subtract the two totals, not every cell pair
Ratio	$A : B$ , cancel common factors, keep the order
Max / min	List the small derived numbers, then pick
Count years	Benchmark once; "more than" excludes equal
Missing cell	Total − known sum; total = average × count

Types of questions asked

Every way this subtopic shows up in exams — how to recognise it, the formula or logic to use, and a solved example.

Type 1: Total or difference of rows / columnsvery common2 practice Q

How to spot it:

'Total production of Q over the years', 'by how much does 2023 exceed 2019' — plain addition or subtraction of cells.

\text{Difference} = \sum \text{row}_1 - \sum \text{row}_2

Locate the row/column (check the unit).
Add in friendly pairs; keep running subtotals.
For a difference of totals, subtract totals once instead of cell by cell.

Why: every total question is only addition — speed comes from grouping.

Example: Production of cars (in thousands) by four companies:

Year	P	Q	R	S
2019	120	90	150	80
2020	135	110	145	95
2021	150	105	160	100
2022	140	125	170	110
2023	165	130	175	120

The total production of company R over the five years is:

$150 + 145 + 160 + 170 + 175 = 800$ thousand.

Type 2: Ratio of cells or of sumsvery common2 practice Q

How to spot it:

'The ratio of X to Y', often of sums of two cells each.

A : B = \frac{A}{B}\ \text{in lowest terms}

Build each side (a cell or a sum of cells).
Cancel the HCF.
Keep the order asked; the reversed ratio is always an option.

Why: a ratio is just a fraction written with a colon.

Example: Production of cars (in thousands) by four companies:

Year	P	Q	R	S
2019	120	90	150	80
2020	135	110	145	95
2021	150	105	160	100
2022	140	125	170	110
2023	165	130	175	120

The ratio of production of Q in 2021 to that of R in 2021 is:

$105 : 160$ ; divide by 5 → $21 : 32$ .

Type 3: Which year / item is the maximum or minimumcommon2 practice Q

How to spot it:

'In which year was the difference / total / growth the highest (or least)?'

Compute the small derived number for each year (gap, total or % rise).
Write them in a row in the margin.
Pick the extreme; check that the question asked least or most.

Why: the setter hides the answer behind one derived number — never guess from raw cells.

Example: Production of cars (in thousands) by four companies:

Year	P	Q	R	S
2019	120	90	150	80
2020	135	110	145	95
2021	150	105	160	100
2022	140	125	170	110
2023	165	130	175	120

In which year was the total production of P and Q together the highest?

Totals: 210, 245, 255, 265, 295 → 2023.

Type 4: Count the years meeting a conditioncommon2 practice Q

How to spot it:

'In how many years was …more than / less than…'

Fix the benchmark (an average, another row, a stated number).
Tick each year that strictly meets the condition.
Equal values do not count for 'more than'.

Why: counting is easy; the traps are the benchmark and the tie.

Example: Production of cars (in thousands) by four companies:

Year	P	Q	R	S
2019	120	90	150	80
2020	135	110	145	95
2021	150	105	160	100
2022	140	125	170	110
2023	165	130	175	120

In how many years was the production of S at least 100 thousand?

100, 110, 120 → 3 years (2021, 2022, 2023). 'At least' includes the equal value.

Type 5: Missing value from a given total or averageoccasional2 practice Q

How to spot it:

A cell is blank or marked '?', and a total or an average is printed.

x = \text{total} - \sum \text{known} = n\bar{x} - \sum \text{known}

Make the total (multiply the average by the count if needed).
Subtract the known cells.

Why: the total is the only thing that ties the cells together.

Example: Sales (₹ lakh): A 240, B ?, C 310, D 185; total 990. Sales of B are:

$990 - 735 = 255$ lakh.

Formulas

Total of a row/column

\text{total}=x_1+x_2+\cdots+x_k

Difference

\text{difference}=|A-B|

Ratio of cells

\text{ratio}=\frac{x_{ij}}{x_{kl}}\ \text{(simplify the fraction)}

Shortcut tricks

⚡ Simplify the fraction before choosing

Ratios like $450:550$ reduce to $9:11$ — reduce before matching options, the unreduced pair is a common distractor.

Example: The table gives male and female employees (450 and 550). Find the ratio of males to females.

$\frac{450}{550}=\frac{9}{11}$ , i.e. $9:11$ .

⚡ Sums of friendly numbers

Group digits that make round numbers (e.g. $60+70+80$ ). DI tables are built so subtotals land on round values.

Example: Unit A produces 60, 70, 80 units in three years; Unit B produces 50, 60, 90. Whose total is larger and by how much?

$A=210$ , $B=200$ ; A leads by 10.

Where students lose marks

Mismatching units across columns (thousands vs units, lakh tonnes vs tonnes).
Adding percentages or ratios from different bases as if they were plain numbers.
Reading the wrong year's column after the question switches reference year.

Practice sets — 13 questions

Sets of 10, mixed across the question types above. Each answer comes with a step-by-step explanation.

Topic test · 13 questions

Suggested time 9 min · wrong answers go to your mistake notebook automatically.