Data Interpretation

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medium importance~2 Q in Tier 119 formulas⚡ 10 shortcuts5 subtopics

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Reading tables: totals, differences, ratios

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⏱ 6 min read🧩 6 question types🎯 13 practice Q

The idea in one minute

A data table gives values for rows (plants, cities, shops) across columns (usually years).

Read the row and column the question names, then do one small sum: a total, an average, a ratio or a count. Nothing more.

Read the table before the question

Scan the rows and columns first: what does each cell hold, in what unit?

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

Cells are thousands of cars. Row totals compare plants; column totals compare years.

Tip: Underline the row or column the question names before touching the numbers. Half the wrong answers in DI come from reading the wrong cell.

Row and column totals

Add across a row to judge one plant over time; add down a column to judge one year.

Plant R total: $150 + 145 + 160 + 170 + 175 = 800$ thousand. Year 2023 total: $165 + 130 + 175 + 120 = 590$ thousand.

Watch: Check unit words in the question ("thousands of cars"). A correct sum with the wrong unit is still a wrong answer.

Comparing two cells

Questions love the ratio or difference of two named cells.

Q in 2021 against R in 2021: $105 : 160 = 21 : 32$ after dividing by 5.

Rule: Reduce ratios fully. Options often keep the unreduced $105:160$ as a trap.

A combined row pair

Add two rows, then compare the sums across columns.

$P + Q$ per year: 210, 245, 255, 265, 295. The biggest joint year is 2023.

Tip: When sums are close, compute each and list them. Guessing "the last year" fails because 2021 dips for Q.

Counting cells that meet a condition

"How many years did S cross 100?" Read one row and tick.

S row: 80, 95, 100, 110, 120. At or above 100 in 2021, 2022, 2023: three years.

Watch: Decide once whether "cross 100" means above 100 or at least 100. Here 100 counts; the exam usually says "at least".

The gap between two rows

"When was R ahead of S by the most?" Subtract the two rows column by column.

$R - S$ per year: 70, 50, 60, 60, 55. The widest gap is 70, in 2019. Note how R stays ahead every year even as S grows.

Tip: Gap questions reward rough work: list the five differences, then compare. Doing each year in your head invites slips.

The average of a row

One row, one sum, one divide.

Plant P average: $710 \div 5 = 142$ thousand cars a year.

Percent tables

When a column already holds percentages, totals may be given separately. A pass-rate table reads the same way: appeared and passed columns give the rate by division.

City B, 2021: $54 \div 60 = 90\%$ , the best rate in the table.

Example: Appeared 50, passed 40 gives 80%. The same table for four city-year pairs is four one-line divisions.

Question types you will see

Each type: how to recognise it, the method step by step, and one question to try.

Type 1very common2 practice Q

Row total

How to spot it:

A table of items across years; the total for one item over all years is asked.

\text{total} = \sum \text{row cells}

Method

Point at the named row.
Add its cells across all columns.
State the unit with the answer.

Why it works:

One row, one addition: the simplest table question there is.

Try this

Production of cars by four plants (in thousands):

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

Total production of Plant R over the five years was:

Show solution

R row: $150 + 145 + 160 + 170 + 175$ .
$= 800$ thousand.

Answer

800 thousand

Type 2common2 practice Q

Ratio of two cells

How to spot it:

Two entries are named (same year, different rows); their ratio is asked.

a : b \text{ reduced}

Method

Pick the two cells named.
Write them as a ratio.
Divide both by their highest common factor.

Why it works:

Ratios compare two cells without any totals.

Try this

Production of cars by four plants (in thousands):

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

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

Show solution

Q in 2021 $= 105$ ; R in 2021 $= 160$ .
Ratio $= 105 : 160 = 21 : 32$ .

Answer

21 : 32

Type 3common2 practice Q

Best year for a row pair

How to spot it:

Two rows are combined and the year with the highest combined value is asked.

\text{best year} = \max_i (a_i + b_i)

Method

Add the two rows column by column.
List the five sums.
Pick the largest and name its year.

Why it works:

Combined strength can peak in a different year than either row alone.

Try this

Production of cars by four plants (in thousands):

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

In which year was the combined production of Plants P and Q the highest?

Show solution

$P+Q$ : 210, 245, 255, 265, 295 for 2019-2023.
Largest is 295.
Year 2023.

Answer

2023

Type 4common2 practice Q

Count the qualifying years

How to spot it:

'For how many years was X at least / more than a value?'

\#\text{years} = \text{count of cells meeting the condition}

Method

Read the named row once.
Tick every cell meeting the condition.
Count the ticks.

Why it works:

It is a reading test, not a calculation.

Try this

Production of cars by four plants (in thousands):

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

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

Show solution

S row: 80, 95, 100, 110, 120.
At least 100 in 2021, 2022, 2023.
Count $= 3$ .

Answer

3 years

Type 5very common2 practice Q

Average of a row

How to spot it:

The average of one item across all columns is asked.

\bar{x} = \frac{\text{row total}}{\text{columns}}

Method

Add the row.
Count the columns.
Divide.

Why it works:

An average is a row total shared over the years.

Try this

Production of cars by four plants (in thousands):

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

The average production of Plant P over the five years is:

Show solution

P total $= 120 + 135 + 150 + 140 + 165 = 710$ .
Average $= 710 \div 5 = 142$ .

Answer

142 thousand

Type 6common

Rate table: appeared and passed

How to spot it:

A table lists appeared and passed counts; the best or worst pass percentage is asked.

\text{rate} = \frac{\text{passed}}{\text{appeared}} \times 100\%

Method

Divide passed by appeared for each row.
Compare the rates.
Name the row with the highest (or lowest).

Why it works:

Raw pass counts mislead; the rate per appeared candidate is the fair compare.

Try this

Pass details of two coaching centres in two years:

Centre	Year	Appeared	Passed
A	2021	50	40
B	2021	60	54
A	2022	64	48
B	2022	70	56

Which centre-year pair shows the highest pass percentage?

Show solution

A 2021: $40/50 = 80\%$ ; B 2021: $54/60 = 90\%$ .
A 2022: $48/64 = 75\%$ ; B 2022: $56/70 = 80\%$ .
Highest: B in 2021.

Answer

B in 2021 (90%)

Formula sheet

Row total

\text{total} = \sum \text{row cells}

Row average

\bar{x} = \frac{\text{row total}}{\text{number of columns}}

Cell ratio

\text{ratio} = a : b \text{ (reduced)}

Rate from counts

\text{rate} = \frac{\text{passed}}{\text{appeared}} \times 100\%

Shortcuts that save time

⚡ Sweep the row with tick marks

For count-type questions (how many years above a value), tick the qualifying cells while reading once. No rewriting, no calculator.

Example

In how many years was Plant S's production at least 100 thousand?

Plant	2019	2020	2021	2022	2023
S	80	95	100	110	120

Show solution

S row: 80, 95, 100, 110, 120.
At least 100: 2021, 2022, 2023.
Count $= 3$ .

Answer

3 years

⚡ Column-first for year questions

Any question about one year (best year, total of a year) lives in a single column. Add that column alone; ignore the rest of the table.

Example

Total production in 2023 was:

Plant	2022	2023
P	140	165
Q	125	130
R	170	175
S	110	120

Show solution

2023 column: $165 + 130 + 175 + 120$ .
$= 590$ thousand.

Answer

590 thousand

Mistakes to avoid

Where most students lose marks on this subtopic.

Mistake 01

Adding the wrong row because two rows look similar.

Finger-point the row label, then read its cells.

Mistake 02

Answering in cars when the table says thousands of cars.

Carry the table's unit into the answer line.

Mistake 03

Leaving a ratio unreduced, such as 105:160.

Divide both terms by their common factor; options use reduced form.

Mistake 04

Counting a boundary value as a miss ('at least 100').

At least includes the boundary; above excludes it.

Mistake 05

Averaging two averages of different-sized groups.

Rebuild totals before dividing.

Quick revision

Read this the night before the exam.

Row questions read one row; year questions read one column.
Totals first, ratio or average after.
Reduce ratios fully; the unreduced pair is a planted option.
Count questions: tick qualifying cells in one sweep.
Rate = passed ÷ appeared, times 100.
Carry the table's unit into the answer.

Practice: 13 questions

Sets of 10, mixed across the question types above. Every answer has a step-by-step explanation.

Topic test · 13 questions

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

Continue learning

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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