Data Interpretation: Reading Tables and Answering Fast

By the end of this lesson you will be able to read a value off a data table, add up row and column totals, find a row or column average, write one cell as a percentage of its total, work out a percentage change on the right base, say by what percent one cell is more or less than another, reduce the ratio of two cells, and combine two rows by weighting rather than by averaging percentages.

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Before this: data interpretation is not a new kind of sum. It is the percentage, ratio and average you already know, applied to a table. If any of those feel shaky, read the Percentage lesson, the Ratio and Proportion lesson and the Average lesson first. Everything below is just those three tools pointed at a grid of numbers.

What a data table is

A data table lays numbers out in rows and columns. Each row is one case (a day, a year, a branch), each column is one measured thing (a product, a subject, a category), and each cell is one number — the value for that row and that column.

Here is a small one. A fruit shop records the kilograms sold on three days.

To read a cell, find the row, then slide across to the column. "Oranges on Tuesday" is the Tue row and the Oranges column: 15 kg. Always check you are on the right row and the right column before you do anything else — most slips happen here, not in the arithmetic. In an exam a table may have more rows and columns than you need; ignore the ones the question does not mention, and you cut the work down at once.

Data interpretation is one of the most reliable scoring areas in SSC and RRB papers, because every question is answered from the numbers in front of you — there is nothing to recall, only to read and compute. A whole set of four or five questions usually hangs off a single table, so time spent understanding the table once pays off across every question in the set.

A few words used below:

• A row total adds every cell in one row (all of Monday's fruit). A column total adds every cell in one column (all the apples across the three days).
• The base is the value you divide by. In every percentage question, deciding the base is the real work; the division is easy once you have it.
• A sub-total is the total of some, but not all, of the cells — say the fruit sold on the first two days, or the apples and bananas but not the oranges. Read exactly which cells the question groups together.

Worked examples

Read each example slowly. The first table shows every step. In the second, some steps are left for you, with the answer just below.

Example 1: Totals, averages, a cell as a percentage, and a ratio

Use the fruit table above.

Part (a): row and column totals.

1. Monday's row total is 60 + 60 + 30 = 150 kg. That is all the fruit sold on Monday.
2. The Apples column total is 60 + 90 + 120 = 270 kg. That is all the apples sold over the three days.
3. A quick check on any table: the sum of all the row totals equals the sum of all the column totals, because both add up every cell once. Here the three row totals are 150, 150 and 180, which sum to 480; the three column totals are 270 apples, 120 bananas and 90 oranges, which also sum to 480.

Part (b): a column average.

1. The average is total ÷ how many, exactly as in the Average lesson.
2. Apples sold per day: total 270 kg over 3 days, so 270 ÷ 3 = 90 kg a day.
3. Check it sits among the three values (60, 90, 120): 90 does. Good — an average that lands outside the values is a sure sign of an arithmetic slip.

Part (c): a cell as a percentage of its total.

1. "What percent of Monday's sales were apples?" The base is Monday's row total, 150 kg — the apples are part of that.
2. 60 ÷ 150 × 100 = 40%.
3. The base is whatever the "of" points at. "Apples as a percent of Monday" uses the Monday row total (150); "Monday's apples as a percent of all apples" would use the Apples column total (270) instead, and give a different answer. Read which total the question wants before you divide.

Part (d): the ratio of two cells.

1. "The ratio of apples to oranges sold on Tuesday" is 90 : 15.
2. Divide both sides by their common factor, 15: 90 : 15 = 6 : 1.
3. A ratio is only finished when it is in its lowest terms. 90 : 15 and 6 : 1 are the same ratio; 6 : 1 is the answer. The order matters too — "apples to oranges" is 6 : 1, while "oranges to apples" would be 1 : 6.

The principle: a total is a sum of cells; an average is that total ÷ how many; a cell as a percentage is cell ÷ (the right total) × 100; a ratio of two cells is reduced to lowest terms. None of this is new — it is Example-1 arithmetic from three earlier lessons, read off a grid.

One cell, two different percentages. The same cell gives different answers depending on which total you choose. Monday's 60 kg of apples is 40% of Monday's sales (60 ÷ 150), because there you read across the row. But it is only about 22% of all the apples sold in the three days (60 ÷ 270 ≈ 22.2%), because there you read down the column. Neither is "the" answer — the question's wording tells you which total is the base. "Apples as a share of Monday" reads across; "Monday as a share of all apples" reads down.

Your turn: what is the average number of bananas sold per day?

Check: the Bananas column totals 60 + 45 + 15 = 120 kg, over 3 days, so 120 ÷ 3 = 40 kg a day.

Example 2: Percentage change, and "more or less than"

A company records the sales (in ₹ lakh) of two branches in January and February.

Part (a): percentage change, on the right base.

1. Percentage change = (new − old) ÷ old × 100, and the old value is the base, exactly as in the Percentage lesson.
2. North rose from 800 to 960. The change is 960 − 800 = 160, and the base is the earlier value, 800.
3. Percentage increase = 160 ÷ 800 × 100 = 20%.
4. South fell from 500 to 350. The change is 500 − 350 = 150, and the base is again the earlier value, 500.
5. Percentage decrease = 150 ÷ 500 × 100 = 30%.
6. The base is the value you are moving away from — here January, because the change runs January → February. Dividing by 960 or by 350 (the new values) is the commonest mistake in the topic.

Part (b): by what percent is one cell more or less than another.

1. This is a comparison, not a change over time. The base is the amount after the word "than".
2. "North's January sales are what percent more than South's January sales?" The base is South, 500. The gap is 800 − 500 = 300.
3. 300 ÷ 500 × 100 = 60%. North sold 60% more than South in January.
4. Turn it around: "South is what percent less than North?" Now the base is North, 800. The same gap, 300, over 800: 300 ÷ 800 × 100 = 37.5%.
5. The two answers differ (60% and 37.5%) because the base changes. "A more than B" and "B less than A" are never the same percentage, even though the gap is identical.

Watch the difference between "percent of" and "percent more than". North's January is 800 ÷ 500 × 100 = 160% of South's, but only 60% more than South's. "Of" compares the whole amount; "more than" compares only the gap. The two answers always differ by exactly 100 percentage points.

Your turn: by what percent did South's sales fall from January to February? First do it correctly, then say what wrong answer you get if you divide by February instead.

Check: correct base is January, 500: 150 ÷ 500 × 100 = 30%. If you wrongly use February (350) as the base you get 150 ÷ 350 × 100 ≈ 42.9%, which is the classic wrong-base trap — the change always divides by the earlier value.

Example 3: Combining rows — average the values, not the percentages

A table often gives a count and an average side by side, and asks for the average over two or more rows together. Here is a test taken by two sections.

Question: what is the average mark of all 50 students taken together?

1. You cannot just average 80 and 60 to get 70. That is right only when the two groups are the same size, and here they are not — Section B has more students, so it should pull the combined average towards its own 60.
2. Go back to totals, as in the Average lesson. Section A's marks total 20 × 80 = 1,600. Section B's total 30 × 60 = 1,800.
3. All together: 1,600 + 1,800 = 3,400 marks, shared among 20 + 30 = 50 students.
4. Combined average = 3,400 ÷ 50 = 68 marks. It is below the plain mean of 70, exactly as expected, because the larger section scored lower.

The principle: to combine groups from a table, turn each average back into a total (average × count), add the totals, and divide by the total count. Never take the plain mean of two percentages or two averages unless the groups are equal in size. The same warning applies to percentages: you cannot average "40% of Monday" and "50% of Tuesday" to get a share of the two days combined — rebuild the actual amounts first.

Your turn: a third section, C, has 10 students averaging 90 marks. What is the average of all 60 students (A, B and C)?

Check: C's total is 10 × 90 = 900. Added to the earlier 3,400 gives 4,300 marks over 60 students, so 4,300 ÷ 60 ≈ 71.7 marks. (Rounded; the exact value is 71⅔.)

How to attack any table question

A steady order turns a scary-looking table into four easy steps.

1. Read the question before the table. Underline what it asks for — a total, an average, a percentage, a percentage change, a comparison, a ratio. Note which rows, which columns, which years.
2. Find the right cells, carefully. Put a finger on the row, slide to the column. Double-check you have not drifted a line up or down.
3. Decide the base, if there is one. For "percent of a total", the base is that total. For a percentage change, the base is the earlier (old) value. For "A more or less than B", the base is B — the amount after "than".
4. Compute, then sanity-check. A part is never more than its whole, so a cell is at most 100% of a total it belongs to. A percentage change can be more than 100%. An average sits between the smallest and largest value. If your answer breaks one of these, re-check before you pick an option.

Two more habits save time under exam pressure:

• Multi-step questions are just these steps in a row. "By what percent did the total change from one year to the next?" is a total, then another total, then a percentage change — three steps you already know, not one hard new move. Do them one at a time and write each intermediate number down; the mistakes come from trying to hold them all in your head.
• Look at the options before you compute the hard way. If the options are 24%, 36%, 40% and 60%, a rough estimate is often enough to rule out three of them, and a wrong-base slip usually lands on one of the distractors — so matching an option is not proof you are right. Trust the method, not the coincidence.

At a glance

In this summary "cell" is one number in the table, and "the right total" is the row or column the question points at.

Common mistakes

• Reading the wrong cell. Drifting one row or one column off is the single biggest source of lost marks. Find the row, then the column, and confirm before computing.
• Using the wrong base for a percentage change. A rise from 800 to 960 is 160 ÷ 800, not 160 ÷ 960. The base is always the earlier (old) value, not the new one.
• Confusing "percent of" with "percent more than". 800 is 160% of 500 but only 60% more than 500. "Of" uses the whole amount; "more than" uses only the gap. They always differ by 100 percentage points.
• Using the wrong total for "percent of". "Apples as a percent of Monday" divides by the Monday row total; "Monday's apples as a percent of all apples" divides by the Apples column total. Read which total the question names.
• Averaging percentages instead of the underlying values. To combine two groups, add the actual amounts and divide by the actual count — never take the plain mean of two percentages unless the groups are the same size.
• Leaving a ratio unreduced. 60 : 10 is not a finished answer; 6 : 1 is. Always divide out the common factor.
• Treating percentage points as a percentage change. A rate moving from 40% to 50% is up 10 percentage points (50 − 40), but up 25% of its old value (10 ÷ 40 × 100). These are different numbers, and a question will mean one or the other — read the wording and do not confuse the two.
• Forgetting the units. If one column is in rupees and another in thousands of rupees, or one row is a count and another a rate, put everything in the same unit before you add or compare. A total built from mixed units is meaningless.
• Trusting an answer just because it matches an option. Distractors are built from the usual slips, so a wrong method often lands squarely on a wrong option. Pick the option because your method gives it, not the other way round.

Next

Data interpretation rewards the same habits every time: read the question first, find the cell, fix the base, then compute. The arithmetic itself is the Percentage, Ratio and Proportion and Average you already know. Keep the Percentage formula cheat sheet beside you while you practise.

Ready to test this lesson? Take the Data Interpretation quiz

How this was made: Drafted with AI assistance; every formula and worked figure recomputed independently; spot-checked by the editor on 29 October 2026.