PYQ Vault
Ebooks

SSC CGL Maths · Data Interpretation

Reading Tables and Graphs

Most data questions start with the same two moves: pick the right cells, then add or subtract them, keeping the unit printed above the table.

All Data Interpretation notes

Why this matters

Twenty-five questions in the bank ask for nothing beyond a total, a difference, a count of rows that pass a test, or a reading of a cumulative table. Twenty-two of them are EASY, so the only way to lose the mark is a wrong cell or a dropped unit.

Concept 1 of 3: Totals and differences of totals from a table

A table is a grid of numbers with a heading on each side. A question names a row or a column, often two of them, and asks how far apart their totals are. You can add each side and subtract, or subtract cell by cell and add the gaps: the answer is the same, and the second way keeps the numbers small.

Definition

  • Read the labels first: which rows, which columns, and the unit line ("in thousands", "in ₹ lakh"). Convert to the unit the options use only at the end.
  • Full method: add each group, then subtract the totals.
  • Fast route: when the two groups have matching entries (same months, same years), subtract pair by pair and add the gaps, keeping each gap's sign. The sum of the gaps is the difference of the totals.
  • If a table already prints a Total row or column, read it instead of adding, and never add it in a second time.
  • A question that defines a new quantity (profit as exports minus imports, calories from distance) is still a total first, then one more step.

Difference of two totals

∑ai−∑bi=∑(ai−bi)\sum a_i - \sum b_i = \sum (a_i - b_i)
  • a_ithe entries of the first group
  • b_ithe matching entries of the second group

Worked example

The table shows the sales (in units) of two shops in three months.
MonthShop PShop Q
January340285
February295310
March410372
By how many units do the total sales of Shop P exceed those of Shop Q?
Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2024 · Tier I, 18 Sep 2024, Shift 1 · Q52Easy

Example 1 · Data Interpretation · Reading Tables and Graphs

The given table shows the number of televisions that were sold by different showrooms in years 2015 to 2019.
Year/ShowroomABCD
2015212200205208
2016210215225220
2017190204212205
2018198212222224
2019218192205203
Find the difference between the sale of televisions from showrooms A, B and C in 2017 and the sale of televisions from showrooms B, C and D in 2019?

Dropping the unit line

A table headed "in thousands" that gives a difference of 8.2 means 8,200, and the options are usually printed in full. Read the unit line before you read the numbers.

Adding a printed Total row again

Some tables print a Total row or column. It is already the sum of the entries above it, so adding it in with them doubles the answer.
Drill 12 more on totals and differences of totals from a table

Concept 2 of 3: Picking out the rows that meet a condition

Questions such as "in how many years", "which item has the least" or "which statement is true" never need a long calculation. Build one new number for every row (a difference, a total, three times a value), write it beside the row, and then scan the column you built.

Definition

  • Build the column the question needs: unsold == produced −- sold, absentees == applied −- present, a year's total across companies.
  • Then scan: count the rows that pass, or pick the largest or smallest.
  • "More than" and "less than" are strict: a row equal to the limit does not count. "At least" and "not less than" include it.
  • Second highest: find the highest, set it aside, take the highest of the rest. Two equal values can share a place.
  • Statement questions: test each statement against the table. One wrong number makes the whole statement false, so stop checking it as soon as one fails.

Worked example

The table shows the stock and the sales of five stores.
StoreStockSold
A420346
B380344
C510429
D295270
E460372
In how many stores were more than 74 items left unsold?
Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2024 · Tier I, 9 Sep 2024, Shift 1 · Q66Moderate

Example 2 · Data Interpretation · Reading Tables and Graphs

The following table shows the total candidates appeared and number of candidates present, in different exam centres – P, Q and R. Study the table and answer the question that follows.
YearP TotalP PresentQ TotalQ PresentR TotalR Present
2016454256455550
2017504575554540
2018646065456555
2019806984727062
2020554480669085
'Total' denotes total candidates applied for the centre,'Present' denotes the candidates appeared. In which year was the number of absentees the second highest in total of all centres?

Counting the row that equals the limit

"More than the average" or "more than 55" leaves out a row exactly equal to it. Only "at least" or "not less than" includes the equal row.

Reading second highest as the second row

Second highest is about size, not position. Build the full column of values first, then take the largest after the largest.
Drill 7 more on picking out the rows that meet a condition

Concept 3 of 3: Reading a cumulative and-above table

In a table headed "40 and above, 30 and above, 20 and above", every column counts everyone who reached that mark or more. So the columns overlap: a student with 45 is counted in all of them. The number in a band comes from subtracting two columns.

Definition

  • Each entry is the number of students who scored that mark or more.
  • In a band: from mark aa up to (but not including) mark bb, take "aa and above" minus "bb and above".
  • Below a mark: total minus "that mark and above".
  • A percentage cut-off: change it to marks first. On a paper out of 60, 40% is 24 marks and 75% is 45 marks.
  • Moving right, towards lower marks, the numbers can only stay equal or grow. A printed row that shrinks is a misprint; use only the column the question needs.

Bands from a cumulative table

Na≤x<b=N≥a−N≥bN<a=Ntotal−N≥aN_{a \le x < b} = N_{\ge a} - N_{\ge b} \qquad N_{< a} = N_{\text{total}} - N_{\ge a}
  • N≥aN_{\ge a}students with a or more marks
  • NtotalN_{\text{total}}everyone, the "0 and above" column

Worked example

The table classifies 240 students by their Science marks (out of 80).
Subject64 and above48 and above32 and above16 and above0 and above
Science34118176221240
How many students scored at least 60% but less than 80%?
Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2024 · Tier I, 17 Sep 2024, Shift 2 · Q73Easy

Example 3 · Data Interpretation · Reading Tables and Graphs

The following table shows the categorisation of 100 students based on their marks in Physics and Chemistry in an examination. Marks out of 50
Subject40 and above30 and above20 and above10 and above0 and above
Physics9328092100
Chemistry4216681100
If a minimum of 40% marks in Chemistry is required to pursue higher studies in Chemistry, how many students will be eligible to pursue higher studies in Chemistry?

Reading a cumulative column as a band

"20 and above" includes everyone with 30, 40 or more. The number who scored from 20 up to 30 is "20 and above" minus "30 and above".

Looking up the percentage instead of the marks

The columns are headed in marks. A cut-off given as a percentage must first be turned into marks out of the paper's maximum.
Drill 3 more on reading a cumulative and-above table

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (2)

  • Totals and differences of totals from a table

    Difference of two totals

    ∑ai−∑bi=∑(ai−bi)\sum a_i - \sum b_i = \sum (a_i - b_i)
  • Reading a cumulative and-above table

    Bands from a cumulative table

    Na≤x<b=N≥a−N≥bN<a=Ntotal−N≥aN_{a \le x < b} = N_{\ge a} - N_{\ge b} \qquad N_{< a} = N_{\text{total}} - N_{\ge a}

Watch out for (6)

Test yourself on Data Interpretation

20 past SSC CGL questions from this chapter, timed at 12 minutes and marked the way the exam marks it. You see your score and every answer the moment you finish. Free to start.

Take the Data Interpretation chapter testDrill all 25 questions