Data Interpretation for CSAT: Tables and PYQs

Data interpretation is the skill of reading numbers presented as tables, charts or graphs and answering questions from them. In CSAT Paper II, a qualifying paper (roughly 33 percent clears it; the marks do not add to your merit rank), these are gift marks: the arithmetic is elementary (percentages, averages, ratios), and the only real test is reading the data correctly under time pressure.

The three faces of DI data

UPSC presents data as tables (rows and columns of numbers, like scooter sales by showroom), bar and line charts (heights or points showing trends over years), and caselets (a paragraph hiding the numbers in words). Before touching any question, spend fifteen seconds on the labels, units and footnotes: what is measured, in what units (thousands? lakhs?), and over which period. Most DI errors are reading errors, not arithmetic errors.

The five computations you will keep repeating

Nearly every DI question reduces to one of five calculations: a percentage share (part divided by whole, times 100), a percentage change (difference divided by the original, times 100), an average (total divided by count), a ratio (one quantity divided by another, reduced), or a comparison (which is largest, smallest, or the difference between two). Learn these five cold; the rest is reading.

Worked set 1: scooter sales (UPSC CDS 2019)

The data: S1 is the percentage distribution of scooters of companies X and Y together sold by five showrooms (total 6400): A 19, B 21, C 15, D 33, E 12. S2 is the distribution of company X scooters alone (total 3000): A 24, B 18, C 20, D 30, E 8. Company Y at any showroom = S1 minus S2 there. The key discipline is converting every percentage to an absolute number before comparing.

Worked example. Y scooters sold by showroom E are what percent of both companies' scooters sold by showroom C? Step 1: both at E = 12 percent of 6400 = 768; X at E = 8 percent of 3000 = 240; so Y at E = 768 minus 240 = 528. Step 2: both at C = 15 percent of 6400 = 960. Step 3: 528 / 960 times 100 = 55 percent, option (c). The trap is dividing by 768 (the wrong base) instead of 960; the stem asks for a percent of showroom C's total.

Worked example. Both companies' scooters sold by showroom B are what percent more than company X's scooters sold by showroom A? Both at B = 21 percent of 6400 = 1344. X at A = 24 percent of 3000 = 720. Percent more = (1344 minus 720) / 720 times 100 = 86.67 percent, about 86 percent, option (c). Note the base: percent more than X at A, so divide by 720, not 1344.

Worked set 2: road accident deaths (UPSC CDS 2019)

The data (deaths in road accidents):

Worked example. What was the average number of pedestrians killed per day in 2017? Total 20457 over 365 days = 56.06, about 56, option (d). Per-day always means divide by 365; a per-month instinct gives the wrong answer.

Worked example. What was the approximate percentage change in pedestrian deaths between 2014 and 2017? Change = 20457 minus 12330 = 8127; divided by the old value 12330, times 100 = 65.9 percent, about 66 percent, option (a). Always divide by the earlier year's figure.

Traps UPSC sets

• Wrong base in percentages. Percent of C's total means divide by C's number (960), not by E's (768); percent more than A means divide by A's number. Circle the base phrase in the stem.
• Per-day means 365. Dividing annual deaths by 12 or 30 is a planted mistake; read whether the stem says per day, per month or per year.
• Change divides by the old value. (20457 minus 12330)/12330 is 66 percent; dividing by 20457 instead gives a wrong 40 percent.
• Units in the header. A table headed in thousands multiplies every answer by 1000; check the unit line before computing.
• Mixing years and categories. Bikers in 2017 (48746) sits next to pedestrians in 2017 (20457); read the row and the column together, never just the nearest number.

Speed tactics

• Approximate to the option band. 20457/365 is clearly between 55 and 57; with options 51, 53, 54, 56 you can stop computing at 56.06 and tick (d).
• Convert percentages once. Turn the whole table into absolute numbers first; then every question is simple arithmetic instead of repeated percentage work.
• Compare by cross-multiplication. To find which share is largest, compare fractions a/b and c/d by comparing a times d with c times b; no decimals needed.
• Differences before totals. Y at E = S1 minus S2 directly (768 minus 240); do not reconstruct company Y's whole column.

Key Terms

• Data interpretation: answering questions from data presented as tables, charts or graphs rather than from prose.
• Table: data arranged in rows and columns; read the row and column headers together to locate any value.
• Bar chart: quantities shown as bars whose heights are proportional to the values, used for comparing categories.
• Line graph: values plotted as points joined by lines, used for showing trends over time.
• Caselet: a short paragraph that hides the numbers in words; the first step is extracting them into a small table.
• Percentage: a part expressed per hundred of a whole; share = part/whole times 100.
• Percentage change: relative growth or fall: (new minus old)/old times 100.
• Average (mean): total divided by the number of items; for per-day figures the divisor is 365.
• Ratio: a comparison of two quantities by division, written a:b in lowest terms.
• Base: the quantity a percentage is computed against; the most error-prone word in any DI stem.

Practice questions

Directions for the following 2 (two) items: read the scooter data below and answer. S1: percentage distribution of scooters of companies X and Y together sold by five showrooms (total 6400): A 19, B 21, C 15, D 33, E 12. S2: distribution of company X scooters alone (total 3000): A 24, B 18, C 20, D 30, E 8.