Data Interpretation

Read the chart's FRAME before its numbers, in this fixed order: title, units (rupees or crores? thousands?), the axis scale, the footnote, and whether the figure shows an absolute value or a percentage. Most lost marks in data interpretation come from a correct calculation on a misread frame — especially a pie chart of shares being treated as if it showed quantities, when the totals of the two years differ. Then approximate: round to convenient numbers, compare fractions rather than computing exact percentages, and only calculate exactly when two options are genuinely close.

• Title, units, then numbers — in that order, every time.

  Read the chart title and axis labels first to know what is even being measured — crores versus lakhs, percentage versus absolute count. A calculation done on the wrong unit is wasted regardless of how carefully it was done.

• Percentage change needs the base, not just the two numbers.

  Percentage change is (new minus old) divided by old, times 100 — always divide by the earlier value, never the later one. This single rule, misapplied, is the most common data-interpretation error under time pressure.

• 1Percentage change from A to B is ((B - A) / A) x 100, using the earlier value A as the base.
• 2In a stacked bar chart the total height is the sum of the segments; in a grouped bar chart, adjacent bars are separate categories at the same time point, not parts of a whole.
• 3A pie chart's slices sum to 100 per cent (or 360 degrees); converting a slice's degree measure to a percentage is degree divided by 3.6.
• 4Where a question gives both a table and a chart on the same data, cross-check one figure between the two before trusting either — mismatches are sometimes deliberate.

• Percentage change = (new value - old value) / old value x 100. The denominator is always the OLD value, and using the new one is the standard error.
• In a pie chart the whole circle is 360 degrees, so each 1% of the total equals 3.6 degrees.
• A pie chart shows shares, not amounts: a larger share of a smaller total can be a smaller absolute quantity, which is the most exploited trap in data interpretation.
• Useful fraction-percentage conversions for fast estimation: 1/8 = 12.5%, 1/6 = 16.67%, 1/3 = 33.33%, 3/8 = 37.5%, 5/8 = 62.5%.
• The average of a set always lies between its smallest and largest values; if your computed average falls outside that range, the arithmetic is wrong.

• Percentage change always divides by the starting value, never the ending value — dividing by the wrong one silently produces a plausible but wrong answer.

• Quantitative Aptitude for Competitive Examinations — R S Aggarwal
• Fast Track Objective Arithmetic — Arihant
• NCERT Class X — Mathematics

• NCERT textbooks (free PDFs)