6.1 Data Interpretation

6.1 Data Interpretation on the NMAT Quantitative Subtest

The CEM Quantitative subtest is 30 items with a recommended ~40 minutes. Official item families include fundamental operations, problem solving, and data interpretation (DI). DI is where many pre-med applicants lose time and accuracy: the arithmetic is often elementary, but the setup is multi-step, and a single wrong-row or wrong-unit mistake sinks the whole chain.

This section trains you to read structure before you calculate, work multi-step table problems cleanly, compute percent change and weighted averages under pressure, and avoid the classic part-to-part vs part-to-whole traps. Medical and public-health themed tables are used so the numbers feel like the health data you will meet later in training—not because NMAT is a medical content test in Part 1.

Quick frame: On every DI item: (1) title and units, (2) row and column labels, (3) what the question actually asks, (4) minimal arithmetic, (5) sanity-check magnitude against the table.

Why DI rewards method more than speed math

Unlike pure computation, DI embeds the answer inside a display—a table, a described bar or line chart, a pie of proportions, or a two-variable comparison. Your job is not to invent numbers; it is to select the correct cells, apply the correct operation, and ignore distractors that use nearby but wrong cells.

Under OCBT conditions you work without a calculator. That means DI practice must build order-of-magnitude sense, fraction fluency, and disciplined scratch work—not reliance on long division for every step.

Read Titles, Units, and Labels First

Before any subtraction or division, fix three anchors:

1. Title / caption — What universe is this? City hospitals? One year? Multiple years?
2. Units — Patients, thousands of cases, percent of total, cases per 100,000 population?
3. Axes or headers — Is the column "2024 admissions" or "2024 percent of admissions"?

Wrong-row and wrong-column errors are the #1 silent killer. A distractor will often be the exact arithmetic you would get if you used the adjacent row or the percent column instead of the count column.

Worked habit: the 10-second scan

Given any table, silently answer:

• How many rows of data (excluding totals)?
• Is there a Total row or column I can use as a check?
• Are numbers counts, rates, or percentages?
• Does the question want a difference, a ratio, a percent of total, or a percent change over time?

Only then write a one-line plan on scratch paper, e.g. (Row B 2025 − Row B 2024) / Row B 2024 × 100.

Tables: Multi-Step Public-Health Example

Table A — Outpatient visits by department, Metro clinic network (counts)

Example 1 — Simple share (part-to-whole)

Question: In 2024, approximately what percent of all outpatient visits were Emergency visits?

Plan: Emergency 2024 ÷ Total 2024.

2,875 / 12,420. Estimate: 2,875 / 12,420 ≈ 2,880 / 12,400 ≈ 0.232 → about 23%.

Exact-ish: 12,420 × 0.23 = 2,856.6; remainder 18.4 → slightly over 23%. Closest answer among typical choices would be 23% (or 23.2% if finer options appear).

Trap: Using 2025 Emergency (3,162) or dividing by 2024 Internal medicine instead of Total.

Example 2 — Percent change

Question: What was the percent increase in Internal medicine visits from 2023 to 2025?

Plan: (5,082 − 4,200) / 4,200.

Difference = 882. 882 / 4,200 = 882 ÷ 4,200.

Simplify: divide by 6 → 147 / 700 = 0.21 = 21%.

Trap: Reporting the raw difference 882 as if it were a percent, or using (2025 − 2024) only, or dividing by the later year (wrong base).

Example 3 — Two-step comparison

Question: From 2023 to 2024, which department had the largest percent increase in visits?

Compute percent change for each:

• IM: (4,620 − 4,200)/4,200 = 420/4,200 = 10%
• Peds: (2,945 − 3,100)/3,100 = (−155)/3,100 ≈ −5% (decrease)
• OB: (1,980 − 1,800)/1,800 = 180/1,800 = 10%
• EM: (2,875 − 2,500)/2,500 = 375/2,500 = 15%

Answer: Emergency at 15%. Notice IM and OB both rose 10% in percent terms even though IM’s absolute gain (420) is larger than OB’s (180). Absolute change and percent change answer different questions—read the stem.

Example 4 — Weighted contribution / multi-row

Question: In 2025, Internal medicine and Obstetrics together accounted for what fraction of total visits?

(5,082 + 2,178) / 13,662 = 7,260 / 13,662.

Estimate: 7,260 / 13,662 ≈ 7,260 / 13,700 ≈ 0.53 → a bit over 53%.

More tightly: 13,662 × 0.53 = 7,240.86; remainder ~19 → ≈ 53.1%.

Trap: Adding three departments when the stem said two, or using 2024 totals.

Bar and Line Descriptions (Text-Presented Charts)

On a text-based study guide (and often in verbalized chart stems), charts appear as described bars or lines. Treat them like tables:

• Bars usually compare categories at one time (or grouped bars across years).
• Lines usually show a variable over time.
• Always note whether the vertical scale starts at zero. A line that “looks steep” on a cropped axis may be a small absolute change.

Example (described line): A chart shows weekly dengue reports in a province: Week 1 = 40 cases, Week 2 = 48, Week 3 = 60, Week 4 = 72.

Question: From Week 1 to Week 4, the number of cases increased by what percent?

(72 − 40) / 40 = 32/40 = 80%.

Question: Which week-to-week interval had the largest absolute increase?

W1→W2: +8; W2→W3: +12; W3→W4: +12. Largest absolute jump is +12 (ties for last two intervals). If asked for largest percent increase: 8/40=20%, 12/48=25%, 12/60=20% → Week 2 to Week 3.

Same data, two different “largest increase” answers—stem language is everything.

Pie Proportions

Pies encode parts of a whole at one moment. If the whole is 100% (or 360°), each slice is a part-to-whole share.

Example: A hospital’s 2025 pharmacy budget is split: Antibiotics 35%, Chronic meds 25%, Vaccines 15%, Other 25%. Total budget = Php 8,000,000.

Antibiotics amount: 0.35 × 8,000,000 = Php 2,800,000.

Antibiotics as a ratio to Vaccines: 35:15 = 7:3 (part-to-part), not 35% of 15%.

Combined chronic + vaccines share: 25% + 15% = 40% of the whole → 0.40 × 8,000,000 = Php 3,200,000.

Pie traps

• Treating two slice percents as if one is “percent of the other” without converting to amounts or a proper ratio.
• Forgetting that pie slices must sum to 100% (use that as a check when reconstructing a missing slice).
• Mixing a pie from Year A with a total budget from Year B.

Two-Variable Comparisons

DI often pairs two variables: e.g. cases vs population, or admissions vs beds. Rates beat raw counts when bases differ.

Table B — Barangay clinic indicators

Raw cases ranking: Luna (700) > San Roque (480) > Mabini (400).

Rate per 1,000 population:

• San Roque: 480/12,000 × 1,000 = 40 per 1,000
• Mabini: 400/8,000 × 1,000 = 50 per 1,000
• Luna: 700/20,000 × 1,000 = 35 per 1,000

If the question asks which barangay has the highest burden per population, the answer is Mabini, not Luna. That is a classic part-to-whole (rate) vs raw-count trap.

Percent Change, Mentally

Formula (always same base = starting value):

[ \text{Percent change} = \frac{\text{New} - \text{Old}}{\text{Old}} \times 100% ]

• Increase if positive; decrease if negative.
• A change from 50 to 75 is +50%, not +25 percentage points (those are different concepts).
• Going up 25% then down 25% does not return to start: 100 → 125 → 93.75.

Percentage points vs percent

If vaccine coverage rises from 40% to 50% of a population, that is a 10 percentage-point rise, but a 25% relative increase ((50−40)/40). Exam stems that say “increased by 10%” when they mean points are ambiguous in real life; on NMAT-style items, read carefully whether the table cells are already percents or counts.

Weighted Averages from Tables

When groups have different sizes, the overall average is not the average of group averages.

Example: Two wards report mean length of stay (LOS):

Wrong: (4+6)/2 = 5.

Right weighted mean: (30×4 + 70×6) / (30+70) = (120 + 420)/100 = 5.4 days.

If a third ward C has 50 patients at mean LOS 5, overall = (120 + 420 + 250) / 150 = 790/150 ≈ 5.27 days.

Any time the stem gives subgroup means and sizes, weight by size.

Common DI Traps (Checklist)

Practice Rhythm for DI

1. Drill scan → plan → compute → check until it is automatic.
2. Build a personal error log: wrong cell, wrong base year, percent vs points, unweighted mean.
3. Time boxes: many DI items should finish in 60–90 seconds if the plan is clean; multi-step items may need ~2 minutes—budget them (see Section 6.2).
4. Link to later Physics: the same unit discipline and multi-step setup transfer to mechanics and circuits in Part 2.

Master DI structure and the Quantitative subtest becomes less about “hard math” and more about reliable extraction of the right numbers under CEM timing.