Data Interpretation: Tables, Graphs & Fire Incident Statistics

Why Data Interpretation Dominates the Analytical Sub-Test

General Ability carries 25 percent of the Fire Officer Examination (FOE) - roughly 37 or 38 of the 150 scored items - split across Verbal, Analytical and Numerical reasoning. A large share of the Analytical items are data interpretation problems: you are handed a table or a chart of fire-service administrative data and asked to locate, combine or compare values. Calculators are prohibited for the entire 3 hours and 5 minutes, so every figure has to come out of your head or off the margin of the test booklet. The Bureau of Fire Protection (BFP) operates the same way - monthly incident returns, Fire Safety Inspection Certificate (FSIC) issuance counts, response-time logs and estimated-damage tallies are read off tables before any resource decision is signed.

The Display Types and What Each Is Good For

Read the title, the units and the key before you read a single number. A pictogram in which one flame symbol equals 50 incidents, or a pie labelled "percentage of total estimated damage in pesos" rather than "percentage of incidents", punishes anyone who starts with the picture.

Locating a Value Versus Deriving One

• Locating means the answer is printed somewhere in the display. Find the intersection of the correct row and the correct column and stop. Most examinees lose these marks by reading the adjacent row.
• Deriving means the answer must be computed - a total, a difference, a share, a ratio, an average or a rate. Before you compute, say the required arithmetic out loud in one sentence. If you cannot state it in one sentence, you have misread the question.

Row Percentages, Column Percentages and the Classic Trap

Work from this practice cross-tabulation of structural fire incidents recorded by one BFP regional office over a calendar year.

The cell holding 45 lighted-cigarette fires in Q4 generates two completely different percentages:

• Row percentage (denominator is the cause total): 45 of 120 lighted-cigarette fires happened in Q4, which is 37.5 percent.
• Column percentage (denominator is the quarter total): 45 of 280 Q4 fires were caused by a lighted cigarette, which is 16.1 percent.

Both are true; they answer different questions. Circle the denominator the question names before you divide. This single habit is worth several marks.

Worked Example: A Multi-Step Comparison

Question. Q4 recorded the highest electrical-ignition count of any quarter. Was electrical ignition also a larger share of Q4 fires than of the year as a whole?

1. Q4 electrical share = 108 / 280. Anchor on 40 percent: 10 percent of 280 is 28, so 40 percent is 112. Since 108 is less than 112, the share is under 40 percent. Refine: 112 - 108 = 4, and 1 percent of 280 is 2.8, so subtract about 1.4 points. Share is about 38.6 percent.
2. Full-year electrical share = 360 / 900 = 40.0 percent exactly.
3. Conclusion: the highest count sits in the quarter with the lowest share. Quarter shares run 40.0, 42.0, 40.0 and 38.6 percent; Q2 leads on share while Q4 leads on volume.

A larger raw count inside a larger total does not mean a larger proportion. Examiners build distractors precisely on that confusion.

Percentage Change Versus Percentage-Point Change

Percentage change = (New value - Old value) / Old value x 100. The denominator is always the old value.

Worked Example: Year-on-Year Incident Growth

BFP logged 18,256 fire incidents nationwide in CY 2024 against 16,433 in CY 2023.

1. Absolute change = 18,256 - 16,433 = 1,823 incidents.
2. Benchmark: 10 percent of 16,433 is 1,643.3; 1 percent is 164.3.
3. 1,823 - 1,643 = 180, and 180 divided by 164.3 is a little over 1. So the increase is about 10 + 1.1 = 11.1 percent.

Contrast that with a percentage-point change. If electrical ignition made up 40.0 percent of one region's fires in CY 2024 and 43.5 percent in CY 2025, the share rose by 3.5 percentage points - but that is a relative rise of 8.75 percent in the share (3.5 divided by 40.0). Write "points" when the figures being subtracted are themselves percentages. Reported damage figures deserve the same caution: BFP put CY 2023 property damage at PhP 13.191 billion and CY 2024 at close to PhP 14 billion. The second figure is rounded, so quoting a four-digit percentage change from it is false precision.

Rates Versus Raw Counts

A rate divides events by exposure - usually population - and multiplies by 1,000 or 100,000.

• District A: 900 fires in a population of 6,000,000, which is 15.0 fires per 100,000.
• District B: 480 fires in a population of 2,400,000, which is 20.0 fires per 100,000.

District B logs 420 fewer fires yet carries the higher incidence. The reverse trap matters just as much: a city whose fires rise from 240 to 264 (up 10 percent) while its population rises from 800,000 to 960,000 (up 20 percent) has moved from 30.0 to 27.5 fires per 100,000 - a rising count with a falling rate.

Cumulative Totals, Interpolation and Extrapolation

Read cumulative rows for "at most" and "within" questions: 297 of 360 calls, or 82.5 percent, were answered within 15 minutes. The median class is the one containing the 180.5th call, which is the 5-to-under-10 band. Interpolation estimates a value between plotted points - if average response time was 8.4 minutes in 2021 and 6.0 minutes in 2025 and the fall looks straight, the 2023 estimate is the midpoint, 7.2 minutes. Extrapolation projects beyond the plotted range and is far weaker; a trend line cannot fall below zero, and a chart alone never justifies a forecast.

What a Display Legitimately Supports

1. It supports statements of quantity, share, order and direction that are visible in the data.
2. It does not support causation. Regions with more fire stations often log more fires, because reporting improves - not because stations start fires.
3. It does not support conclusions about a variable the chart never plots, such as cause, when the chart plots only month.
4. It does not support a comparison between two pie charts of different totals; 30 percent of 900 and 30 percent of 200 are different worlds.

The Traps That Cost Marks

• Confusing a row percentage with a column percentage.
• Reporting a percentage-point move as a percentage change, or the reverse.
• Comparing raw counts across populations of different sizes.
• Reading a value off a chart when a printed table already gives it exactly.
• Ignoring a pictogram key or a "figures in thousands" note.
• Extrapolating a trend line past the plotted range and treating it as fact.

Working Without a Calculator

Anchor everything on 10 percent, 5 percent and 1 percent. For 17 percent of 4,800: 10 percent is 480, 5 percent is 240, 1 percent is 48, so 480 + 240 + 96 = 816. Halve repeatedly for 50, 25 and 12.5 percent. Round to a friendly number, compute, then correct in the direction you rounded - as in the 108 / 280 example above. Because FOE options are usually well separated, a disciplined estimate identifies the answer without exact long division.