NCS Mathematical Skills: Data, Statistics, and Workplace Calculation

Mathematical skills (수리능력) is the second core NCS competency and consistently one of the most feared. Exam questions test your ability to apply arithmetic and statistics to realistic workplace scenarios — not abstract mathematics, but practical calculation with tables, charts, and data.

The Four Sub-Competencies

Sub-competency	Korean	Focus
Basic calculations	기초연산능력	Arithmetic, fractions, percentages
Basic statistics	기초통계능력	Mean, median, mode, variance
Chart comprehension	도표분석능력	Reading tables, bar charts, line graphs, pie charts
Chart production	도표작성능력	Selecting and creating appropriate charts

1. Core Calculation Types

Percentage Change

Percentage increase/decrease: Change% = (New Value − Old Value) / Old Value × 100

Example: Sales were 800 last year and 920 this year. Change = (920 − 800) / 800 × 100 = +15%

Common mistake: Dividing by the new value instead of the old. Always divide by the original value.

Ratio and Proportion

If A:B = 3:5 and total = 240, find A and B. A = 240 × (3/8) = 90, B = 240 × (5/8) = 150

Cross-multiplication: If A/B = C/D, then A×D = B×C (useful for finding unknown values).

Rate Problems

Work rate: If A completes a job in 6 days and B in 4 days, together they complete 1/6 + 1/4 = 5/12 of the job per day → 12/5 = 2.4 days together.

Speed problems: Time = Distance / Speed. When speeds or distances differ in segments, calculate each segment separately.

2. Basic Statistics

Measures of Central Tendency

Mean (평균) = Sum of all values ÷ Count

Most commonly used; sensitive to outliers.

Median (중앙값) = Middle value when sorted; if even count, average of two middle values.

Better for skewed data or when outliers are present.

Mode (최빈값) = Most frequently occurring value.

Measures of Dispersion

Range: Maximum − Minimum (simple but crude)

Variance (분산): Average of squared deviations from the mean. σ² = Σ(xi − μ)² / N

Standard deviation (표준편차): √Variance — same units as original data.

Coefficient of variation (변동계수) = Standard deviation / Mean × 100 — useful for comparing variability between datasets with different scales.

Exam Application: Which Measure to Use?

Situation	Best measure
Normal distribution, no outliers	Mean and standard deviation
Skewed data, outliers present	Median and range
Most popular value needed	Mode
Comparing relative variability	Coefficient of variation

3. Chart Reading (도표분석능력)

Bar Charts

Compare categorical data across groups
Read the scale carefully (y-axis may not start at 0 — this inflates apparent differences)
Grouped vs stacked bars serve different purposes

Exam trap: Bar charts with dual y-axes. Each bar series refers to a different scale — read carefully which axis applies to which series.

Line Graphs

Show change over time (trends)
Steepness of slope indicates rate of change
Intersection points signal when two trends cross

Key questions: Is the trend increasing/decreasing/stable? When does the rate of change accelerate or slow?

Pie Charts

Show proportions of a whole (must sum to 100%)
Convert percentages to actual values using total: Value = % × Total / 100
Compare only same-year or same-total pie charts; cross-pie comparison without totals is misleading

Data type	Best chart
Comparison between categories	Bar chart
Change over time	Line graph
Part-to-whole proportions	Pie chart
Relationship between two variables	Scatter plot
Distribution of data	Histogram

Common Chart Production Rules

Always label axes with names and units
Title should describe the data clearly
Legend required when multiple series are shown
Y-axis scale should start at 0 unless specifically justified

5. Workplace Statistics Scenarios

Productivity rate: Output / Input × 100%

Pass rate calculation: Candidates who passed / Total candidates × 100%

Budget utilization: Amount spent / Budget × 100%

Per-capita calculation: Total amount / Number of people

Weighted average: Σ(value × weight) / Σ(weights) Example: 3 employees score 80, 2 score 90 → Weighted average = (3×80 + 2×90) / 5 = 84

Quick Reference: Common Formulas

Formula	Application
% change = (new−old)/old × 100	Year-on-year comparison
Mean = Σx / n	Central tendency
Variance = Σ(x−μ)² / n	Dispersion
Rate × Base = Amount	Any rate calculation
Work rate = 1/time	Combined work problems

Exam Strategy

Read the question first, then the data. Know what you are looking for before processing numbers.
Estimate before calculating: Approximate to verify your exact calculation is in the right ballpark.
Watch units: Mixing up 백만(million) and 억(100 million) accounts for many exam errors.
Don’t overthink: NCS math questions use clean numbers. If your calculation gives a messy decimal, recheck.
Manage time: Allocate no more than 90 seconds per math question. Skip and return if stuck.