[NCS Numeracy Chapter 03] Practice Data-Interpretation Structures with Original Example Problems

Data-interpretation questions often look difficult because they contain many numbers, but the real difficulty is usually not the arithmetic. It is deciding what should be converted into an actual value and which group a percentage belongs to.

Three Goals of This Post

• Group the most common conversion structures in NCS-style data interpretation.
• Explain how to move from indices, shares, and ratios to actual values.
• Let students practice the same moves through an original problem set.

Five Core Structures in Data Interpretation

Four Lines to Write First

1. What is the total?
2. What is the part?
3. Which group does each percentage belong to?
4. Am I solving for a rate or an actual value?

Quick Check for the Reference Group

• When you see a percentage, rewrite it as percentage of what?
• Mark every place where the group changes, such as total, among them, or for each group.
• Decide whether the final answer should be a rate or an actual value before calculating.

Why Formula Templates Help

• Index interpretation/conversion: compared value / benchmark value = index / 100
• Part-total reconstruction: total = part ÷ rate
• Grouped actual-value combination: find each group's actual value, then add
• Weighted average: weighted average = weighted sum ÷ total amount
• Multi-group value accumulation: convert each subgroup into an actual value, then add all of them

Some problems combine more than one structure. A weighted-average problem, for example, may still require part-total conversion before the final average step.

1. Index Conversion

Key question: what is the benchmark value, and what is the compared value?

In a commuting-cost index, City X is set to 100 and City Y is 135. If the monthly commuting cost in City X is 48,000 won, what is the monthly commuting cost in City Y?

Use a direct ratio:

So,

2. Reconstructing the Total from a Part and Its Share

Key formula: part = total x rate. To recover the total, reverse that formula.

In the reusable tumbler market, Brand A has a market share of 35% and an actual sales volume of 52,500 units. What is the total market sales volume?

If the total is $T$, then

So,

3. Combining Grouped Ratios

This type becomes much easier once you split the population into groups first and avoid mixing percentages with different denominators.

A training program has 400 applicants in total. The planning track accounts for 45% and the operations track for 55%. In the planning track, 60% are from local universities. In the operations track, 40% are from local universities. How many local-university applicants are there in total?

Planning has 180 applicants, so its local-university count is 108. Operations has 220 applicants, so its local-university count is 88. Therefore the total is:

4. Weighted Average

This is not the same as a simple average. Each score matters in proportion to its case count.

Customer-service cases and satisfaction scores are: in-person 120 cases (4.5), phone 180 cases (3.8), and chat 100 cases (4.2). What is the overall weighted average satisfaction score?

The weighted sum is:

Since the total number of cases is 400,

5. Multi-Rate Accumulation

This type asks you to compute actual values inside each subgroup first and combine them only at the end.

A city has 50,000 households. Apartments are 60%, detached houses 25%, and mixed-use housing 15%. The auto-payment usage rates are 40%, 24%, and 32% respectively. How many households use auto-payment in total?

Find each housing group first, then apply the rate inside that group:

• apartments: 30,000 -> 12,000
• detached houses: 12,500 -> 3,000
• mixed-use housing: 7,500 -> 2,400

So the total is:

Try the Original Practice Set

How Students Should Study This Page

1. Mark the total group first.
2. Mark which percentage belongs to which group.
3. Convert percentages into actual values before comparing or averaging.
4. Only do the final sum, difference, or average at the end.

Check Yourself After Studying

• Can you explain which group each percentage belongs to?
• Can you tell whether the answer should be a percentage or an actual value?
• Can you distinguish a weighted average from a simple average?
• Can you solve at least three of the five practice problems again without the solution?

Wrap-Up

In data interpretation, the critical move is not the calculation itself. It is correctly identifying the reference group and converting the rate into an actual value. This page is designed as a student practice page for that exact habit. Later posts can split this even further into index conversion, grouped shares, weighted averages, and condition matching.