9.2 Pie Charts & Percent of a Whole

What a Pie Chart Is

A pie chart is a circle divided into sectors (wedges). Each sector represents one category, and the size of the sector is proportional to that category's share of a total. Two rules are always true:

1. The sectors add up to 100% of the data.
2. The sectors add up to 360° of the circle.

Because 100% maps to 360°, each percent is worth 3.6° (360 ÷ 100 = 3.6). That single conversion lets you move between percent and angle.

Three Conversions to Know

Worked Example: Percent to Angle

A nurse-run clinic classifies its 200 patient visits by reason: 35% routine, 25% acute illness, 20% follow-up, 15% lab, 5% other. What angle should the "acute illness" sector occupy?

Step 1: Take the percent — 25%. Step 2: Multiply by 3.6: 25 × 3.6 = 90°.

A 25% sector is exactly one-quarter of the circle, which matches 90° of 360°. The math and the intuition agree.

Worked Example: Percent to Value

Using the same clinic data with 200 total visits, how many visits were for acute illness?

Step 1: Convert 25% to a decimal: 25 ÷ 100 = 0.25. Step 2: Multiply by the total: 0.25 × 200 = 50 visits.

You can also reason it through: 25% is one quarter, and one quarter of 200 is 50. Both paths reach the same answer; use whichever is faster for you.

Reading a Pie Chart

When the NEX gives you a pie chart, it usually labels each sector with either a percent or a value. Your job is to move between those two forms.

Worked Example: Value to Percent

A pie chart shows a hospital's 1,200 admissions split into four departments. The Medical sector is labeled 420 admissions. What percent of admissions were Medical?

Step 1: Divide the sector value by the total: 420 ÷ 1,200 = 0.35. Step 2: Convert to a percent: 0.35 × 100 = 35%.

Worked Example: Finding a Missing Sector

A pie chart of 500 patients labels three sectors: 40% Surgical, 30% Medical, 20% Pediatric. What is the fourth sector (Other)?

Step 1: Add the known sectors: 40 + 30 + 20 = 90%. Step 2: Subtract from 100%: 100 − 90 = 10%.

Step 3: If you need the count: 10% of 500 = 0.10 × 500 = 50 patients.

This is the most common pie-chart question on the exam: the sectors must total 100%, so a missing sector is found by subtraction.

When to Use a Pie Chart vs a Bar Chart

Pie charts answer one question: how is the whole divided? They are good when:

• You have 2 to 6 categories.
• The categories are mutually exclusive parts of one total.
• You want to show a part-to-whole relationship ("half of all visits were routine").

Bar charts are better when:

• You are comparing categories that are not parts of one whole (length of stay by unit, average BMI by age group).
• You have more than 6 categories (pie charts become unreadable with many thin slices).
• You want to compare exact values, since reading a bar height is more precise than reading a sector angle.

A common NEX trap is a pie chart used for data that is not a single whole — for example, a "pie chart of average blood pressure by age group." Average blood pressures are not parts of a whole; they are separate averages. A bar chart is the correct choice.

A Nursing Example: Fluid Intake

A patient's 24-hour intake totals 2,400 mL, split as: IV fluids 1,200 mL, water 600 mL, juice 360 mL, broth 240 mL.

Question: What percent of intake came from IV fluids?

Step 1: Divide: 1,200 ÷ 2,400 = 0.50. Step 2: Convert: 0.50 × 100 = 50%.

Question: What angle would the "juice" sector occupy?

Step 1: Find juice as a percent: 360 ÷ 2,400 = 0.15 = 15%. Step 2: Multiply by 3.6: 15 × 3.6 = 54°.

Quick Checks

• Sectors must sum to 100% or 360°. If they do not, re-read the chart or find the missing sector by subtraction.
• Percent → angle: multiply by 3.6.
• Percent → value: multiply the decimal form by the total.
• Value → percent: divide by the total and multiply by 100.
• Ask whether the data is truly parts of one whole before choosing a pie chart.