Spread vs Center Examples in Statistics

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Spread vs Center.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Statistics.

Concept Recap

Center describes where the 'middle' of data lies; spread describes how far data extends from that center.

Two pizza delivery services both average 30-minute delivery (same center). But Service A ranges 28-32 minutes, while Service B ranges 10-50 minutes. Same center, wildly different spread. You'd trust A for consistent timing.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Center tells you where the data is located; spread tells you how tightly or loosely packed it is around that center. Both are needed for a full description.

Common stuck point: Students often summarize data with only the mean, ignoring spread entirely, leading to misleading comparisons between groups.

Worked Examples

Example 1

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Two machines fill bottles. Machine A fills: 500, 502, 498, 501, 499 mL. Machine B fills: 490, 510, 480, 520, 500 mL. Both have a mean of 500 mL. Which machine is more reliable?

Solution

  1. 1
    Step 1: Both means are 500 mL, so the centre is the same.
  2. 2
    Step 2: Machine A range: 502 - 498 = 4 mL. Machine B range: 520 - 480 = 40 mL.
  3. 3
    Step 3: Machine A has far less spread, meaning it fills more consistently.

Answer

Machine A is more reliable because it has less spread (range 4 mL vs 40 mL).
Centre alone does not tell the full story. Spread reveals consistency. A good statistical description needs both centre (where the data is) and spread (how variable the data is).

Example 2

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Dataset A: {10, 10, 10, 10, 10}. Dataset B: {2, 6, 10, 14, 18}. Compare their centres and spreads.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

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A restaurant's lunch wait times (minutes) — Week 1: 5, 6, 5, 7, 5. Week 2: 3, 10, 4, 8, 3. Find the mean and range for each week and explain which week had more predictable service.

Example 2

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Two classes both have median score 75. Class A scores are 72, 74, 75, 76, 78. Class B scores are 60, 70, 75, 80, 90. Which class has greater spread, and which class seems more consistent?
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Related Concepts

Data Variability

Background Knowledge

These ideas may be useful before you work through the harder examples.

meanvariability intro