Spread vs Center Statistics Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

medium
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=4502 - 498 = 4 mL. Machine B range: 520−480=40520 - 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).

About Spread vs Center

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

Learn more about Spread vs Center →

More Spread vs Center Examples

Example 2 medium

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

Example 3 medium

A restaurant's lunch wait times (minutes) — Week 1: 5, 6, 5, 7, 5. Week 2: 3, 10, 4, 8, 3. Find the

Example 4 medium

Two classes both have median score 75. Class A scores are 72, 74, 75, 76, 78. Class B scores are 60,

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