Statistics Definitions > Greatest Possible Error

## What is The Greatest Possible Error?

The greatest possible error (GPE) is the **largest amount a ballpark figure can miss the mark.** **It’s one half of the measuring unit you are using.** For example:

- If measuring in centimeters, the GPE is 1/2 cm.
- …or in liters, the GPE is 1/2 L.
- If measuring in feet, the GPE is 1/2 of a foot.
- …or in tenths of a meter, the GPE is 1/2 of tenth of a meter (that’s 1/2 * 1/10 m = 0.05 m).

**Note**: “Error” in statistics doesn’t mean that it’s *wrong*; it just means it’s *imprecise*.

## Ballparking and GPE

The greatest possible error is a formal term for something we do every day: ballparking (i.e. estimating). For example, you might say “I’m about 5’8″.” That doesn’t mean you’re *exactly* 5’8″. It’s safe to say you could be a half inch either way. That half-inch is the GPE (because you’re using inches), so you’re already using the GPE — but may not know it!

## How to Find the Greatest Possible Error — Examples

#### Example problem #1: What is the GPE for 5 meters?.

Step 1: Rephrase the question by putting the word “about” in front of the number:

**What is the GPE for about 5 meters?. **

This should make the sentence sound more familiar (i.e. “It’s about 5 meters”).

Step 2: Identify the unit measurement.

We are measuring in “**meters**.”

Step 3: Multiply the measurement in Step 2 by one half:

“meter” * 1/2 = 1/2 meter.

The GPE for 5 meters is 1/2 meter.

That’s it!

#### Example problem #2: What is the GPE for 3.9 inches?.

Step 1: Rephrase the question by putting the word “about” in front of the number:

**What is the GPE for about 3.9 inches?. **

This should make the sentence sound more familiar (i.e. “It’s about 3.9 inches”).

Step 2: Identify the unit measurement.

We are measuring in “**inches**.”

Step 3: Multiply the measurement in Step 2 by one half:

“Inches” * 1/2 = 1/2 inch.

The GPE for 3.9 inches is 1/2 inch.

That’s it!

#### Example problem #3 (Trick Question!): What is the GPE for 9.76 cm?.

Step 1: Rephrase the question by putting the word “about” in front of the number:

**What is the GPE for about 9.76 cm?. **

This should make the sentence sound more familiar (i.e. “It’s about 9.76 cm”).

But!

We are measuring in centimeters, but notice there’s a couple of decimal places. W

*e aren’t actually measuring in cm, we’re measuring in hundredths of a centimeter.*

**If you have decimal places, then rephrase the statement in words, not numbers.**

“It’s about 9.76 cm” in words is “It’s about 9 cm and 76 hundredths.”

Step 2: Identify the unit measurement.

We are measuring in hundredths of a centimeter (in numbers, that’s 1/100^{ths}).

Step 3: Multiply the measurement in Step 2 by one half:

1/2 * 1/100^{th} cm = 0.005 cm .

The GPE for 9.76 cm is 0.005 cm.

That’s it!

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