Math  /  Data & Statistics

QuestionJohn spent $75\$ 75 on a shopping trip for new clothes last week. He had expected to spend $100\$ 100 on clothes. \begin{tabular}{|c|c|c|c|c|c|} \hline Approximate Value & Exact Value & Error & Absolute Error & Ratio & Percent Error \\ \hline$100\$ 100 & $75\$ 75 & $25\$ 25 & & & \\ \hline \end{tabular}
How much was the absolute error in his estimate? \ \square$

Studdy Solution

STEP 1

What is this asking? How far off was John's guess, ignoring whether it was too high or too low? Watch out! Don't mix up "error" and "absolute error"!
Error can be positive or negative, but absolute error is always positive!

STEP 2

1. Calculate the Error
2. Calculate the Absolute Error

STEP 3

Alright, so John *thought* he'd spend $100\$100, right?
That's his **estimated value**.
But he *actually* spent $75\$75, which is the **exact value**.
We want to find the difference between these two.

STEP 4

The **error** is calculated as: Error=Exact ValueEstimated Value \text{Error} = \text{Exact Value} - \text{Estimated Value} .
This tells us how much John's estimate was off.

STEP 5

Let's plug in the numbers: Error=$75$100=$25 \text{Error} = \$75 - \$100 = -\$25 .
This negative sign means John overestimated; he spent $25\$25 *less* than he thought.

STEP 6

The **absolute error** is simply the *magnitude* of the error.
We just drop the negative sign (if there is one)!
It's always positive, showing just *how far off* the estimate was, regardless of direction.

STEP 7

Since our error was $25-\$25, the absolute error is $25\$25.
Easy peasy!

STEP 8

John's absolute error was $25\$25.

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