Question

a small band performed at a local church. they estimated 50 people would attend, but 80 people showed up to watch them play. what is the percent error of the number of people who attended the event? 37.5%

Explanation:

Step1: Recall percent error formula

The formula for percent error is $\text{Percent Error} = \frac{|\text{Measured Value} - \text{Estimated Value}|}{\text{Estimated Value}} \times 100\%$

Step2: Identify values

Measured value (actual attendance) = 80, Estimated value = 50

Step3: Calculate difference

$|80 - 50| = 30$

Step4: Apply formula

$\text{Percent Error} = \frac{30}{50} \times 100\% = 0.6 \times 100\% = 60\%$ Wait, but the given answer is 37.5%. Wait, maybe I mixed measured and estimated. Wait, no—wait, percent error: sometimes the "true" value is the estimated? Wait, no, in percent error, the formula is $\frac{|\text{Experimental (or actual)} - \text{Theoretical (or estimated)}|}{\text{Theoretical (or estimated)}} \times 100\%$. Wait, but maybe the problem considers the estimated as the "true" or the actual as the measured. Wait, let's recalculate. Wait, 80 is actual, 50 is estimated. So $|80 - 50| = 30$. Then $\frac{30}{80} \times 100\%$? Wait, no, that would be 37.5%. Oh! I see, I used the wrong denominator. The percent error formula can sometimes be $\frac{|\text{Estimated} - \text{Actual}|}{\text{Actual}} \times 100\%$? Wait, no, the standard percent error is $\frac{|\text{Measured} - \text{Accepted}|}{\text{Accepted}} \times 100\%$. But in some cases, if the estimated is the "accepted" or the actual is the measured. Wait, let's check: if the band estimated 50 (accepted), actual is 80 (measured). Then error is $|80 - 50| = 30$. Then percent error is $\frac{30}{50} \times 100\% = 60\%$. But the given answer is 37.5%. So maybe the formula is $\frac{|\text{Estimated} - \text{Actual}|}{\text{Actual}} \times 100\%$. So $|50 - 80| = 30$, then $\frac{30}{80} \times 100\% = 37.5\%$. Ah, so the denominator is the actual value. So the correct formula here (depending on context) is $\frac{|\text{Estimated} - \text{Actual}|}{\text{Actual}} \times 100\%$. So:

Step1: Recall correct formula (contextual)

$\text{Percent Error} = \frac{|\text{Estimated} - \text{Actual}|}{\text{Actual}} \times 100\%$ (if actual is the reference)

Step2: Identify values

Estimated = 50, Actual = 80

Step3: Calculate difference

$|50 - 80| = 30$

Step4: Apply formula

$\frac{30}{80} \times 100\% = 0.375 \times 100\% = 37.5\%$

Answer:

37.5%