The attendance for a basketball game was estimated to be 15,000 people, but 12,500 people actually attended. What was the percent error?
The Correct Answer and Explanation is:
To find the percent error in estimating the attendance at the basketball game, we use the formula for percent error:
[
\text{Percent Error} = \left( \frac{|\text{Estimated Value} – \text{Actual Value}|}{\text{Actual Value}} \right) \times 100
]
Step-by-Step Calculation
- Identify the values:
- Estimated Value = 15,000
- Actual Value = 12,500
- Find the absolute difference between the estimated and actual values:
[
|\text{Estimated Value} – \text{Actual Value}| = |15,000 – 12,500| = 2,500
] - Divide by the actual value:
[
\frac{2,500}{12,500} = 0.2
] - Convert to a percentage by multiplying by 100:
[
0.2 \times 100 = 20\%
]
Thus, the percent error is 20%.
Explanation of Percent Error
Percent error is a measure used in calculations and data analysis to determine the degree of inaccuracy in an estimate compared to the actual value. It’s calculated by taking the difference between the estimated and actual values, dividing this difference by the actual value, and then converting the result into a percentage. This formula helps in quantifying the error in relation to the actual value, making it useful for comparisons.
In this example, the estimated attendance of 15,000 people turned out to be higher than the actual attendance of 12,500 people. By calculating the percent error, we find that the estimation was 20% higher than the actual value. This could help analysts or event organizers understand the discrepancy, which could be due to overestimations or unexpected factors affecting attendance, like weather or competing events. Using percent error provides a standardized way to interpret this difference and assess the accuracy of predictions in various fields, from sports event planning to scientific experiments.