Final answer:
The percent error in Ida's measurement is 6.67%. This percent error indicates the relative difference between the measured amount and the amount stated on the can, acknowledging the expected variation in data due to various factors.
Step-by-step explanation:
To calculate the percent error for the measurement of the soda, we compare the measured amount to the expected amount and use the formula for percent error:
Percent Error = \( \left| \frac{{Actual Value - Theoretical Value}}{{Theoretical Value}} \right| \times 100\% \)
In Ida's case, the actual value is 11.2 oz, and the theoretical value or expected amount stated on the can is 12 oz. Plugging in these values, we get:
Percent Error = \( \left| \frac{{11.2 oz - 12 oz}}{{12 oz}} \right| \times 100\% \)
Percent Error = \( \left| -\frac{{0.8}}{{12}} \right| \times 100\% \)
Percent Error = \( 6.67\% \)
The percent error in Ida's measurement is 6.67%. This calculation takes into account the variation in data that can occur due to measurement errors or slight differences in the manufacturing process. Manufacturers understand this and often run tests to ensure that their products fall within an acceptable range.
These variances are why a consumer like Ida may find a slightly different amount in her can compared to what is stated on the label. It's also important to note that the statistical concepts of mean and standard deviation can help describe the expected distribution of measurements in a sample of cans.