Join thousands of students who trust us to help them ace their exams!Watch the first video
Multiple Choice
A student performs an experiment to determine the density of a sugar solution. She obtains the following results: 1.70 g/mL, 1.75 g/mL, 1.66 g/mL, and 1.68 g/mL. How should she report the average density of her measurements, including the uncertainty?
A
1.70 ± 0.02 g/mL
B
1.70 ± 0.04 g/mL
C
1.70 ± 0.05 g/mL
D
1.70 ± 0.03 g/mL
Verified step by step guidance
1
Step 1: Calculate the average density by summing all the measured densities and dividing by the number of measurements. Use the formula: \( \text{Average Density} = \frac{1.70 + 1.75 + 1.66 + 1.68}{4} \).
Step 2: Determine the deviation of each measurement from the average density. This is done by subtracting the average density from each individual measurement.
Step 3: Calculate the average deviation by summing the absolute values of the deviations obtained in Step 2 and dividing by the number of measurements.
Step 4: The uncertainty in the measurements is often reported as the average deviation. This value represents the spread of the measurements around the average.
Step 5: Report the average density along with the uncertainty as \( \text{Average Density} \pm \text{Uncertainty} \). Ensure that the uncertainty is rounded to one significant figure and the average density is rounded to the same decimal place as the uncertainty.