Question

ty physics accuracy & precision worksheet module 01
accuracy: refers to how close a measurement is to a true, accepted or target value.
precision: refers to the reproducibility of a series of measurements
percent error (difference): \\(\frac{(\text{target value} - \text{measured value}) \times 100}{\text{target value}}\\)

1. the following measurements were made to determine the density of a material whose value was, according to the handbook of chemistry and physics, 1.24 g/ml

trial #1 1.20 g/ml
trial #2 1.22 g/ml
trial #3 1.22 g/ml
a. make a general comment on the accuracy of these results
b. make a general comment on the precision of these results
c. use the average of the three trials as the “measured value” and determine the numerical value for the percent error.

Explanation:

a. Accuracy Comment

Step1: Compare to target (1.24 g/mL). Measured values (1.20, 1.22, 1.22) are not close to 1.24.

b. Precision Comment

Step1: Check reproducibility. Values are 1.20, 1.22, 1.22; small differences indicate high precision.

c. Percent Error Calculation

Step1: Compute average measured value. $\frac{1.20 + 1.22 + 1.22}{3} = \frac{3.64}{3} \approx 1.2133\ \text{g/mL}$.
Step2: Apply percent error formula. $\frac{1.24 - 1.2133}{1.24} \times 100 \approx 2.15\%$.

Answer:

a. The results have low accuracy as measured values are not close to the target 1.24 g/mL.
b. The results have high precision as measurements are reproducible with small differences.
c. 2.15%