Questions: Four research teams measured the length of a rare whale, and what each team wrote in its team notebook is shown in the table below. Suppose a later and more reliable measurement gives 74.0 m for the length of the same whale. Decide which of the earlier measurements was the most accurate, and which was the most precise. team what was written in the notebook most accurate measurement most precise measurement ------------ A " 78 . m " ◯ ◯ B " 76 . m ± 2.0 m " ◯ ◯ C " 70.0 m ± 0.30 % " ◯ ◯ D "between 74.6 m and 75.4 m" ◯ ◯

Four research teams measured the length of a rare whale, and what each team wrote in its team notebook is shown in the table below.
Suppose a later and more reliable measurement gives 74.0 m for the length of the same whale. Decide which of the earlier measurements was the most accurate, and which was the most precise.

team what was written in the notebook most accurate measurement most precise measurement
------------
A " 78 . m " ◯ ◯
B " 76 . m ± 2.0 m " ◯ ◯
C " 70.0 m ± 0.30 % " ◯ ◯
D "between 74.6 m and 75.4 m" ◯ ◯

Transcript text: Four research teams measured the length of a rare whale, and what each team wrote in its team notebook is shown in the table below. Suppose a later and more reliable measurement gives 74.0 m for the length of the same whale. Decide which of the earlier measurements was the most accurate, and which was the most precise. \begin{tabular}{|c|c|c|c|} \hline team & \begin{tabular}{c} what was written \\ in the notebook \end{tabular} & \begin{tabular}{c} most accurate \\ measurement \end{tabular} & \begin{tabular}{c} most precise \\ measurement \end{tabular} \\ \hline$A$ & $" 78 . \mathrm{m} "$ & $\bigcirc$ & $\bigcirc$ \\ \hline$B$ & $" 76 . \mathrm{m} \pm 2.0 \mathrm{~m} "$ & $\bigcirc$ & $\bigcirc$ \\ \hline$C$ & $" 70.0 \mathrm{~m} \pm 0.30 \%$ " & $\bigcirc$ & $\bigcirc$ \\ \hline$D$ & "between 74.6 m and $75.4 \mathrm{m"}$ & $\bigcirc$ & $\bigcirc$ \\ \hline \end{tabular}

Solution

Solution Steps

Step 1: Understand the Definitions

Accuracy refers to how close a measurement is to the true value.
Precision refers to how close repeated measurements are to each other, regardless of their accuracy.

Step 2: Analyze Each Team's Measurement

Team A: The measurement is $78 \, \text{m}$. This is a single value with no uncertainty.
Team B: The measurement is $76 \, \text{m} \pm 2.0 \, \text{m}$. This means the measurement could range from $74 \, \text{m}$ to $78 \, \text{m}$.
Team C: The measurement is $70.0 \, \text{m} \pm 0.30\%$. The uncertainty is $0.30\%$ of $70.0 \, \text{m}$, which is $0.21 \, \text{m}$. So, the measurement could range from $69.79 \, \text{m}$ to $70.21 \, \text{m}$.
Team D: The measurement is between $74.6 \, \text{m}$ and $75.4 \, \text{m}$.

Step 3: Compare Measurements to the True Value

The true value is $74.0 \, \text{m}$.

Team A: $78 \, \text{m}$ is $4 \, \text{m}$ away from the true value.
Team B: $76 \, \text{m}$ is $2 \, \text{m}$ away from the true value, and the range includes the true value.
Team C: $70.0 \, \text{m}$ is $4 \, \text{m}$ away from the true value, and the range does not include the true value.
Team D: The range $74.6 \, \text{m}$ to $75.4 \, \text{m}$ is close to the true value, with the closest point being $74.6 \, \text{m}$, which is $0.6 \, \text{m}$ away.

Step 4: Determine Accuracy and Precision

Most Accurate: Team D, because their range is closest to the true value.
Most Precise: Team C, because their uncertainty is the smallest ($0.21 \, \text{m}$).