Question

The following data was collected: 5.5 m; 5.3 m; 5.4 m. The actual length is 5.4 m. What is the accuracy and precision for this set of measurements?

Answer 1

Answer:

The measurement is precise and accurate

Explanation:

The accuracy of a measurement of length is often indicated by how "precisely" the length measurement can be read depending on the type of measuring instrument used scale.

Looking at the measurement, we can see that the values lie between ±0.1 from the expected values hence it is accurate.

Also, the values differ from each other by ±0.1 hence it the measurements are precise.

Answer 2

Answer:

Accuracy:

5.5 = 98.15%

5.3 = 98.15%

5.4 = 100 %

Precision:

5.5 ± 0.14

5.3 ± 0.14

5.4 ± 0.14

Explanation:

Accuracy is determined using; 100% - % error

% error = absolute error/actual value * 100%

5.5 - 5.4/5.4 * 100% = 1.85%

accuracy = 100 % - 1.85 % = 98.15%

5.3 - 5.4/5.4 * 100 5 = 1.85%

accuracy = 100 % - 1.85 % = 98.15%

5.4 - 5.4/5.4 * 100  % = 0 %

accuracy = 100 % - 0% = 100%

Precision is determined by obtaining the standard deviation of the mean;

s = √{∑(|x - m|)²/(n - 1)}

where x is the value, m is mean of values , n is number of values

mean = (5.5 + 5.3 + 5.4) / 3 = 5.4

deviations from mean, (x - m) are as follows;

|5.5 - 5.4| = 0.1

|5.3 - 5.4| = 0.1

|5.4 - 5.4| = 0

∑(x - m)² = (0.1 + 0.1 + 0) ²= (0.2)² = 0.04

(n - 1) = 3 - 1 = 2

s = √(0.04/2)

s = ± 0.14

Therefore, the precision of each measurement is as follows;

5.5 ± 0.14

5.3 ± 0.14

5.4 ± 0.14