Three students have made multiple measurements of the solubility of sodium chloride (in g of NaCl per 100 g of water). Their results are summarized in the table below. The correct value for the solubility of sodium chloride is 35.9 g.
Nicole - first trial - 35.4g, second trial - 36.1g, 3rd trial - 35.7g
Matthew - first trial - 31.8g, second trial - 34.1g, 3rd trial - 41.5g
leonard - first trial - 39.2g, second trial - 39.3g, 3rd trial - 38.9g
a) Which student measurements have high precision but low accuracy?
b) Which student measurements are both accurate and precise?
Mathew
matthew
a) Ah, high precision but low accuracy, a classic case of "close but no cigar." In this case, Nicole's measurements come into play. She is consistently close to the actual value (35.9 g) but unfortunately not quite hitting the bullseye every time. So, Nicole's measurements have high precision but low accuracy.
b) Now let's find the superstar who is both accurate and precise. Drumroll, please... it's Leonard! His measurements are consistently around 39 g, which is quite close to the actual value of 35.9 g. So Leonard's measurements are accurate and precise. Leonard, you rock!
To determine which student measurements have high precision but low accuracy, and which student measurements are both accurate and precise, we need to understand the concepts of precision and accuracy.
Precision refers to how close the measurements are to each other. If the measurements have small differences or a small range of values, they are considered precise.
Accuracy, on the other hand, refers to how close the measurements are to the true or correct value. If the measurements are close to the accepted or correct value, they are considered accurate.
Now, let's analyze the measurements of each student:
Nicole:
- First trial: 35.4g
- Second trial: 36.1g
- Third trial: 35.7g
Matthew:
- First trial: 31.8g
- Second trial: 34.1g
- Third trial: 41.5g
Leonard:
- First trial: 39.2g
- Second trial: 39.3g
- Third trial: 38.9g
a) High precision but low accuracy:
To determine high precision, we look for measurements that have a small range of values or small differences between them. In this case, Nicole's measurements have a small range of values (36.1g - 35.4g = 0.7g) and small differences. However, they are not accurate because they are not close to the correct value of 35.9g. Therefore, Nicole's measurements have high precision but low accuracy.
b) Accurate and precise measurements:
To determine measurements that are both accurate and precise, we look for values that are close to each other (high precision) and also close to the correct value (high accuracy). None of the students' measurements exactly match the correct value of 35.9g. However, Leonard's measurements (39.2g, 39.3g, 38.9g) have a small range (39.3g - 38.9g = 0.4g) and are relatively close to the correct value. Therefore, Leonard's measurements can be considered both accurate and precise, although not exactly accurate.
In summary:
a) Nicole's measurements have high precision but low accuracy.
b) Leonard's measurements are both accurate and precise.