Question

A single penny has a mass of 2.5 g. Abbie and James each measure the mass of a penny multiple times. Which statement about these data sets is true? Abbie's measurements are both more accurate and more precise than James'. Abbie's measurements are more accurate, but less precise than James'. Abbie's measurements are more precise, but less accurate than James'. Abbie’s measurements are both less accurate and less precise than James'.

Answer 1

The question is missing the data sets.

This is the complete question:

A single penny has a mass of 2.5 g. Abbie and James each measure the mass of a penny multiple times. Which statement about these data sets is true? 

O Abbie's measurements are both more accurate and more precise than James'.

O Abbie's measurements are more accurate, but less precise, than James'. 

O Abbie's measurements are more precise, but less accurate, than James'. 

O Abbie’s measurements are both less accurate and less precise than James'. 

Penny masses (g)

Abbie’s data                                        

2.5, 2.4, 2.3, 2.4, 2.5, 2.6, 2.6 

James’ data


2.4, 3.0, 3.3, 2.2, 2.9, 3.8, 2.9

Answer: first option, Abbie's measurements are both more accurate and more precise than James'.

Explanation:


1) To answer this question, you first must understand the difference between precision and accuracy.

Accuracy is how close the data are to the true or accepted value.


Precision is how close are the data among them, this is the reproducibility of the values.

Then, you can measure the accuracy by comparing the means (averages) with the actual mass of a penny 2.5 g.

And you measure the precision by comparing a measure of spread, as it can be the standard deviation.

2) These are the calculations:

Abbie’s data                      
                 
Average: ∑ of the values / number of values 

Average = [2.5 + 2.4 + 2.3 + 2.4 + 2.5 + 2.6 + 2.6 ] / 7 = 2.47 ≈ 2.5

Standard deviation: √  [ ∑ (x - mean)² / (n - 1) ] = 0.11


James’ data


Average = [2.4 + 3.0 + 3.3 + 2.2 + 2.9 + 3.8 + 2.9] / 7 = 2.56 ≈ 2.6


Standard deviation = 0.53

3) Conclusions:

1) The average of Abbie's data are closer to the accepted value 2.5g, so they are more accurate.

2) The standard deviation of Abbie's data is smaller than that of Jame's data, so the Abbie's data are more precise.

Answer 2

A. Abbie's measurements are both more accurate and more precise then James'