A laboratory instructor gives a sample of amino acids powder to each students,1,2,3and4,and they weigh the samples.The true. value is 8.72g.Their results for three trials are 1:8.72g,8.74g,8.70g 2:8.56g,8.77g,8.83g 3:8.50g,8.48g,8.51g 4:8.41g,8.72g,8.55g.(a)calculate the average mass from each of set of data,and tell which set is the most accurate.(b)precision is a measure of the average of the deviation of each piece of data from average value.which set of data is the most precise?is this set also the most accurate?(c)which set of data is both the accurate and most precise?(d)which set of data is both the least accurate and least precise?
I'm a little confused here. Almost everyone knows how to calculate an average. Have you done that? If not, exactly what don't understand about the question. I shall be glad to help you but I don't want to do a lot of busy work you already know how to do.
(a): You can do that.
(b), (c), and (d): Google "accuracy vs. precision" and I think that will help you get on the right track.
To calculate the average mass from each set of data, we sum up the measurements and divide by the number of trials:
(a) Average mass for each set of data:
1st set: (8.72g + 8.74g + 8.70g) / 3 = 8.72g
2nd set: (8.56g + 8.77g + 8.83g) / 3 = 8.72g
3rd set: (8.50g + 8.48g + 8.51g) / 3 = 8.50g
4th set: (8.41g + 8.72g + 8.55g) / 3 = 8.56g
The set with the most accurate average mass is the 2nd set, which has an average mass of 8.72g, closest to the true value of 8.72g.
(b) Precision can be measured by calculating the deviation of each piece of data from the average value and taking the average of those deviations. The set with the smallest average deviation would be the most precise.
Deviation for each set of data:
1st set: (8.72g - 8.72g) + (8.74g - 8.72g) + (8.70g - 8.72g) / 3 = 0.0067g
2nd set: (8.56g - 8.72g) + (8.77g - 8.72g) + (8.83g - 8.72g) / 3 = 0.1233g
3rd set: (8.50g - 8.50g) + (8.48g - 8.50g) + (8.51g - 8.50g) / 3 = 0.0067g
4th set: (8.41g - 8.56g) + (8.72g - 8.56g) + (8.55g - 8.56g) / 3 = 0.0467g
The set with the smallest average deviation is the 1st set, which has a deviation of 0.0067g. However, the 1st set is not the most accurate since its average mass is 8.72g instead of the true value of 8.72g. Therefore, the 2nd set is the most precise but not the most accurate.
(c) The set of data that is both accurate and precise would be the 2nd set, with an average mass of 8.72g (closest to the true value) and a relatively small average deviation.
(d) The set of data that is both the least accurate and least precise would be the 3rd set, with an average mass of 8.50g (farthest from the true value) and the same average deviation as the 1st set, which is relatively small compared to the other sets.
To solve this question, we need to calculate the average mass for each set of data and then analyze the accuracy and precision of the results. Let's break it down step by step:
(a) To calculate the average mass for each set of data, we add up the values and divide by the number of trials. Here are the results:
Set 1: (8.72 + 8.74 + 8.70) / 3 = 8.72g
Set 2: (8.56 + 8.77 + 8.83) / 3 = 8.72g
Set 3: (8.50 + 8.48 + 8.51) / 3 = 8.49g
Set 4: (8.41 + 8.72 + 8.55) / 3 = 8.56g
Comparing the average masses, we find that Set 1 and Set 2 have the same average mass of 8.72g.
The set with the most accurate results is the one with the average mass closest to the true value of 8.72g. In this case, both Set 1 and Set 2 have an average mass of 8.72g, which makes them equally accurate.
(b) Precision is a measure of how close individual data points are to each other. To determine the precision, we need to calculate the average deviation for each set. The formula for average deviation is: Sum of |individual data value - average mass| divided by the number of trials.
Here are the average deviations for each set:
Set 1: (|8.72 - 8.72| + |8.74 - 8.72| + |8.70 - 8.72|) / 3 = 0.02g
Set 2: (|8.56 - 8.72| + |8.77 - 8.72| + |8.83 - 8.72|) / 3 = 0.09g
Set 3: (|8.50 - 8.49| + |8.48 - 8.49| + |8.51 - 8.49|) / 3 = 0.01g
Set 4: (|8.41 - 8.56| + |8.72 - 8.56| + |8.55 - 8.56|) / 3 = 0.09g
From the above calculations, we find that Set 3 has the smallest average deviation of 0.01g. Therefore, Set 3 is the most precise. However, it is not the most accurate since its average mass (8.49g) deviates the most from the true value (8.72g).
(c) To find the set that is both accurate and precise, we need to identify the one with both a small average deviation and an average mass closest to the true value.
From the calculations, we can see that Set 1 has an average mass of 8.72g, which equals the true value, making it accurate. However, its average deviation is 0.02g, not the smallest. Therefore, it is not the most precise.
(d) The set that is both the least accurate and least precise is Set 3. It has an average mass of 8.49g, which deviates the most from the true value of 8.72g. Additionally, it also has the smallest average deviation of 0.01g, making it the least precise.
In summary:
(a) Set 1 and Set 2 have the same average mass of 8.72g, making them equally accurate.
(b) Set 3 has the smallest average deviation of 0.01g, making it the most precise, but it is not the most accurate.
(c) Set 1 has an average mass equal to the true value of 8.72g, making it accurate, but it is not the most precise.
(d) Set 3 is both the least accurate and least precise.