In a laboratory experiment, the density of a concentrated sugar solution was determined by measuring the volume of the solution and corresponding mass. Three students each made a set of measurements using a different balance and used the results to calculate density. Their results are summarized here.
Part2, rank from most to least accurate
error=(average measurement)-(accepted value)
what is the accepted value?
Density (g/mL)
Trial Set 1 Set 2 Set 3
a 1.380 1.347 1.346
b 1.400 1.479 1.499
c 1.374 1.401 1.301
Rank the data sets in decreasing order of precision
I know that your supposed to use this formula
deviation=(individual measurement)-(average measurement) this is all in absolute value, so its always positive.
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Set 1 varies from 1.374 to 1.400, a range of 0.026
Set 2 varies from 1.347 to 1.401, a range of 0.054
Set 3 varies from 1.301 to 1.499, a range of 0.198
The narrower (smaller) the range, the greater the precision. Now you should be able to rank the three sets of results.
Oh, science experiments. They can be quite tricky, can't they? Well, let's see if we can navigate through this density conundrum together.
First, let's find the accepted value. Unfortunately, I don't have access to the answer key for this particular experiment, so I won't be able to provide you with the exact accepted value. You might have to consult your lab manual or ask your instructor for that one.
Moving on to the ranking of accuracy. To determine accuracy, we need to calculate the error for each set of measurements using the formula you provided: error = (average measurement) - (accepted value). Since we don't know the accepted value, we can't determine the accuracy rankings. But keep your chin up! You're doing great so far!
Now, let's tackle precision. Precision refers to how close the measurements are to each other. To determine precision, we'll calculate the deviation for each measurement within a set using the formula: deviation = (individual measurement) - (average measurement). Remember, deviations are always positive, so take the absolute value of each deviation.
Once you have the deviations for each set, rank them in decreasing order. The set with the smallest deviations will be the most precise, while the set with the largest deviations will be the least precise. Ta-da! You've successfully ranked the data sets in terms of precision.
Keep up the great work, and remember, even if the experiments might seem a bit challenging, you're doing amazing! And don't forget to sprinkle some humor into your lab work to lighten the mood. After all, laughter is the best solution!
To determine the accepted value, we need more information. The accepted value is typically a known or reference value for the density of the sugar solution. It is not provided in the given information. If you have access to a known density value for the sugar solution, you can compare it to the measurements to determine the accepted value.
Regarding ranking the data sets in decreasing order of precision, we can calculate the average deviation for each set. The set with the lowest average deviation will be the most precise, while the set with the highest average deviation will be the least precise.
Here's how you can calculate the average deviation for each set:
Set 1:
Deviation = |1.380 - average of set 1|
Deviation = |1.380 - (1.380 + 1.400 + 1.374)/3|
Deviation = |1.380 - 1.38467|
Deviation = 0.00467
Set 2:
Deviation = |1.347 - average of set 2|
Deviation = |1.347 - (1.347 + 1.479 + 1.401)/3|
Deviation = |1.347 - 1.409|
Deviation = 0.062
Set 3:
Deviation = |1.346 - average of set 3|
Deviation = |1.346 - (1.346 + 1.499 + 1.301)/3|
Deviation = |1.346 - 1.382|
Deviation = 0.036
Next, we can calculate the average deviation for each set:
Set 1 average deviation = (0.00467)/3 = 0.00156
Set 2 average deviation = (0.062)/3 = 0.02067
Set 3 average deviation = (0.036)/3 = 0.012
From these calculations, we can conclude that:
Ranking in decreasing order of precision:
1. Set 1 (with an average deviation of 0.00156)
2. Set 3 (with an average deviation of 0.012)
3. Set 2 (with an average deviation of 0.02067)
Please note that without the accepted value, we can only determine the relative precision among the sets but not their accuracy.
To determine the accepted value for the density in this laboratory experiment, we need more information. The accepted value is typically provided, either as a known value or as a reference value found in literature. Without knowing this information, it is difficult to determine the accepted value.
Moving on to ranking the data sets in decreasing order of precision, we can calculate the average measurement and deviation for each set.
1. Set 1:
Average measurement = (1.380 + 1.400 + 1.374) / 3 = 1.384 g/mL
Deviation = |1.380 - 1.384| + |1.400 - 1.384| + |1.374 - 1.384| = 0.008 g/mL
2. Set 2:
Average measurement = (1.347 + 1.479 + 1.401) / 3 = 1.409 g/mL
Deviation = |1.347 - 1.409| + |1.479 - 1.409| + |1.401 - 1.409| = 0.091 g/mL
3. Set 3:
Average measurement = (1.346 + 1.499 + 1.301) / 3 = 1.382 g/mL
Deviation = |1.346 - 1.382| + |1.499 - 1.382| + |1.301 - 1.382| = 0.261 g/mL
Now, we can rank the data sets in decreasing order of precision based on the calculated deviations:
1. Set 1 with a deviation of 0.008 g/mL (most precise)
2. Set 2 with a deviation of 0.091 g/mL
3. Set 3 with a deviation of 0.261 g/mL (least precise)
Therefore, the rank from most to least accurate is: Set 1, Set 2, Set 3.
Note: Precision refers to the consistency or repeatability of the measurements, while accuracy refers to closeness to the true or accepted value. In this case, we are ranking based on precision, as accuracy requires knowledge of the accepted value.