The mean yield from process A is estimated to be 80 ± 5, where the units are percent of a theoretical maximum. The mean yield from process B is estimated to be 90 ± 3. The relative increase obtained from process B is therefore estimated to be (90 − 80)/80 = 0.125. Find the uncertainty in this estimate.
The mean yield from process A is estimated to be 80 ± 5, where the units are percent of a theoretical maximum. The mean yield from process B is estimated to be 90 ± 3. The relative increase obtained from process B is therefore estimated to be (90 − 80)/80 = 0.125. Find the uncertainty in this estimate.
The mean yield from process A is estimated to be 80 ± 5, where the units are percent of a theoretical maximum. The mean yield from process B is estimated to be 90 ± 3. The relative increase obtained from process B is therefore estimated to be (90 − 80)/80 = 0.125. Find the uncertainty in this estimate.
The mean yield from process A is estimated to be 80 ± 5, where the units are percent of a theoretical maximum. The mean yield from process B is estimated to be 90 ± 3. The relative increase obtained from process B is therefore estimated to be (90 − 80)/80 = 0.125. Find the uncertainty in this estimate.
Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...
Expert Solution
Step 1
The mean yield from process A is estimated to be A= 80±5 and the mean yield from process B is estimated to be B= 90±3.
The form of the measurements of a process is,
Measured value(μ)± Standard deviation(σ).
Here, for a random sample the measured value will be sample mean and the population standard deviation will be sample standard deviation.
The form of the measurements of mean yield from process A is A= 80±5.
Here, the measured value of mean yield from process A is A= 80 and the uncertainty in the mean yield from process A is σA=5.
The form of the measurements of mean yield from process B is B= 90±3
Here, the measured value of mean yield from process B is B= 90 and the uncertainty in the mean yield from process B is σB=3.
Step 2
Uncertainty:
The uncertainty of a process is determined by the standard deviation of the measurements. In other words, it can be said that the measure of the variability of a process is known as the uncertainty of the process.
Therefore, it can be said that uncertainty is simply (σ).
Standard deviation:
The standard deviation is based on how much each observation deviates from a central point represented by the mean. In general, the greater the distances between the individual observations and the mean, the greater the variability of the data set.
The general formula for standard deviation is,
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