Four sets of measurements were taken on the same response...

Name: Problem 10, Chapter 15: Principles and Applications of Electrical Engineering
Uploaded: 2020-07-28T05:37:47-08:00
Duration: 6 min 15 s
Channel: Nicole Powell
Description: Four sets of measurements were taken on the same response variable of a process using four different sensors. The true value of the response was known to be constant. The four sets of data are shown in Figure P15.10. Rank these data sets (and hence the sensors) with respect to: a. Precision. b. Accuracy.

Four sets of measurements were taken on the same response variable of a process using four different sensors. The true value of the response was known to be constant. The four sets of data are shown in Figure P15.10. Rank these data sets (and hence the sensors) with respect to: a. Precision. b. Accuracy.

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Key Concepts

Precision

Precision refers to the degree of consistency or repeatability in a set of measurements. It focuses on the spread or variability of the data points, regardless of whether they are close to the true value. When measurements are highly precise, they are closely clustered together even if they might all be offset from the correct value.

Accuracy

Accuracy describes how close a measured value is to the true value or accepted standard. It is an indication of the correctness of the measurement, meaning that even if the measurements are consistent (precise), they must also align closely with the actual value to be considered accurate.

Systematic Error (Bias)

Systematic error, often called bias, represents a consistent deviation of the measurements from the true value. It is an error inherent to the measurement process that causes all measurements to be offset in one direction, impacting the accuracy of the data.

Measurement Variability

Measurement variability reflects the random errors or fluctuations inherent in any measurement process. It affects precision by determining how scattered the data points are around their mean. Low variability indicates high precision, whereas high variability indicates low precision.

Transcript

00:01 In order to find the average of a set of values, you just add them together and divide by the number of values there are.

00:07 So in this case, three.

00:10 In order to find, doing that for student one, we get 26 .16 divided by 3, which is 8 .72.

00:22 In order to, for student 2, we get an average of also 26 .16 over 3, which is 8 .72.

00:34 And this unit here is grams.

00:39 For student 3, we get an average value of 25 .49 divided by 3, which is equal to 8 .50 grams.

00:51 And finally, for student 4, we get an average of 25 .68 divided by 3, which is 8 .56 grams.

01:04 In order to see which of these is the most accurate, we have to compare the average value to the actual value of the mass of the sample.

01:17 Student 1's average is 0 grams from the true value, and student 2 has an average that is also 0 grams from the true value.

01:31 Student 3 has a mass that is 0 .22 grams from true value, and student 4 has the mass that is 0 .16 grams from the true value.

01:52 This means that both student one and student two have the most accurate results.

01:59 In order to know which of the student's data is most precise, we have to calculate the average deviation from the true value.

02:10 So let's start with student one.

02:15 The deviation for one value is the absolute value of the first data point minus the actual value...

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