Three apprentice tailors (X, Y, and Z) are assigned the task of measuring the seam of a pair of

Name: Problem 40, Chapter 1: Chemistry
Uploaded: 2020-07-02T17:53:35-08:00
Duration: 1 min 10 s
Channel: David Collins
Description: Three apprentice tailors (X, Y, and Z) are assigned the task of measuring the seam of a pair of trousers. Each one makes three measurements. The results in inches are X(31.5,31.6,31.4) ; Y(32.8,32.3,32.7) Z(31.9,32.2,32.1) . The true length is 32.0 in Comment on the precision and the accuracy of each tailor's measurements.

step 1 For the first tailor, we have pretty good precision because the numbers only differ by a value o

Question

Three apprentice tailors $(\mathrm{X}, \mathrm{Y},$ and $\mathrm{Z})$ are assigned the task of measuring the seam of a pair of trousers. Each one makes three measurements. The results in inches are $\mathrm{X}(31.5,31.6,31.4) ; \mathrm{Y}(32.8,32.3,32.7)$ $\mathrm{Z}(31.9,32.2,32.1) .$ The true length is $32.0 \mathrm{in}$ Comment on the precision and the accuracy of each tailor's measurements.

   Three apprentice tailors $(\mathrm{X}, \mathrm{Y},$ and $\mathrm{Z})$ are assigned the task of measuring the seam of a pair of trousers. Each one makes three measurements. The results in inches are $\mathrm{X}(31.5,31.6,31.4) ; \mathrm{Y}(32.8,32.3,32.7)$
$\mathrm{Z}(31.9,32.2,32.1) .$ The true length is $32.0 \mathrm{in}$
Comment on the precision and the accuracy of each tailor's measurements.

Chemistry

Raymond Chang, Jason… 13th Edition

Chapter 1, Problem 40

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Solved by Expert David Collins

07/02/2020

Step 1

The average will help us determine how close each tailor's measurements are to the true length of 32.0 inches. - For Tailor X: \[ \text{Average}_X = \frac{31.5 + 31.6 + 31.4}{3} = \frac{94.5}{3} = 31.5 \] - For Tailor Y: \[ \text{Average}_Y = Show more…

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Three apprentice tailors $(\mathrm{X}, \mathrm{Y},$ and $\mathrm{Z})$ are assigned the task of measuring the seam of a pair of trousers. Each one makes three measurements. The results in inches are $\mathrm{X}(31.5,31.6,31.4) ; \mathrm{Y}(32.8,32.3,32.7)$ $\mathrm{Z}(31.9,32.2,32.1) .$ The true length is $32.0 \mathrm{in}$ Comment on the precision and the accuracy of each tailor's measurements.

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Key Concepts

Precision

Precision refers to the consistency or repeatability of a set of measurements. It measures how close the individual measurements are to each other, regardless of whether they are near the true value. High precision indicates that the measurements are clustered together, even if there is a systematic error present.

Accuracy

Accuracy indicates how close a measurement or the average of a set of measurements is to the true or accepted value. High accuracy means that a measurement or its average is near the actual value, reflecting low systematic bias in the measurement process.

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