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Chapter 3: Q13P (page 62)

Cheryl, Cynthia, Carmen, and Chastity shot the following targets at Girl Scout camp. Match each target with the proper description.

(a) accurate and precise

(b) accurate but not precise

(c) precise but not accurate

(d) neither precise nor accurate

Short Answer

Expert verified

A. The points in Carmen's goal are close together (just in the innermost circle) and match the target (only in the inner circle). As a result, it's precise and precise.

B. Although the points in Cynthia's aim are not close to each other (in the innermost circle and beyond), they do agree on the goal in other respects (only in the innermost circle and the next). As a result, it's accurate but not precise.

C. Chastityl's target has points that are close together but not in line with the target (near the outer boundary). As a result, it's accurate but not precise.

D. The points in Cheryl's goal aren't close to each other (they're strewn throughout the place).

Step by step solution

01

Definition of systematic and random error.

  • Systematic errors are mistakes that are not caused by chance, but rather by an inherent inaccuracy in the system (including either the observation or measurement process). The term "systematic error" can also refer to a mistake with a nonzero mean that has no impact when the observations are averaged.
  • The term "random error" refers to an unanticipated disruption in the experiment caused by an unknown source. In theory, you may track down the cause of the mistake and eliminate it in a better trial, bringing the measured mean closer to the real mean. Random mistake can be either beneficial or harmful, and it can't be avoided.
02

Determine whether the error in (a)-(d) is systematic or random.

  • The points in Carmen's goal are quite near to each other (only in the innermost circle) and agree with the target (only in the inner circle). As a result, it's exact and accurate.
  • The points in Cynthia's target are not near to each other (in the innermost circle and next to that), but they do agree on the goal in other ways (only in the innermost circle and the next). As a result, it is precise but not exact.
  • The points in Chastityl's target are close together but not in accord with the target (near the outer boundary). As a result, it is precise but not exact.
  • The points in Cheryl's objective are neither near to each other (scattered throughout the chart) nor in accord with the target (only one at the innermost circle). As a result, it is neither exact nor precise.

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Most popular questions from this chapter

Avogadro's number can be computed from the following measured properties of pure crystalline silicon: 5

(1) atomic mass (obtained from the mass and abundance of each isotope), (2) density of the crystal, (3) size of the unit cell (the smallest repeating unit in the crystal), and (4) number of atoms in the unit cell. For the material that was used, the average atomic mass of Si is role="math" localid="1663313481329" msi=28.0853842(35)g/mol, where 35 is the uncertainty (standard deviation) in the last two digits. The density is p=2.3290319(18)g/cm3, the size of the cubic unit cell is c0=5.43102036(33)×10-8cm, and there are 8 atoms per unit cell. Avogadro's number is computed from the equation

NA=mSi(pc03)/8

From the measured properties and their uncertainties, compute Avogadro's number and its uncertainty.

To find the uncertainty of con3 use the function y=x4in Table 3-1.

Round each number to three significant figures:

(a) 0.21674

(b) 0.2165

(c) 0.2165003

Explain the difference between systematic and random error.

What is the true mass of water in vacuum if the apparent mass weighed in air at 24°Cis 1.0346±0.0002g? The density of air is 0.0012±0.0001g/mL and the density of balance weights is 8.0±0.5g/mL. The uncertainty in the density of water in Table 2-7 is negligible in comparison to the uncertainty in the density of air.

Controlling the appearance of a graph. Figure 3-3 requires gridlines to read buret corrections. In this exercise, you will format a graph so that it looks like Figure 3-3 . Follow the procedure in Section 2-11 to graph the data in the following table. For Excel 2007 or 2010, insert a Chart of the type Scatter with data points connected by straight lines. Delete the legend and title. With Chart Tools, Layout, Axis Titles, add labels for both axes. Click any number on the abscissa ( x axis) and go to Chart Tools, Format. In Format Selection, Axis Options, choose Minimum =0 , Maximum =50 , Major unit =10 , and Minor unit =1 . For Major tick mark type, select Outside. In Format Selection, Number, choose Number and set Decimal places =0. In a similar manner, set the ordinate ( y -axis) to run from -0.04 to +0.05 with a Major unit of 0.02 and a Minor unit of 0.01 and with Major tick marks Outside. To display gridlines, go to Chart Tools, Layout, and Gridlines. For Primary Horizontal Gridlines, select Major & Minor Gridlines. For Primary Vertical Gridlines, select Major & Minor Gridlines. To move axis labels from the middle of the chart to the bottom, click a number on the y axis (not the x axis) and select Chart Tools, Layout, Format Selection. In Axis Options, choose Horizontal axis crosses Axis value and type in -0.04 . Close the Format Axis window and your graph should look like Figure 3-3 .
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