Data analysis: precision, accuracy, standard deviation and significant figures - Question Bank

1. If a measurement is reported as 25.0 ± 0.2 mL, what is the absolute uncertainty?
A) 25.0 mL
B) 0.2 mL
C) 25.2 mL
D) 24.8 mL
2. Which of the following is NOT a way to express uncertainty?
A) Absolute uncertainty
B) Relative uncertainty
C) Standard deviation
D) Variance
3. A single outlier value in a data set can significantly affect which statistical measure?
A) Mode
B) Median
C) Mean and Standard Deviation
D) Range
4. What is the primary purpose of using significant figures in scientific calculations?
A) To make numbers look neater.
B) To indicate the precision of the measurements used.
C) To increase the accuracy of the results.
D) To ensure all numbers have the same number of digits.
5. If multiple measurements are very close to each other but far from the true value, this indicates:
A) High accuracy, low precision
B) Low accuracy, high precision
C) High accuracy, high precision
D) Low accuracy, low precision
6. Which statistical measure best describes the spread of data relative to the mean?
A) Mean
B) Median
C) Standard Deviation
D) Mode
7. The standard deviation of a population is denoted by the Greek letter:
A) mu (μ)
B) sigma (σ)
C) delta (Δ)
D) rho (ρ)
8. When reporting a measurement, the last significant digit is:
A) An exact value.
B) An estimated digit.
C) Always zero.
D) Always one.
9. Which of the following would be considered a gross error?
A) Reading a meniscus incorrectly.
B) A faulty instrument calibration.
C) Forgetting to add a reagent.
D) Slight variations in ambient temperature.
10. Percent error is calculated as:
A) |(Experimental - Accepted) / Accepted| * 100
B) |(Accepted - Experimental) / Experimental| * 100
C) |(Experimental - Accepted) / Experimental| * 100
D) |(Accepted - Experimental) / Accepted| * 100
11. If the accepted value for a sample is 15.00 g and your experimental value is 14.50 g, what is the percent error?
A) 3.33%
B) 3.45%
C) 103.45%
D) 0.50%
12. What is the result of (3.14159 * 2.7) + 0.5, rounded to the appropriate number of significant figures?
A) 8.482283
B) 8.48
C) 8.5
D) 8.482
13. Trailing zeroes in a number without a decimal point are:
A) Always significant
B) Never significant
C) Ambiguous
D) Sometimes significant
14. Trailing zeroes in a number with a decimal point are:
A) Never significant
B) Always significant
C) Sometimes significant
D) Ambiguous
15. Leading zeroes (zeroes to the left of the first non-zero digit) are:
A) Always significant
B) Never significant
C) Sometimes significant
D) Ambiguous
16. Zeroes between non-zero digits are always:
A) Not significant
B) Significant
C) Sometimes significant
D) Ambiguous
17. Which digit is always considered significant in any non-zero number?
A) The first non-zero digit
B) The last non-zero digit
C) Any digit from 1 to 9
D) All digits
18. When reporting the result of a measurement with its uncertainty, which format is most appropriate?
A) Value ± Absolute Uncertainty
B) Value ± Relative Uncertainty
C) Value ± Standard Deviation
D) Value ± Variance
19. A higher RSD value generally indicates:
A) Better precision
B) Worse precision
C) Better accuracy
D) Worse accuracy
20. The relative standard deviation (RSD), also known as coefficient of variation, is calculated as:
A) (Standard Deviation / Mean) * 100
B) (Mean / Standard Deviation) * 100
C) (Standard Deviation / Median) * 100
D) (Mean / Median) * 100
21. What is the mode of the following data set: 5, 7, 8, 7, 5, 7, 9?
A) 5
B) 7
C) 8
D) 9
22. What is the median of the following data set: 10, 12, 15, 11, 13?
A) 10
B) 11
C) 12
D) 13
23. In statistical analysis, what does the mean represent?
A) The middle value of a data set.
B) The most frequent value in a data set.
C) The average of a data set.
D) The range of a data set.
24. Which of the following is a way to minimize systematic errors?
A) Repeating measurements and averaging.
B) Using a more sensitive instrument.
C) Calibrating instruments against known standards.
D) Reducing the number of steps in the procedure.
25. Which of the following is a way to minimize random errors?
A) Using a properly calibrated instrument.
B) Repeating measurements and averaging the results.
C) Ensuring consistent environmental conditions.
D) Following the correct experimental procedure.
26. A student weighs a sample of pure NaCl and gets 0.585 g. The actual mass is 0.580 g. This indicates:
A) Good accuracy and good precision
B) Poor accuracy and poor precision
C) Good accuracy and poor precision
D) Poor accuracy and good precision
27. If a chemist performs a titration multiple times and obtains results like 25.1 mL, 25.0 mL, 25.2 mL, this indicates:
A) High accuracy but low precision
B) Low accuracy but high precision
C) High accuracy and high precision
D) Low accuracy and low precision
28. Which type of error is often due to the limitations of the measuring instrument itself?
A) Gross error
B) Random error
C) Systematic error
D) Personal error
29. What is the result of 15.00 mL - 0.5 mL, expressed with the correct number of significant figures?
A) 14.50 mL
B) 14.5 mL
C) 15 mL
D) 14 mL
30. What is the result of 9.876 g / 1.23 g, expressed with the correct number of significant figures?
A) 8.03 g
B) 8.0 g
C) 8.030 g
D) 8 g
31. What is the result of 10.5 m * 2.0 m, expressed with the correct number of significant figures?
A) 21 m
B) 21.0 m
C) 21.00 m
D) 20 m
32. What is the result of 2.5 cm + 3.15 cm, expressed with the correct number of significant figures?
A) 5.65 cm
B) 5.7 cm
C) 5.6 cm
D) 6 cm
33. How many significant figures are in the number 500.0?
A) 1
B) 2
C) 3
D) 4
34. How many significant figures are in the number 500?
A) 1
B) 2
C) 3
D) Ambiguous
35. How many significant figures are in the number 120.0?
A) 3
B) 4
C) 5
D) 6
36. How many significant figures are in the number 0.00450?
A) 2
B) 3
C) 4
D) 5
37. Which rule applies when multiplying or dividing numbers with significant figures?
A) The result should have the same number of decimal places as the number with the fewest decimal places.
B) The result should have the same number of significant figures as the number with the fewest significant figures.
C) The result should have the same number of significant figures as the number with the most significant figures.
D) The result should have the same number of decimal places as the number with the most decimal places.
38. Which rule applies when adding or subtracting numbers with significant figures?
A) The result should have the same number of significant figures as the number with the fewest significant figures.
B) The result should have the same number of decimal places as the number with the fewest decimal places.
C) The result should have the same number of decimal places as the number with the most decimal places.
D) The result should have the same number of significant figures as the number with the most significant figures.
39. A thermometer consistently reads 2°C higher than the actual temperature. This is an example of:
A) Random error
B) Gross error
C) Systematic error
D) Indeterminate error
40. Systematic errors most often affect which aspect of a measurement?
A) Precision
B) Accuracy
C) Randomness
D) Reproducibility
41. Which of the following is NOT a source of random error?
A) Fluctuations in temperature
B) Imprecise reading of an instrument scale
C) Calibration error of an instrument
D) Unpredictable variations in reaction conditions
42. If you have a sample size of n=5, how many degrees of freedom are there for calculating the sample standard deviation?
A) 3
B) 4
C) 5
D) 6
43. What is the formula for calculating the sample standard deviation (s)?
A) sqrt(sum((xi - mean)^2) / n)
B) sum((xi - mean)^2) / (n-1)
C) sqrt(sum((xi - mean)^2) / (n-1))
D) sum(xi) / n
44. In which scenario is standard deviation most useful?
A) Determining the true value of a measurement.
B) Assessing the reproducibility of measurements.
C) Comparing the closeness of a measurement to a known standard.
D) Identifying systematic errors.
45. What does a large standard deviation indicate about a set of measurements?
A) The measurements are consistent.
B) The measurements are precise.
C) The measurements are spread out from the mean.
D) The measurements are accurate.
46. What does a small standard deviation indicate about a set of measurements?
A) The measurements are far from the mean.
B) The measurements are clustered closely around the mean.
C) The measurements are highly accurate.
D) The measurements have a wide range.
47. If measurements of a substance are 2.55 g, 2.57 g, and 2.56 g, and the true value is 3.00 g, what is indicated?
A) High accuracy and high precision
B) Low accuracy and low precision
C) Low accuracy and high precision
D) High accuracy and low precision
48. If a balance consistently shows a reading of 10.05 g for a 10.00 g standard weight, what characteristic is demonstrated?
A) High accuracy, low precision
B) Low accuracy, high precision
C) High accuracy, high precision
D) Low accuracy, low precision
49. Which term describes how close multiple measurements are to each other?
A) Accuracy
B) Validity
C) Precision
D) Sensitivity
50. Which term describes how close a measured value is to the true or accepted value?
A) Precision
B) Accuracy
C) Reproducibility
D) Reliability
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