Q: A laboratory technician uses a pipet to deliver 10 mL of solution 50 times. The mean volume delivered is 9.982 mL with a standard deviation of 0.0056 mL. What is the spread of the measurements?

Spread = Maximum value - Minimum value = $$9.994\ \text{mL} - 9.969\ \text{mL} = 0.025\ \text{mL}$$

Q: Which of the following is the correct formula for the relative standard deviation (RSD)?

$$\text{RSD} = \frac{s}{\overline{X}}$$

Q: A set of measurements yields a mean value of $$3.117 g $$and a standard deviation of $$0.051 g. $$What is the percent relative standard deviation (%RSD)?

$$\frac{0.051}{3.117} \times 100\% = 1.6\%$$

Question 1

Which of the following statements best describes the difference between accuracy and precision in analytical chemistry?

Accepted Answer

Accuracy is the degree of agreement between measured value and the true value, while precision is the degree of agreement between replicate measurements of the same quantity.

Question 2

A student measures the mass of a coin seven times and obtains the following values (in grams): 3.080, 3.094, 3.107, 3.056, 3.112, 3.174, 3.198. What is the mean mass of the coin?

Accepted Answer

$$\frac{3.080 + 3.094 + 3.107 + 3.056 + 3.112 + 3.174 + 3.198}{7} = 3.117\ 	ext{g}$$

Question 3

Which equation is used to calculate the sample standard deviation for a set of measurements?

Accepted Answer

$$s = \sqrt{\frac{\sum_{i=1}^{n} (X_i - \overline{X})^2$}{n - 1}}$$

Question 4

A laboratory technician uses a pipet to deliver 10 mL of solution 50 times. The mean volume delivered is 9.982 mL with a standard deviation of 0.0056 mL. What is the spread of the measurements?

Accepted Answer

Spread = Maximum value - Minimum value = $$9.994\ 	ext{mL} - 9.969\ 	ext{mL} = 0.025\ 	ext{mL}$$

Question 5

Which of the following is an example of a determinate (systematic) error?

Accepted Answer

A pipet that consistently delivers less volume than indicated due to faulty calibration.

Question 6

What is the correct way to round off the result of $$89.332 + 1.1$$ according to significant figure rules for addition?

Accepted Answer

Round to one digit after the decimal point: $$90.4$$

Question 7

Which formula is used to calculate the population standard deviation?

Accepted Answer

$$\sigma = \sqrt{\frac{\sum_{i=1}^{N} (x_i - \mu)^2$}{N}}$$

Question 8

A chemist is analyzing a sample and suspects contamination from reagents. Which procedure should be used to detect this type of error?

Accepted Answer

Blank determination

Question 9

Which of the following best describes the distribution of random errors in analytical measurements?

Accepted Answer

Random errors follow a Gaussian (normal) distribution.

Question 10

If a measurement is reported as $$6.0 \pm 0.1 mL$$, what is the range of possible values delivered?

Accepted Answer

$$5.9 to$$ $$6.1 mL$$

Question 11

Which of the following is the correct formula for the relative standard deviation (RSD)?

Accepted Answer

$$	ext{RSD} = \frac{s}{\overline{X}}$$

Question 12

A set of measurements yields a mean value of $$3.117 g $$and a standard deviation of $$0.051 g. $$What is the percent relative standard deviation (%RSD)?

Accepted Answer

$$\frac{0.051}{3.117} 	imes 100\% = 1.6\%$$

Question 13

Which of the following is NOT a source of systematic error?

Accepted Answer

Random fluctuations in temperature during measurement

Question 14

Which equation represents the Gaussian (normal) distribution?

Accepted Answer

$$y = \frac{e$$^{-(x-\mu)^2/2\sigma^2}$$}{\sigma \sqrt{2\pi}}$$

Question 15

Which of the following is the correct formula for the sample mean?

Accepted Answer

$$\overline{X} = \frac{\sum_{i=1}^{n} X_i}{n}$$

Question 16

A chemist performs a titration and consistently overshoots the endpoint due to excess indicator. What type of error is this?

Accepted Answer

Method error (systematic)

Question 17

Which of the following best describes the effect of increasing sample size on the difference between sample mean and population mean?

Accepted Answer

The difference decreases rapidly as sample size increases, becoming negligible for $$N \geq 20 to$$ $$30.$$

Question 18

Which of the following is the correct formula for the pooled standard deviation?

Accepted Answer

$$s_{	ext{pooled}} = \sqrt{\frac{\sum_{j=1}^{N_1$} (x_j - \overline{x}_1)^2$ + \sum_{j=1}^{N_2$} (x_j - \overline{x}_2)^2$ + \cdots}{N_1$ + N_2$ + \cdots - N_t}}$$

Question 19

Which of the following is the correct formula for the standard error of the mean?

Accepted Answer

$$s_m = \frac{s}{\sqrt{N}}$$

Data Handling, Errors, and Statistics in Analytical Chemistry

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