Q: A student’s grades and credits are: A (3 credits), A (4 credits), B (3 credits), C (3 credits), F (1 credit). Using the quality points A=4, B=3, C=2, F=0, what is her GPA (weighted mean)?

$$\frac{(3\times4)+(4\times4)+(3\times3)+(3\times2)+(1\times0)}{3+4+3+3+1} = 3.07$$

Q: Which of the following is the correct formula for the coefficient of variation (CV) for a sample?

$$CV = \frac{s}{\bar{x}} \times 100$$

Question 1

Which of the following best describes the mean of a data set?

Accepted Answer

The sum of all data values divided by the number of data values.

Question 2

Given the data set: 38.5, 55.6, 22.4, 14.1, 23.1 (all in Mbps), what is the sample mean $$\bar{x}$$?

Accepted Answer

$$\bar{x} = \frac{38.5+55.6+22.4+14.1+23.1}{5} = 30.74$$

Question 3

A student’s grades and credits are: A (3 credits), A (4 credits), B (3 credits), C (3 credits), F (1 credit). Using the quality points A=4, B=3, C=2, F=0, what is her GPA (weighted mean)?

Accepted Answer

$$\frac{(3	imes4)+(4	imes4)+(3	imes3)+(3	imes2)+(1	imes0)}{3+4+3+3+1} = 3.07$$

Question 4

Which measure of center is most appropriate for describing the middle value of a skewed data set?

Accepted Answer

Median

Question 5

What is the range of the data set: 38.5, 55.6, 22.4, 14.1, 23.1?

Accepted Answer

$$55.6 - 14.1 = 41.5$$

Question 6

Which formula is used to calculate the sample standard deviation $$s$$?

Accepted Answer

$$s = \sqrt{\frac{\sum (x - \bar{x})^2$}{n-1}}$$

Question 7

If a data set has a mean of 100 and a standard deviation of 15, what is the z-score for a value of 130?

Accepted Answer

$$z = \frac{130 - 100}{15} = 2.00$$

Question 8

According to the Empirical Rule, approximately what percentage of data falls within two standard deviations of the mean in a bell-shaped distribution?

Accepted Answer

95%

Question 9

A platelet count of 75 (mean $$=239.4$$, $$s=64.2) is $$observed. What is the z-score, and is it significantly low?

Accepted Answer

$$z = \frac{75 - 239.4}{64.2} = -2.56$$, which is significantly low

Question 10

Which of the following is NOT a property of the standard deviation?

Accepted Answer

It is a resistant measure, unaffected by outliers.

Question 11

A data set has a mean of 50 and a standard deviation of 5. According to the range rule of thumb, what is the approximate range of the data?

Accepted Answer

$$4 	imes 5 = 20$$

Question 12

Which of the following statements about the mode is correct?

Accepted Answer

A data set can have more than one mode.

Question 13

If a data value has a z-score of 2.5, how would you interpret this value?

Accepted Answer

It is significantly high.

Question 14

Which of the following is the correct formula for the coefficient of variation (CV) for a sample?

Accepted Answer

$$CV = \frac{s}{\bar{x}} 	imes 100$$

Question 15

A data set has the following five-number summary: 2, 5, 8, 12, 20. What is the interquartile range (IQR)?

Accepted Answer

$$IQR = Q_3$ - Q_1$ = 12 - 5 = 7$$

Question 16

Which of the following best describes a boxplot?

Accepted Answer

A graph that displays the five-number summary of a data set.

Question 17

If the 40th percentile of a data set is 11.7 Mbps, what does this mean?

Accepted Answer

40% of the data values are less than or equal to 11.7 Mbps.

Question 18

Which of the following is NOT part of the five-number summary?

Accepted Answer

Mean

Question 19

Chebyshev’s Theorem states that for any data set, at least what proportion of values lie within 2 standard deviations of the mean?

Accepted Answer

$$1 - \frac{1}{2^2$} = 0.75 or 75$$%

Describing, Exploring, and Comparing Data: Measures of Center, Variation, and Relative Standing CHAP 3

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