Question 1

Which formula correctly represents the sample mean $$\bar{x}$$ for a data set with $$n$$ observations $$x_1$$, $$x_2$$, ..., x_n$$?

Accepted Answer

$$\bar{x} = \dfrac{\sum x_i}{n}$$

Question 2

A data set is highly skewed to the right. Which measure of central tendency is most appropriate to describe the 'average' value?

Accepted Answer

Median

Question 3

Given the following travel times to work (in minutes): 23, 36, 23, 18, 5, 26, 43. What is the population mean?

Accepted Answer

$$\mu = \dfrac{23 + 36 + 23 + 18 + 5 + 26 + 43}{7} = 24.857$$

Question 4

Which of the following statements about the mean is TRUE?

Accepted Answer

The mean uses all data values in its calculation.

Question 5

If a distribution is symmetric, which measure of central tendency should be used and why?

Accepted Answer

Mean, because it uses all data values and is the center of gravity.

Question 6

Which of the following is the correct formula for the population standard deviation $$\sigma$$?

Accepted Answer

$$\sigma = \sqrt{\dfrac{\sum (x_i - \mu)^2$}{N}}$$

Question 7

A sample of three travel times is 5, 26, and 36 minutes. What is the sample standard deviation $$s$$?

Accepted Answer

$$s = \sqrt{\dfrac{500.67}{2}} = 15.83$$

Question 8

Which histogram (A or C) in the provided image has a larger standard deviation, and why?

Accepted Answer

Histogram C, because its values are more spread out from the mean.

Question 9

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

Accepted Answer

95%

Question 10

A student scores 20 on a math test (mean = 16, standard deviation = 2.5) and 83 on a science test (mean = 75, standard deviation = 9). Which test did the student perform better on, based on z-scores?

Accepted Answer

Math test, because $$z = \dfrac{20-16}{2.5} = 1.6 is $$higher than $$z = \dfrac{83-75}{9} = 0.89.$$

Question 11

Which formula is used to calculate the z-score for a population value $$x$$?

Accepted Answer

$$z = \dfrac{x - \mu}{\sigma}$$

Question 12

What does the interquartile range (IQR) measure?

Accepted Answer

The range of the middle 50% of the data.

Question 13

Given Q1 = 28 and Q3 = 38 for a data set, what is the IQR?

Accepted Answer

$$IQR = Q_3$ - Q_1$ = 38 - 28 = 10$$

Question 14

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

Accepted Answer

Mean

Question 15

How do you determine if a value is an outlier using quartiles and the IQR?

Accepted Answer

If it is less than $$Q_1 - 1.5$$ 	imes IQR$$ or greater than Q_3$ + 1.5 	imes IQR$$

Question 16

Which measure of dispersion is most appropriate for a symmetric distribution?

Accepted Answer

Standard deviation

Question 17

A boxplot shows a long whisker on the right side. What does this indicate about the distribution?

Accepted Answer

The distribution is skewed right.

Question 18

If a data set has no repeated values, what can you say about its mode?

Accepted Answer

The data set has no mode.

Question 19

Which of the following best describes the relationship between mean and median in a left-skewed distribution?

Accepted Answer

Mean \u003c Median

Question 20

Which measure of central tendency is the only one that can be used for nominal data?

Accepted Answer

Mode

Numerically Summarizing Data: Measures of Central Tendency, Dispersion, and Position

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