Question 1

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

Accepted Answer

The mean is greater than the median.

Question 2

Given a data set with values: 5, 7, 8, 12, 15, 18, 20, calculate the sample mean $$\bar{x}.$$

Accepted Answer

$$\bar{x} = 12.14$$

Question 3

Which measure of center is most resistant to extreme values (outliers)?

Accepted Answer

Median

Question 4

A sample of exam scores has a mean of 80 and a standard deviation of 10. According to the Empirical Rule, approximately what percentage of scores fall between 70 and 90?

Accepted Answer

About 68%

Question 5

For a bell-shaped distribution with mean $$\mu = 50$$ and standard deviation $$\sigma = 8$$, what interval contains approximately 95% of the data values?

Accepted Answer

$$[34, 66]$$

Question 6

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

Accepted Answer

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

Question 7

A data set has $$Q_1 = 20$, Q_3$ = 40. $$What is the interquartile range (IQR)?

Accepted Answer

$$IQR = 20$$

Question 8

If a data value is more than $$1.5 	imes IQR$$ above $$Q_3$$, what is it considered?

Accepted Answer

A potential outlier

Question 9

A population has mean $$\mu = 100$$ and standard deviation $$\sigma = 15. $$What is the $$z-$$score for a value $$x = 130$$?

Accepted Answer

$$z = 2$$

Question 10

Which of the following statements about Chebyshev’s Rule is correct?

Accepted Answer

At least 75% of data values lie within 2 standard deviations of the mean for any data set.

Question 11

A boxplot is most useful for which of the following?

Accepted Answer

Displaying the five-number summary and identifying potential outliers

Question 12

Which of the following is a parameter?

Accepted Answer

Population mean $$\mu$$

Question 13

A sample of 78 data values is bell-shaped with mean 28 and standard deviation 5. Approximately how many data values lie between 18 and 38?

Accepted Answer

About 74

Question 14

Which of the following best describes a left-skewed distribution?

Accepted Answer

The mean is less than the median.

Question 15

If a data set has a five-number summary of 10, 20, 30, 40, 50, what is the median?

Accepted Answer

30

Question 16

Which of the following is NOT a measure of central tendency?

Accepted Answer

Standard deviation

Question 17

A student scored 1.5 standard deviations above the mean on a test. What is the student's $$z-$$score?

Accepted Answer

$$z = 1.5$$

Question 18

Which of the following is true about the standard deviation?

Accepted Answer

It is not resistant to extreme values.

Question 19

If the mean salary at a company is heavily influenced by a few very high salaries, which measure of center would be most appropriate to report?

Accepted Answer

Median

Question 20

Which of the following best describes the Empirical Rule for a bell-shaped distribution?

Accepted Answer

About 68% of data within 1 standard deviation, 95% within 2, and 99.7% within 3 standard deviations of the mean.

Descriptive Measures in Statistics: Center, Variation, and Distribution Shape

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