Question 1

Which of the following best describes the difference between descriptive and inferential statistics?

Accepted Answer

Descriptive statistics summarize and describe data sets, while inferential statistics use sample data to make generalizations about a population.

Question 2

A researcher collects the heights (in cm) of 100 students. Which type of data is this?

Accepted Answer

Quantitative (numerical) data

Question 3

Given the data set $$\{3, 26, 4, 15, 0.8\}$$, what is the median?

Accepted Answer

$$4$$

Question 4

Which measure of central location is least sensitive to extremely large or small data points?

Accepted Answer

Median

Question 5

Suppose a manufacturer claims that the average battery life is $$60$$ months, but the guarantee is only for $$36$$ months. If the battery life is normally distributed with mean $$60$$ and standard deviation $$8$$, what percentage of batteries will last less than $$44$$ months?

Accepted Answer

About $$2.5\%$$

Question 6

Which of the following is NOT a property of the sample mean?

Accepted Answer

It is always equal to the mode.

Question 7

Given the sample data $$\{3, 1, 4, 2\}$$, calculate the sample variance $$s^2.$$

Accepted Answer

$$1.67$$

Question 8

Which statement about Chebyshev's Rule is correct?

Accepted Answer

At least $$1 - \frac{1}{k^2$} of $$the data will fall within $$k$$ standard deviations of the mean for any $$k \u003e 1.$$

Question 9

A z-score is calculated as $$z = \frac{x - \mu}{\sigma}. $$What does a z-score of $$-2$$ mean?

Accepted Answer

The value $$x is$$ $$2$$ standard deviations below the mean.

Question 10

Which of the following best describes the interquartile range (IQR)?

Accepted Answer

It is the range covered by the middle $$50\% of $$the data.

Question 11

A sample of $$n = 5$$ has values $$\{2, 4, 6, 8, 10\}. $$What is the sample mean?

Accepted Answer

$$6$$

Question 12

Which graphical method is most appropriate for displaying the distribution of a small set of numerical data?

Accepted Answer

Stem-and-leaf display

Question 13

If a data set is symmetric and bell-shaped, which of the following is true?

Accepted Answer

The mean, median, and mode are all equal.

Question 14

A survey reports a margin of error of $$\pm 3\%$$ for the results. What does this mean?

Accepted Answer

The sample result may differ from the true population value by up to $$3\%$$ due to sampling variability.

Question 15

Which of the following is NOT a measure of variability?

Accepted Answer

Median

Question 16

A box plot shows a long whisker on the right side. What does this indicate about the data?

Accepted Answer

The data is skewed to the right.

Question 17

If the sample standard deviation $$s = 4$$ for a mound-shaped distribution, approximately what percentage of the data falls within $$8$$ units of the mean?

Accepted Answer

$$95\%$$

Question 18

Which of the following is a correct interpretation of an outlier in a box plot?

Accepted Answer

It is a value that falls outside the inner fences and is considered unusual.

Question 19

A random sample is defined as:

Accepted Answer

A sample in which each population unit has an equal chance of being selected.

Question 20

Suppose the mean score on a test is $$70$$ and the standard deviation is $$10. $$What is the z-score for a student who scored $$85$$?

Accepted Answer

$$1.5$$

Descriptive and Inferential Statistics: Data Summarization and Measures

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