Question 1

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

Accepted Answer

Descriptive statistics summarize and describe the pattern of a data set, while inferential statistics make generalizations or predictions about a population based on sample data.

Question 2

A researcher collects the heights (in cm) of 20 students and wants to display the distribution. Which graphical method is most appropriate?

Accepted Answer

Stem-and-leaf display

Question 3

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

Accepted Answer

$$4$$

Question 4

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

Accepted Answer

Variance

Question 5

Suppose the battery life of a certain brand is normally distributed with a mean of $$60$$ months and a standard deviation of $$6$$ months. What percentage of batteries will last between $$54$$ and $$66$$ months?

Accepted Answer

Approximately $$68\%$$

Question 6

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 7

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

Accepted Answer

$$1.67$$

Question 8

A z-score is calculated using which formula for a sample?

Accepted Answer

$$z = \frac{x - \bar{x}}{s}$$

Question 9

If a data set has a mean of $$50$$ and a standard deviation of $$5$$, what is the z-score for a value of $$60$$?

Accepted Answer

$$3$$

Question 10

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

Accepted Answer

The range that covers the middle $$50\% of $$the data.

Question 11

A sample of 1000 consumers is given a blind taste test to choose between Brand A and Brand B. Which of the following is the variable of interest?

Accepted Answer

The preference for Brand A or Brand B.

Question 12

Which of the following is a qualitative (categorical) variable?

Accepted Answer

Blood type of a patient

Question 13

If the distribution of data is mound-shaped (bell-shaped), which statement is true according to the Empirical Rule?

Accepted Answer

Approximately $$68\% of $$the data falls within $$1$$ standard deviation of the mean.

Question 14

Which of the following is NOT a correct interpretation of a box plot?

Accepted Answer

The median is always equal to the mean.

Question 15

A sample of 16 grocery bills (in dollars) is collected. Which measure would best describe the spread of the data?

Accepted Answer

Standard deviation

Question 16

Which of the following is a correct definition of the mode?

Accepted Answer

The value that occurs most frequently in a data set.

Question 17

A random sample is best described as:

Accepted Answer

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

Question 18

Which of the following is a measure of variability?

Accepted Answer

Variance

Question 19

Suppose a survey result is reported as $$55\% \pm 3\%. $$What does the $$3\%$$ represent?

Accepted Answer

The margin of error

Descriptive and Inferential Statistics: Data Summarization and Measures

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