Question 1

Which of the following best describes a continuous variable?

Accepted Answer

A variable that can take any value within a range, with no gaps between possible values.

Question 2

In constructing a histogram for a sample of 50 coffee cup volumes ranging from 11.40 to 12.66 ounces, which bin width would be most appropriate if you want about 13 bins?

Accepted Answer

Use a bin width of $$0.10$$ ounces.

Question 3

Given the following frequency distribution table for coffee cup volumes, in which bin does the value $$12.40$$ fall?

Bins:
$$12.30 to$$ $$12.40$$
$$12.40 to$$ $$12.50$$

Accepted Answer

It falls in the bin $$12.40 to$$ $$12.50.$$

Question 4

Which of the following statements about bins in a histogram is TRUE?

Accepted Answer

Bins should collectively span all sample values without gaps or overlaps.

Question 5

A sample of 100 values ranges from $$42.3 to$$ $$98.8. If $$you want to use $$15$$ bins, what is a suitable bin width?

Accepted Answer

Bin width of $$4.0.$$

Question 6

Which of the following is NOT a correct description of a variable?

Accepted Answer

A variable must always be quantitative.

Question 7

In a discrete probability distribution, which property must always be satisfied?

Accepted Answer

The sum of all probabilities must equal $$1.$$

Question 8

A binary variable is best represented by which of the following probability distributions?

Accepted Answer

A pie chart with two sections.

Question 9

If a sample has the values $$4, 8, 8, 11, 12, 13$$, what is the mode of the sample?

Accepted Answer

The mode is $$8.$$

Question 10

Which notation is used to represent the sum of all sample values $$x_1$$, $$x_2$$, ..., x_n$$?

Accepted Answer

$$\sum_{i=1}^{n} x_i$$

Question 11

Which of the following best explains why increasing sample size improves the accuracy of a histogram in representing the underlying distribution?

Accepted Answer

Larger sample sizes reduce random variability and make the histogram shape more closely resemble the true distribution curve.

Question 12

Which of the following is a plausible reason for choosing a bin width that is a 'round number' when constructing a histogram?

Accepted Answer

It makes the bins easier to interpret and the histogram easier to scale.

Question 13

Which of the following is TRUE about the mode of a probability distribution?

Accepted Answer

It is the value aligned with the peak of the distribution graph.

Question 14

A frequency distribution table for a sample must satisfy which of the following conditions?

Accepted Answer

The sum of all frequencies equals the sample size.

Question 15

Which of the following is an example of a discrete variable?

Accepted Answer

The number of library visits per week by a student.

Question 16

If you are constructing a histogram and the range of your data is $$1.26$$ and you want $$13$$ bins, what is the approximate bin width you should use?

Accepted Answer

$$\frac{1.26}{13} \approx 0.10$$

Question 17

Which of the following is a correct statement about categorical variables?

Accepted Answer

Categorical variables can be binary or have three or more categories.

Question 18

In a probability distribution for a continuous variable, what does the area under the curve represent?

Accepted Answer

The probability of the variable falling within a specified interval.

Question 19

Which of the following is the best reason for using interval notation when describing bins in a histogram?

Accepted Answer

It clearly defines the range of values included in each bin, avoiding ambiguity.

Early Ideas with Probability Distributions and Data: Study Notes for Introductory Statistics

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