Q: A medical research team studied the ages of patients who had strokes caused by stress. If you are asked to construct a frequency distribution using class intervals of width 6 starting at 25, which formula would you use to determine the number of classes needed?

$$\text{Number of classes} = \frac{\text{Range}}{\text{Class width}}$$

Q: If the average cost to rent a studio increased from $$400 in 2002 to 500 in 2003$$, what is the percentage increase?

$$\frac{500 - 400}{400} \times 100\% = 25\%$$

Q: In a frequency distribution, what is the formula for relative frequency?

$$\text{Relative frequency} = \frac{\text{Frequency of class}}{\text{Total frequency}}$$

Question 1

Which of the following best describes the type of variable represented by the 'Box office sales ($ millions)' column in the movie table?

Accepted Answer

Continuous variable

Question 2

Given the table of mountain heights and ranks, what type of data is represented by the 'Rank' column?

Accepted Answer

Ordinal data

Question 3

In the table showing the average weight of offensive linemen for football teams, what is the variable under consideration in the second column?

Accepted Answer

Average weight (pounds)

Question 4

A medical research team studied the ages of patients who had strokes caused by stress. If you are asked to construct a frequency distribution using class intervals of width 6 starting at 25, which formula would you use to determine the number of classes needed?

Accepted Answer

$$	ext{Number of classes} = \frac{	ext{Range}}{	ext{Class width}}$$

Question 5

In the homework time table, if 5 students spent 0–14 minutes on homework and there are 20 students in total, what is the relative frequency for this class?

Accepted Answer

$$0.25$$

Question 6

Which of the following is a correct interpretation of a relative frequency histogram?

Accepted Answer

It shows the proportion of the total data that falls within each class interval.

Question 7

When constructing a stem-and-leaf diagram, which of the following statements is TRUE?

Accepted Answer

Different choices of stems and leaves can result in different diagrams for the same data.

Question 8

A bar graph is truncated by starting the vertical axis at 300 instead of 0. What effect does this have on the visual interpretation of the data?

Accepted Answer

It exaggerates the apparent differences between the bars.

Question 9

If the average cost to rent a studio increased from $$400 in 2002 to 500 in 2003$$, what is the percentage increase?

Accepted Answer

$$\frac{500 - 400}{400} 	imes 100\% = 25\%$$

Question 10

Given the frequency distribution for the number of TVs per household: 1 TV: 20, 2 TVs: 50, 3 TVs: 15, 4 TVs: 10, 5 TVs: 5. What is the relative frequency for households with 2 TVs?

Accepted Answer

$$\frac{50}{100} = 0.5$$

Question 11

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

Accepted Answer

Number of TVs in a household

Question 12

If you are given a list of blood types for a group of patients, what type of data is this?

Accepted Answer

Nominal data

Question 13

Which of the following best describes the difference between a frequency histogram and a relative frequency histogram?

Accepted Answer

A frequency histogram shows counts, while a relative frequency histogram shows proportions.

Question 14

If a class interval in a frequency distribution is 25–30, what is the class width?

Accepted Answer

$$30 - 25 + 1 = 6$$

Question 15

Which of the following is NOT a reason to use grouping in frequency distributions?

Accepted Answer

To increase the number of classes as much as possible

Question 16

If you have a data set with values ranging from 25 to 66, and you want to use 5 classes, what is the appropriate class width?

Accepted Answer

$$\frac{66 - 25 + 1}{5} = 8.4$$

Question 17

Which of the following is a correct statement about continuous data?

Accepted Answer

Continuous data can take any value within a given range.

Question 18

In a frequency distribution, what is the formula for relative frequency?

Accepted Answer

$$	ext{Relative frequency} = \frac{	ext{Frequency of class}}{	ext{Total frequency}}$$

Question 19

Which of the following is an example of ordinal data?

Accepted Answer

Rank of mountains by height

Question 20

If a histogram has a class with a relative frequency of 0.5, what does this mean?

Accepted Answer

Half of the data falls within this class interval.

Fundamental Concepts and Data Representation in Statistics

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