Q: If a class in a frequency distribution has a frequency of 12 and the total number of data values is 60, what is the relative frequency (as a percentage) for that class?

$$\frac{12}{60} \times 100 = 20\%$$

Q: Which of the following is the correct formula for calculating the class width in a frequency distribution?

$$\text{Class width} = \frac{\text{Maximum data value} - \text{Minimum data value}}{\text{Number of classes}}$$

Question 1

Which of the following best describes a frequency distribution?

Accepted Answer

A table that shows how data are partitioned among several categories (or classes) by listing the categories along with the number of data values in each of them.

Question 2

Given a data set with a maximum value of 98, a minimum value of 50, and you want to create 6 classes, what is the appropriate class width (rounded up to the next convenient number)?

Accepted Answer

$$\frac{98 - 50}{6} = 8$$; round up to 10

Question 3

Which of the following is NOT a step in constructing a frequency distribution?

Accepted Answer

Calculate the mean and standard deviation of the data.

Question 4

A relative frequency distribution is best described as:

Accepted Answer

A table where each class frequency is replaced by the proportion or percentage of the total number of data values.

Question 5

If a class in a frequency distribution has a frequency of 12 and the total number of data values is 60, what is the relative frequency (as a percentage) for that class?

Accepted Answer

$$\frac{12}{60} 	imes 100 = 20\%$$

Question 6

Which type of graph is most appropriate for displaying the distribution of categorical data such as causes of accidental deaths?

Accepted Answer

Pareto chart

Question 7

A stem-and-leaf plot is particularly useful because it:

Accepted Answer

Displays the shape of the distribution and retains the original data values.

Question 8

Which of the following best describes a right-skewed (positively skewed) distribution?

Accepted Answer

The tail on the right side of the distribution is longer than the left.

Question 9

Which of the following statements about correlation is TRUE?

Accepted Answer

Correlation does not imply causation.

Question 10

A scatter plot of hours spent studying and exam grades shows a distinct straight-line pattern sloping upwards. What does this indicate?

Accepted Answer

There is a positive correlation between hours spent studying and exam grades.

Question 11

Which of the following is the correct formula for calculating the class width in a frequency distribution?

Accepted Answer

$$	ext{Class width} = \frac{	ext{Maximum data value} - 	ext{Minimum data value}}{	ext{Number of classes}}$$

Question 12

Which type of plot is best for visualizing the relationship between two quantitative variables, such as height and weight?

Accepted Answer

Scatter plot

Question 13

A time-series graph is most useful for which of the following purposes?

Accepted Answer

Displaying trends in data over time, such as monthly sales figures.

Question 14

If a pie chart shows that 45% of accidental deaths are due to motor vehicle accidents, what is the central angle (in degrees) for this category?

Accepted Answer

$$0.45 	imes 360 = 162$$ degrees

Question 15

Which of the following is a key feature of a dotplot?

Accepted Answer

Each data value is represented by a dot, and dots are stacked for repeated values.

Question 16

A cumulative frequency distribution for test scores shows that 70 students scored less than 110. If there are 100 students in total, what is the cumulative relative frequency for the class 'less than 110'?

Accepted Answer

$$\frac{70}{100} = 0.7 or$$ $$70\%$$

Question 17

Which of the following scenarios is most likely to produce a left-skewed (negatively skewed) distribution?

Accepted Answer

A study of human life expectancy, where most people live to an old age but a few die young.

Question 18

Which of the following statements about scatter plots is FALSE?

Accepted Answer

Scatter plots are used to display the distribution of a single variable.

Question 19

If a frequency distribution has classes 10-19, 20-29, 30-39, and so on, and a data value is 29, to which class does it belong?

Accepted Answer

20-29

Question 20

Which of the following best explains why the sum of the percentages in a relative frequency distribution must equal 100%?

Accepted Answer

Because all data values are accounted for and each is included in exactly one class.

Frequency Distributions, Graphs, and Correlations: Study Notes for Statistics

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