Q: If the relative frequency of a class is $$0.19$$ and the sample size is $$365$$, what is the frequency of the class?

$$0.19 \times 365 = 69.35$$, so $$69$$

Question 1

Given a data set with a minimum value of 10, a maximum value of 93, and 6 classes, what is the appropriate class width to use when constructing a frequency distribution?

Accepted Answer

$$\displaystyle \frac{93-10}{6} = 13.83$$, so round up to $$14$$

Question 2

A frequency distribution has the following lower class limits: 10, 24, 38, 52, 66, 80. What is the class width?

Accepted Answer

$$14$$

Question 3

If a class in a frequency distribution has lower and upper class limits of 41 and 45, respectively, what is the class midpoint?

Accepted Answer

$$\displaystyle \frac{41 + 45}{2} = 43$$

Question 4

A class in a frequency distribution has a lower class limit of 55 and an upper class limit of 59. What are the class boundaries?

Accepted Answer

$$54.5$$ and $$59.5$$

Question 5

Given the following frequency distribution for employee salaries (in thousands): 32 (30), 42 (270), 52 (170), 62 (40), 72 (30), 82 (15), 92 (10), what is the total number of classes and the class width?

Accepted Answer

There are $$7$$ classes and the class width is $$15$$

Question 6

A histogram shows that about half of the employees' salaries are between $$40,000 and 49$$,000. What does this pattern suggest about the distribution of salaries?

Accepted Answer

The distribution is approximately symmetric

Question 7

If the frequency polygon for the number of children of 43 world leaders shows that most had fewer than 3 children, what does this indicate about the data?

Accepted Answer

The data are right-skewed

Question 8

Given the following class frequencies: 138-202 (12), 203-267 (7), 268-332 (7), 333-397 (3), 398-462 (1), which class has the greatest relative frequency?

Accepted Answer

138-202

Question 9

For a data set with class limits 50-54, 55-59, 60-64, 65-69, 70-74, 75-79, and 80-84, and frequencies 2, 4, 7, 6, 4, 1, 0, at which class does the greatest increase in cumulative frequency occur?

Accepted Answer

60-64

Question 10

If the relative frequency of a class is calculated as $$\displaystyle \frac{f}{n}$$, where $$f is $$the class frequency and $$n is $$the sample size, what is the relative frequency of a class with frequency 68 in a sample of 365?

Accepted Answer

$$0.19$$

Question 11

A cumulative frequency distribution is constructed by:

Accepted Answer

Adding the frequency of each class to the sum of the frequencies of all previous classes

Question 12

Given a class with lower class limit 27.5 and upper class limit 32.5, what are the class boundaries?

Accepted Answer

$$27.25$$ and $$32.75$$

Question 13

If a frequency distribution for time spent reading a blog in a day (in minutes) has classes 0-5, 6-11, 12-17, 18-23, 24-29, with frequencies 18, 12, 7, 2, 1, which class has the least frequency?

Accepted Answer

24-29

Question 14

A histogram is constructed for a data set. Which of the following statements is true about the bars in a histogram?

Accepted Answer

The bars must touch each other

Question 15

If the class boundaries for a class with limits 41-45 are 40.5 and 45.5, what is the width of the class boundary interval?

Accepted Answer

$$45.5 - 40.5 = 5$$

Question 16

A frequency polygon is best used to:

Accepted Answer

Show the shape of the distribution by connecting midpoints of each class with straight lines

Question 17

If a class in a frequency distribution has a lower class limit of 57 and an upper class limit of 61, what is the midpoint?

Accepted Answer

$$\displaystyle \frac{57 + 61}{2} = 59$$

Question 18

In a cumulative frequency ogive, the greatest increase in cumulative frequency occurs at which class interval?

Accepted Answer

The class with the highest frequency

Question 19

If the relative frequency of a class is $$0.19$$ and the sample size is $$365$$, what is the frequency of the class?

Accepted Answer

$$0.19 	imes 365 = 69.35$$, so $$69$$

Frequency Distributions and Graphical Representation in Statistics

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