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Chapter 2: Q. 2.48 (page 68)

Explain the difference between a frequency histogram and a relative-frequency histogram.

Short Answer

Expert verified

The main difference between a frequency histogram and a relative frequency histogram is that in a relative histogram, the height of each bar equals the relative frequencies of the class rather than the frequency of the class.

Step by step solution

01

Concept introduction

In statistics, a histogram is a solid figure or diagram made up of rectangular bars. It's one of the most used types of bar graph, and it's used to visualise any numeric data in a practical way.

02

Explanation

A frequency histogram is a sort of bar graph that displays the frequency, or number of times, a data set's outcome happens. To graphically show the data, it has a title, an x-axis, a y-axis, and vertical bars.

A relative frequency histogram is a variant of the standard frequency histogram. We use this axis to express the overall proportion of data values that fall into this bin, rather than utilising a vertical axis to represent the count of data values that fall into a certain bin.

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Most popular questions from this chapter

Give an example, other than those presented in this section, of

a) Qualitative Variable

b) Discrete Qualitative Variable

c) Continuous Quantitative Variable

Old Faithful. Old Faithful is a geyser in Yellowstone National Park that erupts at relatively predictable intervals. Since 2000, the eruptions of Old Faithfull occur on average every 90 minutes. Information on the daily eruptions of Old Faithful can be found on the website of The Geyser Observation and Study Association (GOSA). The following data provide the times between eruptions, in minutes, for Old Faithful over a two-day period.

96

68

99

97

92

61

105


89


95

71

93

104

85

107

91


97


99

86

102

93

99

64

102


86


101

81

117

87

106

93

106

106


a. Use cutpoint grouping with a first class of 60 -under 70 to construct a frequency histogram of the times between eruptions.

b. Identify the shape of the distribution with regard to modality.

c. Identify the shape of the distribution with regard to symmetry (or nonsymmetry).

d. If the distribution is unimodal and nonsymmetric, classify it as either right skewed or left skewed.

We have drawn a smooth curve that represents a distribution,

a. Identify the shape of the distirbution with regard to modality.

b. Identify the shape of the distribution with regard to symmetry (or non symmetry)

c . If the distribution is unimodal and non symmetric, classify it as either right skewed or left skewed.

Adjusted Gross Incomes. The Internal Revenue Service (IRS) publishes data on adjusted gross incomes in Statistics of Income, and Individual Income Tax Returns. The following relative frequency histogram shows one year's individual income tax returns for adjusted gross incomes of less than \(50,000.

Use the histogram and the fact that adjusted gross incomes are expressed to the nearest whole dollar to answer each of the following questions.

a. Approximately what percentage of the individual income tax returns had an adjusted gross income between\)10,000and \(19,999, inclusive?

b. Approximately what percentage had an adjusted gross income of less than \)30,000?

c. The IRS reported that \(89,928,000individual income tax returns had an adjusted gross income of less than \)50,000. Approximately how many had an adjusted gross income between \(30,000and \)49,999, inclusive?

Detroit Tigers. From the Baseball Almanac website, we found the heights, in inches, of the players on the 2012 World Series runner-up Detroit Tigers baseball team.

Use the graph to answer the following questions. Note that cholesterol levels are always expressed as whole numbers.

a. Construct a stem-and-leaf diagram of these data with five lines per stem.

b. Why is it better to use five lines per stem here instead of one or two lines per stem?
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