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Chapter 2: Problem 33

Explain for what kind of frequency distribution an ogive is drawn. Can you think of any use for an ogive? Explain.

Short Answer

Expert verified
An ogive is drawn for a frequency distribution that has been divided into categories, generally when the data set has a large range or numerous distinct values. It is useful for determining the number of observations below or above a specific value and to visually represent statistics like the median, quartiles, and percentiles. Furthermore, it can be used to determine if a distribution is skewed and for comparing different data sets.

Step by step solution

01

Understand an Ogive

An ogive is a graphical representation of the cumulative frequency or relative cumulative frequency. It is constructed by plotting the cumulative frequency (or relative cumulative frequency) on the vertical axis and the intervals (class boundaries) on the horizontal axis. It is useful for determining the number of observations below or above a particular value. It's also useful to visually express basic statistical results such as median, quartiles, and percentiles.
02

Frequency distribution for an Ogive

An ogive is used for a frequency distribution that has been organized into some categories, also known as bins. It's generally used when the data set has a large range or a large number of different possible data values.
03

Uses of an Ogive

1. Ogives are used to determine the median, percentiles and quartiles of a distribution graphically. 2. It also aids in determining whether a distribution is skewed left or skewed right. 3. It can be utilized to compare different data sets. 4. Ogives can provide a quick visual check for normality of a data set.

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Most popular questions from this chapter

Thirty adults were asked which of the following conveniences they would find most difficult to do without: television ( \(\mathrm{T}\) ), refrigerator (R), air conditioning (A), public transportation (P), or microwave (M). Their responses are listed below. \(\begin{array}{llllllllll}\mathrm{R} & \mathrm{A} & \mathrm{R} & \mathrm{P} & \mathrm{P} & \mathrm{T} & \mathrm{R} & \mathrm{M} & \mathrm{P} & \mathrm{A} \\ \mathrm{A} & \mathrm{R} & \mathrm{R} & \mathrm{T} & \mathrm{P} & \mathrm{P} & \mathrm{T} & \mathrm{R} & \mathrm{A} & \mathrm{A} \\ \mathrm{R} & \mathrm{P} & \mathrm{A} & \mathrm{T} & \mathrm{R} & \mathrm{P} & \mathrm{R} & \mathrm{A} & \mathrm{P} & \mathrm{R}\end{array}\) a. Prepare a frequency distribution table. b. Calculate the relative frequencies and percentages for all categories. c. What percentage of these adults named refrigerator or air conditioning as the convenience that they would find most difficult to do without? d. Draw a bar graph for the relative frequency distribution.

A July 2011 ESPN SportsNation poll asked, "Which is the best Fourth of July weekend sports tradition?" (http://espn.go.com/espn/fp/flashPollResultsState?sportIndex=frontpage\&pollid=116290). The choices were Major League baseball game (B), Nathan's Famous International Hot Dog Eating Contest (H), Breakfast at Wimbledon (W), or NASCAR race at Daytona (N). The following data represent the responses of a random sample of 45 persons who were asked the same question. \(\begin{array}{lllllllll}\text { H } & \text { H } & \text { B } & \text { W } & \text { N } & \text { B } & \text { H } & \text { N } & \text { W } \\\ \text { N } & \text { H } & \text { B } & \text { W } & \text { H } & \text { N } & \text { N } & \text { H } & \text { H } \\ \text { B } & \text { B } & \text { W } & \text { H } & \text { H } & \text { B } & \text { W } & \text { H } & \text { B } \\ \text { H } & \text { B } & \text { B } & \text { H } & \text { B } & \text { H } & \text { B } & \text { N } & \text { H } \\ \text { B } & \text { B } & \text { H } & \text { H } & \text { H } & \text { B } & \text { H } & \text { H } & \text { N }\end{array}\) a. Prepare a frequency distribution table. b. Calculate the relative frequencies and percentages for all categories. c. What percentage of the respondents mentioned Major League baseball game or Breakfast at Wimbledon? d. Draw a bar graph for the frequency distribution.

Consider the following stem-and-leaf display. $$ \begin{array}{l|lllllll} 4 & 3 & 6 & & & & & & \\ 5 & 0 & 1 & 4 & 5 & & & & \\ 6 & 3 & 4 & 6 & 7 & 7 & 7 & 8 & 9 \\ 7 & 2 & 2 & 3 & 5 & 6 & 6 & 9 & \\ 8 & 0 & 7 & 8 & 9 & & & & \end{array} $$ Write the data set that is represented by this display.

What is a stacked dotplot, and how is it used? Explain.

Briefly explain the concept of cumulative frequency distribution. How are the cumulative relative frequencies and cumulative percentages calculated?
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