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Chapter 2: Q. 2.23 (page 98)

The following data are the number of pages in 40 books on a shelf. Construct a box plot using a graphing

calculator, and state the interquartile range.

136;140;178;190;205;215;217;218;232;234;240;255;270;275;290;301;303;315;317;318;326;333;343;

349;360;369;377;388;391;392;398;400;402;405;408;422;429;450;475;512

Short Answer

Expert verified

We may deduce from the box plot that the distribution is more or less symmetrical, and that there are no outliers in the data.

Step by step solution

01

Given

Here we have136;140;178;190;205;215;217;218;232;234;240;255;270;275;290;301;303;315;317;318;326;333;343;

349;360;369;377;388;391;392;398;400;402;405;408;422;429;450;475;512

02

Solution

The box plot of the given number of pages is

By calculation we get the IQR as161.

03

Explanation of Solution

Theshapeofthedistributionisdefinedbytheboxplot.
Itprovidesanoverviewofthequartiles.
Asaresult,wecanquicklygrasptheconceptsofskewnessandmedian.
Thefundamentalaspectofaboxplotisthatitisprimarilyusedtofindoutliers.
Anoutlierisastarthatisoutsideoftheacceptablerangeandisindicatedontheplot.
Thereisnooutlierinoursituation.
The 1st quartile is represented by the end point of the boxplot below, while the 3rdquartile is represented by the end point of the boxplot above.
So the data in the boxplot is 50%of the data, and the data outside of the interval is 50%of the data.
We must also calculate IQR=3rdquartile -1stquartile as a result of this.
1st quartile =235.5,3rdquartile =396.5, according to the graph.
As a result, the IQR is=396.5-235.5=161.

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Most popular questions from this chapter

In a study collecting data about the repair costs of damage to automobiles in a certain type of crash test, a certain model of car had $1700in damage and was in the 90th percentile. Should the manufacturer and the consumer be pleased or upset by this result? Explain and write a sentence that interprets the 90th percentile in the context of this problem.

Use the following information to answer the next six exercises. Sixty-five randomly selected car salespersons were asked the number of cars they generally sell in one week. Fourteen people answered that they generally sell three cars; nineteen generally sell four cars; twelve generally sell five cars; nine generally sell six cars; eleven generally sell seven cars.

First quartile = _______

Given the following box plot, answer the questions

a. Think of an example (in words) where the data might fit into the above box plot. In 2–5 sentences, write down the example.

b. What does it mean to have the first and second quartiles so close together, while the second to third quartiles are far apart?

Six hundred adult Americans were asked by telephone poll, "What do you think constitutes a middle-class income?" The results are in Table 2.69. Also, include left endpoint, but not the right endpoint.

a. What percentage of the survey answered "not sure"?

b. What percentage think that middle-class is from \(25,000 to \)50,000? c. Construct a histogram of the data.

i. Should all bars have the same width, based on the data? Why or why not?

ii. How should the <20,000 and the 100,000+ intervals be handled? Why? d. Find the 40th and 80th percentiles

e. Construct a bar graph of the data

What does the frequency column in Table 2.42sum to? Why?
See all solutions

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