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Chapter 2: Q. 2.153 (page 82)

The Beatles. In the article, "Length of The Beatles" Songs" (Chance, Vol. 25, No, 1, Pp. 30-33), T. Koyama discusses aspects and interpretations of the lengths of songs by The Beatles. Data on the length, in seconds, of 229 Beatles songs are presented on the WeissStats site.

a. use the technology of your choice to identify the modality and symmetry (or non-symmetry) of the distribution of the data set.

b. if unimodal, classify the distribution as symmetric right-skewed. or left-skewed.

Short Answer

Expert verified

a) The distribution is unimodal and non-symmetric.

b) The distribution is right-skewed.

Step by step solution

01

Part (a) Step 1: Given Information

To find the modality and symmetry of the distribution.

02

Part (a) Step 2: Explanation 

The frequency distribution is :

The frequency histogram will have the bars of height equal to frequency.

Unimodal: A single distinct peak or most frequent value characterises a unimodal distribution.

Because there is just one peak in the distribution, it is unimodal.

Because the apex of the distribution is not in the center of the graph, the distribution is generally non-symmetric.

03

Part (b) Step 1: Given Information

To determine the shape of the distribution is right-skewed or left-skewed.

04

Part (b) Step 2: Explanation 

It should be obvious that symmetrical indicates that both sides of anything are identical; asymmetrical means that two faces are different in some way. Asymmetrical items are irregular and crooked, and when folded in half, they do not match up exactly.

The tail of a "skewed right" distribution is on the right side.

The left side of a "skewed left" distribution has the tail.

Here, the graph's peak is to the left of the histogram, the distribution is right-skewed.

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Most popular questions from this chapter

Discuss the relative advantages and disadvantages of stem-and leaf diagrams versus frequency histograms.

Construct a stem-and-leaf diagram for the data, using one line per stem.

A variable of a population has a left-skewed distribution.

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