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Chapter 2: Q. 2.15 (page 82)

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.

a. Use cut point grouping with a first class of 60-under 70to 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 non-symmetry).

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

Short Answer

Expert verified

(b) The modality is unimodal

(c) The distribution is non-symmetric.

(d) The distribution has been left-skewed.

(a)

Step by step solution

01

Part (a) Step 1: Given information

The given data is

02

Part (a) Step 2: Explanation

As shown below, the frequency is the number of values that fall within the class

The frequency histogram will now contain bars of the same height as the frequency, thus

03

Part (b) Step 1: Given information

The given data is

04

Part (b) Step 2: Explanation

The distribution in terms of modality is unimodal since it has only one peak.

05

Part (c) Step 1: Given information

The given data is

06

Part (c) Step 2: Explanation

Because the peak of the distribution is not roughly in the middle, the symmetry of the distribution is non-symmetric.

07

Part (d) Step 1: Given information

The given data is

08

Part (d) Step 2: Explanation

Because the graph's peak is to the right, the distribution has been left skewed.

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Most popular questions from this chapter

Some users of statistics prefer pie charts to bar charts because people are accustomed to having the horizontal axis of a graph show order. For example, someone "Republican" is less than "Other" because "Republican" is shown to the left of "Other" on the horizontal axis. Pie charts do not lead to such inferences. Give other advantages and disadvantages of each method.

Forearm Length. In 1903, K. Pearson and A. Lee published the paper "On the Laws of Inheritance in Man. I. Inheritance of Physical Characters" (Biometrika, Vol. 2, pp. 357-462). The article examined and presented data on forearm length, in inches, for a sample of 140 men, which we present on the Weiss Stats 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.

Sample distribution.

Weights of 18- to 24-Year-Old Males. Refer to the weight data in Table 2.8on page 54 . Note that there are 37 observations, the smallest and largest of which are 129.2and278.8, respectively. Apply the preceding procedure to choose classes for cut point grouping. Use approximately eight classes. Note: If in Step 2 you decide on 20 for the class width and in Step 3 you choose 120 for the lower cut point of the first class, then you will get the same classes as used in Example 2.14; otherwise, you will get different classes (which is fine).

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