Q. 2.15 - Elementary Statistics

Question

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 $70$ 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 non-symmetry).

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

Step-by-Step Solution

Answer

(b) The modality is unimodal 

(c) The distribution is non-symmetric. 

(d) The distribution has been left-skewed.

(a) 

Part (a) Step 1: Given information

The given data is 

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

Part (b) Step 1: Given information

The given data is 

Part (b) Step 2: Explanation

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

Part (c) Step 1: Given information

The given data is 

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.

Part (d) Step 1: Given information

The given data is 

Part (d) Step 2: Explanation

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