Q. 2.150 - 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.

96	68	99	97	92	61	105	89
95	71	93	104	85	107	91	97
99	86	102	93	99	64	102	86
101	81	117	87	106	93	106	106

a. Use cutpoint 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 nonsymmetry).

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

Step-by-Step Solution

Answer

Ans:  

(a)  According to Minitab output, it is clear that the heigtht of the bar represents the frequency. 

(b)   According to histogram, it is clear that there is a single high value. therefore the allocation of time is just the same. 

(c)  According to the histogram section (a), it is clear that the distribution is nonsymetric. 

(d)  According to the histogram, it is clear that the distances extend to the tail on the left. It is therefore doomed to the left-skewed. 

Step 1. Given information.

given,

      

96	68	99	97	92	61	105	89
95	71	93	104	85	107	91	97
99	86	102	93	99	64	102	86
101	81	117	87	106	93	106	106

Step 2. (a) Find frequent distribution using cutpoint grouping with first class of 60 - u n d e r   70 s .

Given that the first class is $60 - less than 70$ and the class time range is 10. So, the second category 70 - under 80 and so on. Also, the maximum view is 117. Therefore, the final phase is $110 -under 120$. Therefore, the frequency distribution using cut point grouping is given below:

Cutpoint grouping classes	Frequency
60 -under 70	3
70 -under 80	1
80 -under 90	6
90 -under 100	12
100 -under 110	9
110 -under 120	1
Total	32

Step 3. Use MINITAB to create a given data histogram of time between explosions,

The cutpoint represents the horizontal line across the histogram.

MINITAB process:

Step 1)  Select Graph> Histogram.

Step 2)  Select Easy, then click OK.

Step 3)  For graph variables, enter the corresponding column for TIME.

Step 4)  Click OK.

Step 4. Minitab Output,

According to Minitab output, it is clear that the heigtht of the bar represents the frequency.

Step 5. (b) Identify the shape of the distribution with respect to modality.

According to histogram, it is clear that there is a single high value. therefore the allocation of time is just the same.  

 

Step 6. (c) Identify distribution status with respect to symmetric (or nonsymmetric).

According to the histogram section (a), it is clear that the distribution is nonsymetric.

 

Step 7. (d) Arrange each histogram as a right or left skewed.

According to the histogram, it is clear that the distances extend to the tail on the left. It is therefore doomed to the left-skewed.