Question 5.63

33. How much oil the wells in a given field will ultimately produce is key information in deciding whether to drill more wells. Below are the estimated total amounts of oil recovered from 64 wells in the Devonian Richmond Dolomite area of the Michigan basin, in thousands of barrels. [Source: J. Marcus Jobe and Hutch Jobe, A statistical approach for additional infill development, Energy Exploration and Exploitation, 18 (2000): 89-103.]

2.0 18.5 34.6 47.6 69.5
2.5 20.1 34.6 49.4 69.8
3.0 21.3 35.1 50.4 79.5
7.1 21.7 36.6 51.9 81.1
10.1 24.9 37.0 53.2 82.2
10.3 26.9 37.7 54.2 92.2
12.0 28.3 37.9 56.4 97.7
12.1 29.1 38.6 57.4 103.1
12.9 30.5 42.7 58.8 118.2
14.7 31.4 43.4 61.4 156.5
14.8 32.5 44.5 63.1 196.0
17.6 32.9 44.9 64.9 204.9
18.0 33.7 46.4 65.6

233

  1. Make a histogram and describe its main features.
  2. Find the mean and median of the amounts recovered. Explain how the relationship between the mean and the median reflects the shape of the distribution.
  3. Give the five-number summary and explain briefly how it reflects the shape of the distribution.

33.

(a) The histogram below shows the distribution to be unimodal and right-skewed. There are some potential outliers. (Histograms can vary depending on the choice of class width.)

image

(b) , ; the long right tail inflates the mean.

(c) The five-number summary is 2.0, 21.5, 37.8, 60.1, 204.9. (Note: Results for and may differ if calculated using computer software.) and the maximum are much farther above the median than and the minimum are below it, showing that the right side of the distribution has more variability than the left side.