Q46E Surface roughness of oil field p... [FREE SOLUTION]

91影视

Statistics For Business And Economics

James T. McClave, P. George Benson, Terry Sincich

$Math Studyset 91影视 Explanations$ Math

13th Edition 路 888 pages

ISBN: 9780134506593

Chapter 2: Q46E (page 96)

Surface roughness of oil field pipe.Oil field pipes are internally coated to prevent corrosion. Researchers at the University of Louisiana, Lafayette, investigated the influence that coating may have on the surface roughness of oil field pipes (Anti-corrosion Methods and Materials, Vol. 50, 2003). A scanning probe instrument was used to measure the surface roughness of each in a sample of 20 sections of coated interior pipe. The data (in micrometers) are provided in the table.
(1.72, 2.50, 2.16, 2.13, 1.06, 2.24, 2.3,1 2.03, 1.09, 1.40, 2.57, 2.64, 1.26, 2.05, 1.19, 2.13, 1.27, 1.51, 2.41, 1.95)
a.Find and interpret the mean of the sample.
b.Find and interpret the median of the sample.
c.Which measure of central tendency鈥攖he mean or the median鈥攂est describes the surface roughness of the sampled pipe sections? Explain.

Short Answer

Expert verified

a) Mean = 1.881

b) Median = 1.99

c) Mean

Step by step solution

Finding and Interpreting the Mean

$M e a n = \frac{S u m o f a l l o b s e r v a t i o n s}{N u m b e r o f o b s e r v a t i o n s} = \frac{(1.72 + 2.50 + 2.16 + 2.13 + 1.06 + 2.24 + 2.31 + 2.03 + 1.09 + 1.40 + 2.57 + 2.64 + 1.26 + 2.05 + 1.19 + 2.13 + 1.27 + 1.51 + 2.41 + 1.95)}{20} = \frac{37.62}{20} = 1.881$

The mean is 1.881. It indicates that, on average, the roughness of the pipes is around 1.881 micrometers.

Calculating and Understanding the Median

To calculate the median we will first arrange the data in ascending order,
(1.06, 1.09, 1.19, 1.26, 1.27, 1.40, 1.51, 1.64, 1.72, 1.95, 2.03, 2.05, 2.13, 2.16, 2.24, 2.31, 2.41, 2.50, 2.57, 2.64)

Now, as the sample size is even,

$M e d i a n = \frac{S u m o f t w o v a l u e s i n t h e c e n t r e}{2} = \frac{1.95 + 2.03}{2} = \frac{3.98}{2} = 1.99$

Therefore, the median is 1.99 micrometer, the roughness of 10 pipes is less than 1.99, and the roughness of the other 10 pipes is more than 1.99.

Determining the best measure of central tendency

Mean is the better measure of the central tendency to describe the surface roughness of pipes because it takes into consideration the roughness of all the pipes. Whereas the median only takes into consideration the middle values of the data set.