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—the mean or the median—best describes the surface roughness of the sampled pipe sections? Explain.

$$\begin{gathered} Mean=\frac{Sumofallobservations}{Numberofobservations} \\ =\frac{\left(1.72+2.50+2.16+2.13+1.06+2.24+2.31+ \\ 2.03+1.09+1.40+2.57+2.64+1.26+2.05+ \\ 1.19+2.13+1.27+1.51+2.41+1.95\right)}{20} \\ =\frac{37.62}{20} \\ =1.881 \end{gathered}$$

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

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,

$$\begin{gathered} Median=\frac{Sumoftwovaluesinthecentre}{2} \\ =\frac{1.95+2.03}{2} \\ =\frac{3.98}{2} \\ =1.99 \end{gathered}$$

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.

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.