Chapter 3, Problem 11CRP

In west Texas, water is extremely important. The follow mg data represent pH levels in groundwater for a random sample of 102 west Texas wells. A pH less than 7 is acidic and a pH above 7 is alkaline. Scanning the data, you can see that water in this region tends to be hard (alkaline). Too high a pH means the water is unusable or needs expensive treatment to make it usable (Reference: C. E. Nichols and V. E. Kane. Union Carbide Technical Report K/UR-1).

x: pH of Ground Water in 102 West Texas Wells

7.0	7.0	7.0	7.0	7.0	7.0	7.0	7.0	7.1	7.1	7.1	7.1
7.1	7.1	7.1	7.1	7.1	7.1	7.2	7.2	7.2	7.2	7.2	7.2
7.2	7.2	7.2	7.2	7.3	7.3	7.3	7.3	7.3	7.3	7.3	7.3
7.3	7.3	7.3	7.4	7.4	7.4	7.4	7.4	7.4	7.4	7.4	7.4
7.5	7.5	15	7.5	7.5	7.5	7.5	15	7.6	7.6	7.6	7.6
7.6	7.6	7.6	7.6	7.6	7.7	7.7	7.7	7.7	7.7	7.7	7.8
7.8	7.8	7.8	7.8	7.9	7.9	7.9	7.9	7.9	8.0	8.1	8.1
8.1	8.1	8.1	8.1	8.1	8.2	8.2	8.2	8.2	8.2	8.2	8.2
8.4	8.5	8.6	8.7	8.8	8.8

(a) Verily that $\Sigma x=772.9\text{ and }\Sigma x^{2}5876.6$.

(b) Compute the sample variance, sample standard deviation, and coefficient of variation for the given data. Is the sample standard deviation small relative to the mean pH?

These data are also available for download at the Companion Sites for this text. For convenience, the data are presented in increasing order.