Question

Consider the accompanying data on flexural strength (MPa) for concrete beams of a certain type.

11.8	6.3	7.1	9.7	6.5	8.1	6.8
8.7	6.8	7.0	7.8	7.4	10.7	9.0
7.7	5.4	6.3	7.9	7.7	7.0	8.7
7.3	11.6	11.3	7.2	8.2	9.7

a.)Calculate a point estimate of the population standard deviation σ. [Hint: Σx_i² = 1862.79.]

b.)Calculate a point estimate of the population coefficient of variation σ/μ.

Answer 1

a. To find standard deviation we need to first find mean

Create the following table.

data	data-mean	(data - mean)2
11.8	3.663	13.417569
6.3	-1.837	3.374569
7.1	-1.037	1.075369
9.7	1.563	2.442969
6.5	-1.637	2.679769
8.1	-0.037	0.001369
6.8	-1.337	1.787569
8.7	0.563	0.316969
6.8	-1.337	1.787569
7.0	-1.137	1.292769
7.8	-0.337	0.113569
7.4	-0.737	0.543169
10.7	2.563	6.568969
9.0	0.863	0.744769
7.7	-0.437	0.190969
5.4	-2.737	7.491169
6.3	-1.837	3.374569
7.9	-0.237	0.056169
7.7	-0.437	0.190969
7.0	-1.137	1.292769
8.7	0.563	0.316969
7.3	-0.837	0.700569
11.6	3.463	11.992369
11.3	3.163	10.004569
7.2	-0.937	0.877969
8.2	0.063	0.003969
9.7	1.563	2.442969

So

b. Point estimate of coefficient of variation is