Question

Given the following data:

0.83	0.88	0.88	1.04	1.09	1.12	1.29	1.31
1.48	1.49	1.59	1.62	1.65	1.71	1.76	1.83

Calculate a point estimate of the mean value and find the (estimated) standard error of the estimator you used.

Answer 1

S.No		X	(X-x̄)	(X-x̄)2
1		0.83	-0.51813	0.2685
2		0.88	-0.46813	0.2191
3		0.88	-0.46813	0.2191
4		1.04	-0.30813	0.0949
5		1.09	-0.25813	0.0666
6		1.12	-0.22813	0.0520
7		1.29	-0.05813	0.0034
8		1.31	-0.03813	0.0015
9		1.48	0.13188	0.0174
10		1.49	0.14188	0.0201
11		1.59	0.24188	0.0585
12		1.62	0.27188	0.0739
13		1.65	0.30188	0.0911
14		1.71	0.36188	0.1310
15		1.76	0.41188	0.1696
16		1.83	0.48188	0.2322
Σx		21.57	Σ(X-x̄)2=	1.719
x̄=Σx/n		1.3481	s2=Σ(x-x̄)2/(n-1)=	0.1146
			s=√s2    =	0.3385

from above:

  point estimate of the mean value =1.3481

and standard error of the estimator =s/√n =0.3385/√16=0.0846