Question

Calculate the sample standard deviation of the data set below and what does the number describe about the data set.

4，5，6，20，4，34，34

Answer 1

S.No		X	(X-x̄)	(X-x̄)2
1		4	-11.29	127.367
2		5	-10.29	105.796
3		6	-9.29	86.224
4		20	4.71	22.224
5		4	-11.29	127.367
6		34	18.71	350.224
7		34	18.71	350.224
Σx		107	Σ(X-x̄)2=	1169.4286
x̄=Σx/n		15.29	s2=Σ(x-x̄)2/(n-1)=	194.9048
			s=√s2    =	13.9608

sample standard deviation =13.9608

this indicate that a random data value deviate from the mean by 13.9608 on average.