how do I get the Sample Standard Deviation of 167, 211, 187, 176, 170, 158, 198, 218, 145, 232

Question

How do I find the Sample Standard Deviation of 167, 211, 187, 176, 170, 158, 198, 218, 145, 232,

Answer 1

First, we find the mean, which is the sum of all the data divided by the amount of data:

1862/10=186.2.

Next we find the sample variance, which is the sum of the squares of the differences between each datum and the mean m, 186.2.

X	X-m	(X-m)^2
167	-19.2	368.64
211	24.8	615.04
187	0.8	0.64
176	-10.2	104.04
170	-16.2	262.44
158	-28.2	795.24
198	11.8	139.24
218	31.8	1011.24
145	-41.2	1697.44
232	45.8	2097.64
	TOTAL:	7091.20

Next, we divide the total by 9 (1 less than the amount of data)=787.92 approx. The standard deviation is the square root of the variance=28.07 approx. So the sample standard deviation is 28.07.