Sample standard deviation measures the spread of the numbers in the sample, Just type “sample standard deviation” into youtube you will get plenty of examples.

*If all the numbers in the sample are close together then the standard deviation is small if the numbers are far apart the standard deviation is large

*You need to find the sample mean before calculating the sample standard deviation because the sample standard deviation measures how close the numbers in the sample are to the sample mean

You should understand standard deviation by looking at the examples below, The formula are

Sample mean: x̄= 1n∑i=1

nx i

Sample variance:s2=

∑i=1

n(x− x̄ )2

n−1= 1n−1 (∑i=1

nx i

2−n x̄2)= 1n−1 (∑i=1

nx i

2−(∑i=1

nx i )

2

n )Sample standard deviation: s=√s2

Example 1 For the sample 1,7,4The sample size is n=3

The sample mean x=1+7+4

3=4

The sample standard deviation squared method 1 (it does not matter which method you use)

s2=12+72+42−3×42

3−1=1+49+16−3×16

2=66−48

2=18

2=9

The sample standard deviation squared method 2 (it does not matter which method you use)

s2=(1−4 )2+(7−4 )2+( 4−4 )2

3−1=

(−3 )2+32+02

2= 9+9+0

2=18

2=9

So sample standard deviation s= √s2=√9=3

Example 2

What is the sample size n, sample mean x and sample standard deviation s of the sample 3,5,1

Solution n=3, x=3+5+1

3 =3 , s=√(3−3)2+(5−3)2+(1−3 )2

3−1 =2

Example 3

If you have the following sample of observations 306,314,298,290,292 the sample size n=5,

The sample mean x=306+314+298+290+292

5 =300

The standard variance s2=(306−300) 2 +(314−300 )2+(298−300)2+(290−300)2+(292−300 )2

5−1=100

so the sample standard deviation = √100=10