Question

Compute the standard deviation for the set of data.

2, 4, 6, 8, 10

a.2.83

c.6.32

b.8

d.64

Answer 1

σ =2√2 .....

Explanation:

Lets find the mean first

mean = 2+4+6+8+10/5

m = 30/5

m = 6

σ =√1/5[(2-6)²+(4-6)²+(6-6)²+(8-6)²+(10-6)²]

σ = √1/5[(-4)²+(-2)²+(0)²+(2)²+(4)²]

σ=√1/5[(16+4+0+4+16)]

σ = √1/5(40)

σ = √8

Take the square root of 8.

σ =2√2 .....

Answer 2

a. 2.83

Explanation:

The standard deviation is the square root of the variance. That is, the square root of the mean of the squares of the deviation scores.

Hence, to calculate the standard deviation, we need to know the mean of the data set.

`mean=(2+4+6+8+10)/(5)=(30)/(5)=6`

stdev = standard deviation

`stdev=\sqrt{(2^(2)+4^(2)+6^(2)+8^(2)+10^(2) )/(5)-mean^(2)}=\sqrt{(4+16+36+64+100 )/(5)-6^(2)}=\sqrt{(220 )/(5)-36}=√(44-36)=√(8)=2.83`

Hope this hepls!