Describing Data

Question

Calculate standard deviation for the following population of scores: 11, 0, 2, 9, 9, 5

Standard deviation=

Answer 1

Hi Tra'von,

Given that this is a population, not a sample, formula is:

sd=sqrt[sum(x_i-mu)²/n]

x_i=Each individual x-value.

mu=mean

n=sample size

mu=(11+0+2+9+9+5)/6

mu=6

n=6

Now, we need sum(x_i-mu)² So:

(11-6)² + (0-6)² + (2-6)² + (9-6)² + (9-6)² + (5-6)² =96

But recall:

sd=sqrt[sum(x_i-mu)²/n]

We now know sum(x_i-mu)² and n, so:

sd= sqrt(96/6)

sd=sqrt(16)

sd=4

Ultimately, you will likely use calculators or software to compute standard deviation, as the computation can get cumbersome when we have ten or more data points. I hope this helps.

Answer 2

Population Standard Deviation, σ: 4

Count, N:	6
Sum, Σx:	36
Mean, μ:	6
Variance, σ2:	16

Steps

σ2 =	(1/N)*Σ(xi - μ)2
= (11 - 6)2 + ... + (5 - 6)2
Then divide the above sum by 6.
= 96/6
= 16
σ =	√16
=	4