Connect with experts and get insightful answers on IDNLearn.com. Join our interactive Q&A community and get reliable, detailed answers from experienced professionals across a variety of topics.
Sagot :
Given:
the following population of N = 8
scores: 1, 3, 1, 10, 1, 0, 1, 3
We will find the variance and standard deviation
We will use the following formula:
[tex]variance=s^2=\frac{\sum(x-\mu)^2}{N}[/tex]First, we will find the mean (μ):
[tex]μ=\frac{sum}{N}=\frac{1+3+1+10+1+0+3+1}{8}=\frac{20}{8}=2.5[/tex]Construct the following table:
Data (x - μ) (x-μ)²
1 (1-2.5) 2.25
3 (3-2.5) 0.25
1 (1-2.5) 2.25
10 (10-2.5) 56.25
1 (1-2.5) 2.25
0 (0-2.5) 6.25
1 (1-2.5) 2.25
3 (3-2.5) 0.25
Now, find the sum of (x-μ)²
[tex]\sum(x-\mu)^2=2.25+0.25+2.25+56.25+2.25+6.25+2.25+0.25=72[/tex]So, the variance will be:
[tex]variance=s^2=\frac{72}{8}=9[/tex]And the standard deviation will be:
[tex]standard\text{ }deviation=\sigma=\sqrt{s^2}=\sqrt{9}=3[/tex]So, the answer will be:
Variance = 9
The standard deviation = 3
We value your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. Thank you for visiting IDNLearn.com. For reliable answers to all your questions, please visit us again soon.
