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Can someone explain to me what D below is asking? I know how to find the answers to A, B, C and E, but have NO idea what to do for D!

 

Thanks so much for any help or guidance.

 

 

Given the sample data.

x: 16 21 23 30 22

 

Questions:

A. Find the Range

my answer: 14

 

B. Verify that Σx = 112 and Σx2 = 2610

 

C. Use the results of part (b) and appropriate computation formulas to compute the sample variance s2 and sample standard deviation s.

s2: 25.3

s: 5.0

 

D. Use the defining formulas to compute the sample variance s2 and sample standard deviation s.

s2: 

s: 

 

E. Suppose the given data comprise the entire population of all x values. Compute the population variance σ2 and population standard deviation σ.

σ2: 20.2

σ: 4.4

ctyler009  Aug 31, 2017
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How did you calculate c) part?
I believe it's supposed to go like this:

\(DX = EX^2 - (EX)^2 = \frac{1}{5}2610 - (\frac{1}{5}112)^2=20.24\)

 

And for d) you would use formula:

\(\frac{1}{n} \sum_{i=1}^n (X_i - X_m)^2\)

where \(X_m = \frac{1}{n}\sum X_i\)

In your case: \(\frac{1}{5} (6.4^2 + 1.4^2 + 0.6^2 + 7.6^2 + 0.4^2) = 20.24\)

So, same stuff, just using different technique.

 

Cheers. 

Guest Sep 1, 2017

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