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Variability, with range, standard deviation, and cariance

1. Calculate SS, variance, and standard deviation for the following sample:

4, 7, 3, 1, 5

2. Find the range for the following population of scores:

3, 4, 4, 1, 7, 3, 2, 6, 4, 2
1, 6, 3, 4, 5, 2, 5, 4, 3, 4

3. Construct a frequency distribution table for the following sample data. Calculate the mean, sum of squares, variance, and standard deviation.

28, 24, 22, 23, 30, 30, 29, 27, 28, 28, 25, 30, 28, 29, 27, 26, 26, 24, 30, 26

Solution Preview

1. Calculate SS, variance, and standard deviation for the following sample:

4, 7, 3, 1, 5

Solution:

Sum of the squares (SS) = (4)^2+(7)^2+ (3)^2 +(1)^2 + (5)^2

SS= 16+ 49+9+1+25

SS= 100

We know that the formula for find the variance = Σ x^2/n - ( Σx/n)^2

Where n is the number of data's

Now we have to find Σx = 4+7+3+1+5

Σx = 20

Σ x^2 = (4)^2+(7)^2+ (3)^2 +(1)^2 + (5)^2

Σx^2= 100

Here n= 5

Now, plug in those values in the above formula, we get

Variance = 100/5 - (20/5)^2

= 20 - (4)^2

= 20 - 16

Variance(σ^2) = 4.

Variance denoted by σ^2

Now, we have to find the Standard deviation. ...

Solution Summary

The solution provides a lengthly, detailed explanation regarding variability, and how to find the range, standard deviation, and cariance of multiple questions. The expert provides step-by-step instructions on how to achieve an accurate answer for each question.

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