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# Variability - ANOVA - Mean Sum

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1. Variability in a dataset may be caused by various sources. Provide an example sample dataset where are more than one sources causing its variability. Explain briefly?with one or two lines explanations of those sources. Also, calculate the sample variance for the example data set that you have provided.

2. Organize the sample data you have presented in DQ 1 into groups according to the levels of one source of (or cause of variation) variation. Now compute the Mean Sum of Square Between and Mean Sum of Square Within. How do you characterize the Mean Sum of Square Between in your example? Is it too large, why or why not?

3. While doing and ANOVA you found the following:

The Mean Sum of Square Between (MSSB) = 2.76 with df 5 and the Mean Sum of square Within (MSSW)= 10.89 with df 11. What conclusion can you draw regarding the null hypothesis of the equality of the means?

Note: The test statistic in this case, F = MSSB/MSSW with numerator df = 5 and the denominator df = 11.

https://brainmass.com/statistics/analysis-of-variance/variability-anova-mean-sum-214536

#### Solution Preview

1. Variability in a dataset may be caused by various sources. Provide an example sample dataset where are more than one sources causing its variability. Explain briefly—with one or two lines explanations of those sources. Also, calculate the sample variance for the example data set that you have provided.

Variability could be a result of 2 factors. For example, there are three ways of drying green concrete (say A, B, and C), and you want to find the one that gives you the best compressive strength. The concrete is mixed in batches that are large enough to produce exactly three cylinders. However, your production engineer believes that ...

#### Solution Summary

Variability, ANOVA, and Mean Sum are analyzed.

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