# SOLUTION: ILS 4430 Johnson and Wales Symmetry & Non Symmetric Data Set Questions

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Symmetry Paper (Non-Symmetric Data Set)

Section I: Histogram of Non-Symmetric Data Set

μ = 26.66086957

σ = 17.37556611

Section II: Calculations for Non-Symmetric Data Set

Mean of Data Set: μ = 26.7

Standard Deviation of Data Set: σ = 17.4

Calculated Mean of Sample Means (samples of bulk 10, 30, 100): μx̅ = μ = 26.7

σ

Calculated Standard Deviation of Sample Means (samples of bulk 10): σx̅ =

√n

Calculated Standard Deviation of Sample Means (samples of bulk 30): σx̅ =

√n

σ

Calculated Standard Deviation of Sample Means (samples of bulk 100): σx̅ =

=

=

σ

√n

𝟏𝟕.𝟒

√10

𝟏𝟕.𝟒

√30

=

= 5.5

= 3.2

𝟏𝟕.𝟒

√100

= 1.7

Section III: Histograms of Sample Means and Actual and Calculated

Statistics of Sample Means for Non-Symmetric Data Set

Histogram of Sample Means for Samples of Bulk 10:

Actual Statistics

μx̅ = 24.9

σx̅ = 4.6

Calculated Statistics

μx̅ = 26.7

σx̅ = 5.5

Histogram of Sample Means for Samples of Bulk 30:

Actual Statistics

μx̅ = 25.7

σx̅ = 3.3

Calculated Statistics

μx̅ = 26.7

σx̅ = 3.2

Histogram of Sample Means for Samples of Bulk 100:

Actual Statistics

μx̅ = 26.1

σx̅ = 0.8

Calculated Statistics

μx̅ = 26.7

σx̅ = 1.7

S...

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