# 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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