Suppose the value of Young's modulus (GPa) was determined for cast plates consisting of certain intermetallic substrates, resulting in the following sample observations. 116.6 115.5 114.7 115.2 115.9 (a) Calculate × (in GPa). GPa Calculate the deviations from the mean. 116.6 115.5 114.7 115.2 115.9 deviation (b) Use the deviations calculated in part (a) to obtain the sample variance (in GPa?). s2 = |GP22 Use the deviations calculated in part (a) to obtain the sample standard deviation (in GPa). (Round your answer to three decimal places.) S = GPa (c) Calculate s² (in GPA²) by using the computational formula for the numerator S GPa? (d) Subtract 100 from each observation to obtain a sample of transformed values. Now calculate the sample variance (in GPa) of these transformed values. GPa?

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### Young's Modulus Data Analysis

Suppose the value of Young's modulus (GPa) was determined for cast plates consisting of certain intermetallic substrates, resulting in the following sample observations:

**Sample Observations (GPa):**  
116.6, 115.5, 114.7, 115.2, 115.9

#### (a) Mean Calculation

Calculate the mean \(\bar{x}\) (in GPa).  
____ GPa

Calculate the deviations from the mean.

| \(x\)    | 116.6 | 115.5 | 114.7 | 115.2 | 115.9 |
|----------|-------|-------|-------|-------|-------|
| deviation|       |       |       |       |       |

#### (b) Variance and Standard Deviation

Use the deviations calculated in part (a) to obtain the sample variance (in GPa²).

\(s^2 =\) ____ GPa²

Use the deviations calculated in part (a) to obtain the sample standard deviation (in GPa). (Round your answer to three decimal places.)

\(s =\) ____ GPa

#### (c) Computational Formula

Calculate \(s^2\) (in GPa²) by using the computational formula for the numerator \(S_{xx}\).

____ GPa²

#### (d) Transformed Variance Calculation

Subtract 100 from each observation to obtain a sample of transformed values. Now calculate the sample variance (in GPa²) of these transformed values.

____ GPa²
Transcribed Image Text:### Young's Modulus Data Analysis Suppose the value of Young's modulus (GPa) was determined for cast plates consisting of certain intermetallic substrates, resulting in the following sample observations: **Sample Observations (GPa):** 116.6, 115.5, 114.7, 115.2, 115.9 #### (a) Mean Calculation Calculate the mean \(\bar{x}\) (in GPa). ____ GPa Calculate the deviations from the mean. | \(x\) | 116.6 | 115.5 | 114.7 | 115.2 | 115.9 | |----------|-------|-------|-------|-------|-------| | deviation| | | | | | #### (b) Variance and Standard Deviation Use the deviations calculated in part (a) to obtain the sample variance (in GPa²). \(s^2 =\) ____ GPa² Use the deviations calculated in part (a) to obtain the sample standard deviation (in GPa). (Round your answer to three decimal places.) \(s =\) ____ GPa #### (c) Computational Formula Calculate \(s^2\) (in GPa²) by using the computational formula for the numerator \(S_{xx}\). ____ GPa² #### (d) Transformed Variance Calculation Subtract 100 from each observation to obtain a sample of transformed values. Now calculate the sample variance (in GPa²) of these transformed values. ____ GPa²
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