The minimum injection pressure (psi) for injection molding specimens of high amy

Question

The minimum injection pressure (psi) for injection molding specimens of high amylose corn was determined for eight different specimens (higher pressure corresponds to greater processing difficulty), resulting in the following observations. 14.5 12.9 18.0 14.0 12.0 10.9 9.2 8.2 (a) Determine the values of the sample mean x, sample median x, and 12.5% trimmed mean Xtr. (Round your answers to two decimal places.) psi psi psi Xtr Compare these values. O The mean is much larger than the median and trimmed mean, indicating positive skewness. O The median is much larger than the mean and trimmed mean, indicating negative skewness O All three measures of center are similar, indicating little skewness to the data set O The mean is much larger than the median and trimmed mean, indicating negative skewness The median is much larger than the mean and trimmed mean, indicating positive skewness. (b) By how much could the smallest sample observation, currently 8.2, be increased without affecting the value of the sample median? psi (c) Suppose we want the values of the sample mean and median when the observations are expressed in kilograms per square inch (ksi) rather than psi. Is it necessary to reexpress each observation in ksi, or can the values calculated in part (a) be used directly? [Hint: 1 kg 2.2 lb.] O Yes, it is necessary to reexpress each observation. No, the values obtained in part (a) can be used directly.

Explanation / Answer

Sample Mean = 12.4625 ( Sum/8)

Sample median = (12+12.9)/2=12.45

Trimmed Mean = (Sum of middle 6)/6= 12.25

All three measures are similar, indicating little skewness

8.2 can be increased uptil 12 without affecting the value of median or by (12-8.2)=3.8

No, the values can be used directly.

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