The minimum injection pressure psi for injection molding spe

The minimum injection pressure (psi) for injection molding specimens of high amylose corn was determined for eight different specimens (higher pressure corresponds to greaten processing difficulty), resulting in the following observations. 14.9 13.0 17.7 14.4 12.1 11.0 9.1 8.5 (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.) Compare these values. All three measures of center are similar, indicating little skewness to the data set. The median is much larger than the mean and trimmed mean, indicating positive skewness. 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 negative skewness. The mean is much larger than the median and trimmed mean, indicating positive skewness. (b) By how much could the smallest sample observation, currently 8.5, be increased without affecting the value of the sample median? (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 Re express each observation in ksi, or can the values calculated in part (a) be used directly? [Hint: 1 kg = 2.2 lb.] Yes, it is necessary to re express each observation. No, the values obtained in part (a) can be used directly.

Solution

Ordering them,

8.5
9.1
11
12.1
13
14.4
14.9
17.7

As

Mean = Sum(x) / n

then

Mean = 12.5875 = 12.59 [answer]

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The median is the average of the 2 middle terms, 12.1 and 13. Thus,

Median = 12.55 [answer]

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As 12.5% of 8 = 1, then we trim the 1 lowest and 1 highest terms.

Thus, we are left with

9.1
11
12.1
13
14.4
14.9

Taking the mean of these,

Trimmed mean = 12.41666667 = 12.42 [answer]

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As we see, they are similar. Thus, we choose

OPTION A: All three measures of center are similar, indicating little skewness to the data set. [answer]

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