Five Samples of Size 4 Were Taken from a Process $\bar{x}$

question 50

Multiple Choice

Five samples of size 4 were taken from a process. A range chart was developed that had LCLR = 0 and UCLR = 2.50. Similarly, an average chart was developed with the average range from the five samples, with LCL $\bar{x}$ = 15.0 and LCL $\bar{x}$ = 24.0. The ranges for each of the five samples were 1.75, 2.42, 2.75, 2.04, and 2.80, respectively. The values of the sample average for each sample were 19.5, 22.3, 17.4, 20.1, and 18.9, respectively. What can you tell management from this analysis?

• A) The process variability is out of control, and we cannot make a statement about the process average.
• B) The process variability is out of control, but the process average is in control.
• C) The process variability and the process average are out of control.
• D) We cannot tell if the process variability or the process average is out of control.

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Definitions:

Real Rate

The interest rate adjusted for inflation, reflecting the true return on an investment over time.

Dividend

A portion of a company's earnings that is distributed to shareholders, usually in the form of cash payments or additional shares.

Geometric Average

A method of calculating the average rate of return that accounts for compounding by taking the nth root (where n is the count of numbers) of the product of the values.

Arithmetic Average

A simple mean calculated by adding a set of numbers and dividing the sum by the count of those numbers, used to determine central tendencies.