An X Chart Based on Standard Deviations (Instead of Ranges)

question 19

Essay

An x chart based on standard deviations (instead of ranges) is made by plotting sample means with a centerline
at x and control limits at x + A3 s and x - A3 s where A3 is found in the Control Chart Constants table and s is
the mean of the sample standard deviations. Construct an x chart based on standard deviations for the data
below.
A manufacturer of high intensity video projector lightbulbs picks 6 lightbulbs at random each day for quality
control. The mean, standard deviation, and range (in hours) of the lifetimes of the 6 lightbulbs are calculated.
The results for 12 consecutive days are shown in the table below. $$\begin{array} { c | c | c | c } \text { Day } & \bar { x } & \text { Range } & \mathrm { s } \\\hline 1 & 21.1 & 3.4 & 1.2 \\2 & 23.4 & 4.7 & 1.7 \\3 & 20.9 & 3.1 & 0.9 \\4 & 25.6 & 6.2 & 2.3 \\5 & 21.3 & 4.7 & 1.3 \\6 & 20.5 & 3.7 & 1.7 \\7 & 25.8 & 5.8 & 2.1 \\8 & 23.7 & 6.2 & 2.9 \\9 & 29.8 & 2.1 & 0.8 \\10 & 22.7 & 4.4 & 1.6 \\11 & 20.0 & 2.7 & 0.7 \\12 & 24.6 & 7.8 & 3.0\end{array}$$

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Definitions:

Correlation

A statistical measure that indicates the extent to which two or more variables fluctuate together, showing the strength and direction of a relationship.

+.86

This could represent a statistical value, such as a correlation coefficient, indicating a strong positive relationship between two variables.

Discriminant Validity

A measure of the extent to which a construct is truly distinct from other constructs by demonstrating low correlations with measures of unrelated constructs.

Depression

A psychiatric condition marked by a constant state of low mood or a lack of enjoyment in activities, which considerably disrupts daily functioning.