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

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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.  Day xˉ Range s121.13.41.2223.44.71.7320.93.10.9425.66.22.3521.34.71.3620.53.71.7725.85.82.1823.76.22.9929.82.10.81022.74.41.61120.02.70.71224.67.83.0\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}


Definitions:

Client-Centred

A therapeutic approach emphasizing the importance of understanding and valuing the client's perspective and feelings in the counseling process.

Economic Pressures

Financial stressors and constraints faced by individuals, families, communities, or countries, often leading to varied psychological and social outcomes.

Group Therapy

A form of psychotherapy that involves one or more therapists working with several people at the same time.

Mental Health

Refers to cognitive, behavioral, and emotional wellbeing; how individuals think, feel, and behave.

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