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1. Describe how the mean, mode, median, standard deviation and range work together to
describe the data presented in a histogram format.
A histogram groups data according to a range of values, rather than by the number of time each
value occurs. The range is the difference between the highest and lowest numbers that are
represented in a series of values. When constructing a histogram, the range is calculated by
subtracting the lowest observed value from the highest observed value. The mean is the
determined by adding up all of the values and then dividing the sum by the total number of
values. I could add all of the data collected for a histogram to determine the average number of
items or occurrences that took place. The median is the value that divides a series of numbers
so that there’s an equal amount of values on either side of the center. The mode is the value that
is repeated most often, which will be reflected as the highest peak on a histogram. Standard
deviation further describes the data presented in a histogram by describing how the individual
values fall in relation to their averages, and provides a more accurate level of information.
2. What is meant by the phrase: measures of dispersion
Measures of dispersion refer to the various ways that are used to measure how spread out a set
of data is by where they fall in relation to each other and to the mean (the average of the sum of
all the values). Since measures of dispersion help to describe where the data is dispersed on
either side of a central value, they help to create a more complete picture of distribution. Two
diverse samples may have the same mean or median, but completely different levels of
variability, or vice versa. Range, standard deviation, skewness and kurtosis are all examples of
ways to measure and describe dispersion.
3. What is meant by the phrase: the central tendency of the data?
The central tendency of the data are statistical values that define the center of distribution. The
three most common measures of central tendency are the mean, median and mode. Mean (or
average) is the sum of the numbers divided by the number of numbers in a set of data and is
probably the most commonly used measure of central tendency. Median is the number present in
the middle when the numbers in a set of data are arranged in ascending or descending order.
Mode is the value that occurs most frequently in a set of data.
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4. Why is statistical process control interested in reducing the variation present in the
process?
Statistical process control is interested in reducing the variation present in processes because
variations cause inefficiencies, which can lead to waste, decreased profits and productivity and
unsatisfied customers. Variations in processes are studied by sampling in order to determine if
the variations are due to chance, or common causes or if they’re due to assignable causes.
Chance causes are small random changes in the process that can’t be avoided. This type of
variation is stable and predictable. Assignable causes are variations in the process that can be
identified as having a specific cause and are not part of the process on a regular basis. This type
of variation is unstable and unpredictable and may be caused by circumstances outside of the
process. It’s important to know which you’re dealing with in order to know how to approach it. If
it’s a chance cause, you would have to change the whole system in order to address the
inefficiencies. If it’s an assignable cause, you have to identify the cause(s), and resolve them in
order to address the inefficiencies.
5. Though only seven averages and range values are available, the engineers studying the
bottle filling process have decided to create X-bar and R charts for the samples measuring
the air gap in the bottle.
Calculate the center line and control limits for the following information:
Sum of X-bars = 339.4
Sum of R's = 3.4
m=7
n=5
Step 1: Define the problem – Too much or too little of an air gap in the bottles
Step 2: Select the quality characteristic to be measured – The air gap
Step 3: Choose a rational subgroup to be measured – Keep the subgroup size the same for each
subgroup taken
Step 4: Collect the data – Must be sufficient to accurately reflect the statistical control of the
process
Step 5: Determine the trial centerline for the X chart – The process average
Step 6: Determine the trial control limits for the X chart – The control limits will be symmetrical
about the center line
Step 7: Determine the trial control limits for the R chart – The control limits will be symmetrical
about the center line
Step 8: Examine the process; control chart interpretation – Is it a trend that that must be dealt
with or a random variation natural to the process?
Step 9: Revise the chart – Existing calculations can be revised if a chart exhibits good control and
any changes made to improve the process are permanent and if patterns exist, provided that the
patterns have been identified and eliminated
Step 10: Achieve the purpose – Was there a decrease in variation inherent in the process over
time?
6. Why is it critical to utilize your understanding of measures of dispersion when interpreting
control charts?
The correct interpretation of the measures of dispersion are crucial to understanding what the
data is telling you and how you’re going to use that information to make improvements. As stated
in the answer to #2, two diverse samples may have the same mean or median, but completely
different levels of variability, or vice versa. Knowing and understating what the root causes are
for those variances and knowing what kinds of adjustments to make will allow for better planning,
better quality, enhanced customer satisfaction and an overall increase in profitability.
7. Why is the use and interpretation of the R chart so critical when examining an X-bar chart?
What does the X-bar chart show? What does the R chart show?
An X-bar chart is used to monitor the variation of the subgroup averages that are calculated from
the individual sampled data. It shows the average values that indicate change rather than
individual values, which would take longer to compile and analyze. An R chart is a control chart
in which the subject group is used to evaluate the stability of the variability within a process. X
and R charts are used together to show both the mean value and the range. The X portion of the
chart shows any changes in the mean value of the process, while the R portion shows any
changes in the dispersion of the process. This chart is a very useful tool for management in that it
shows changes in mean value and dispersion of the process at the same time, which allows for
quick detection and correction of problem areas within the process.
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