Mean and Standard Deviation
The mean, indicated by μ (a lower case Greek mu), is the statistician's jargon for the average value of a signal. It is found just as you would expect: add all of the samples together, and divide by N. It looks like this in mathematical form:

In words, sum the values in the signal, xi, by letting the index, i, run from 0 to N-1. Then finish the calculation by dividing the sum by N. This is identical to the equation: μ =(x0 + x1 + x2 + ... + xN-1)/N. If you are not already familiar with Σ (upper case Greek sigma) being used to indicate summation, study these equations carefully, and compare them with the computer program in Table 2-1. Summations of this type are abundant in DSP, and you need to understand this notation fully. In electronics, the mean is commonly called the DC (direct current) value. Likewise, AC (alternating current) refers to how the signal fluctuates around the mean value. If the signal is a simple repetitive waveform, such as a sine or square wave, its excursions can be described by its peak-to-peak amplitude. Unfortunately, most acquired signals do not show a well defined peak-to-peak value, but have a random nature, such as the signals in Fig. 2-1. A more generalized method must be used in these cases, called the standard deviation, denoted by σ (a lower case Greek sigma). As a starting point, the expression,|xi-μ|, describes how far the ith sample deviates (differs) from the mean. The average deviation of a signal is found by summing the deviations of all the individual samples, and then dividing by the number of samples, N. Notice that we take the absolute value of each deviation before the summation; otherwise the positive and negative terms would average to zero. The average deviation provides a single number representing the typical distance that the samples are from the mean. While convenient and straightforward, the average deviation is almost never used in statistics. This is because it doesn't fit well...

...I'll be honest. Standarddeviation is a more difficult concept than the others we've covered. And unless you are writing for a specialized, professional audience, you'll probably never use the words "standarddeviation" in a story. But that doesn't mean you should ignore this concept.
The standarddeviation is kind of the "mean of the mean," and often can help you...

...StandardDeviation (continued)
L.O.: To find the mean and standarddeviation from a frequency table.
The formula for the standarddeviation of a set of data is [pic]
Recap question
A sample of 60 matchboxes gave the following results for the variable x (the number of matches in a box):
[pic].
Calculate the mean and standarddeviation for...

...StandardDeviation
objective
• Describe standarddeviation and
it’s importance in biostatistics.
Measure of Dispersion
• Indicates how widely the scores
are dispersed around the central
point (or mean.)
-StandarddeviationStandardDeviation.
• The most commonly used method
of dispersion in oral hygiene.
• The larger the standard...

...is the impact of the new point on the standarddeviation?
The new point has made the standarddeviation to go up to over 2.07
b) Follow the instructions to create the next two graphs then answer the following question: What did you do differently to create the data set with the larger standarddeviation.
What I did differently was to have two outliners on both ends of the outline so I can create...

...selected.
c) reasonably large due to the “cluster” effect.
d) 100 divided by the size of the population of Laramie.
Costs for standard veterinary services at a local animal hospital follow a Normal distribution with a mean of $80 and a standarddeviation of $20. Answer the next three questions.
8. Give the sample space for the costs of standard veterinary services.
a) {X ≥ 0}
b) { 0 ≤ X ≤ 80}
c)...

...Standarddeviation can be difficult to interpret as a single number on its own. Basically, a small standarddeviationmeans that the values in a statistical data set are close to the mean of the data set, on average, and a large standarddeviationmeans that the values in the data set are farther away from the mean, on average.
The standard...

...has a mean equal to 3.9 milligrams of tar per cigarette and a standarddeviation equal to 1.0 milligram. Suppose a sample of 100 low-tar cigarettes is randomly selected from a day’s production and the tar content is measured in each. Assuming that the tobacco company’s claim is true, what is the probability that the mean tar content of the sample is greater than 4.15 milligrams?
[0.00621]
2. The safety limit of a crane is...

...Deviation
Definition:
Behavior commonly seen in children that is the result of some obstacle to normal development such behavior may be commonly understand as negative (a timid child, a destructive child) or positive (a quite child), both positive and negative deviation will disappear once the child begins to concentrate on a piece of work freely chosen by him.
The physical deforms are easier to identify. This can be by birth due to an accident...

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