The standard deviation is a popular measure of variability. It is used both as a separate entity and as a part of other analyses, such as computing confidence intervals and in hypothesis testing. The standard deviation is the square root of the variance. The population standard devia¬tion is denoted by σ. Like the variance, the standard deviation utilizes the sum of the squared deviations about the mean (SSx). It is computed by averaging these squared deviations (SSX/N) and taking the square root of that average. One feature of the standard deviation that distin¬guishes it from a variance is that the standard deviation is expressed in the same units as the raw data, whereas the variance is expressed in those units squared. The meaning of standard deviation is more readily understood from its use. Although the standard deviation and the variance are closely related and can be computed from each other, differentiating between them is important, because both are widely used in statistics. What is a standard deviation? What does it do, and what does it mean? The most precise way to define standard deviation is by reciting the formula used to compute it. However, insight into the concept of standard deviation can be gleaned by viewing the manner in which it is applied. Two ways of applying the standard deviation are the empirical rule and Chebyshev’s theorem.

•The empirical rule is an important rule of thumb that is used to state r/.v approximate per-centage of values that lie within a given number of standard deviations from the mean of a set of data if the data are normally distributed. The empirical rule is used only for three numbers of standard deviations: 1σ, 2σ, and 3σ.

•The empirical rule applies only when data are known to be approximately normally distributed. What do researchers use when data are not normally distributed or when the-shape of the distribution is unknown? Chebyshev's theorem applies to all distribu¬tions...

...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 find the story behind the data. To...

...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 x....

...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 standarddeviation,
the...

...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) {0 ≤ X ≤ 160}
d) None of these.
9. What is the probability that one bill for veterinary services costs less than $95?...

...answer the following question: What 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...

...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 known to be 32 tons. The mean weight...

...Mean and StandardDeviation
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...

...Kuleshov
Frequency Distributions
This assignment is based on Frequency Distributions and will include the following information:
1. The ability to describe the information provided by the StandardDeviation.
2. The ability to use the StandardDeviation to calculate the percentage of occurrence of a variable either above or below a particular value.
3. The ability to describe a normal distribution as...

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