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# learn standard deviation for continuous series

From Wikipedia

Continuity tester

A continuity tester is an item of electrical test equipment used to determine if an electrical path can be established between two points; that is if an electrical circuit can be made. The circuit under test is completely de-energized prior to connecting the apparatus.

The tester consists of an indicator in series with a source of electrical power - normally a battery, terminating in two test leads. If a complete circuit is established between the test-leads, the indicator is activated.

The indicator may be an electric light or such a device might also be fitted with a buzzer. This led to the term "buzzing out a circuit" (which means to test for continuity). This term remains in use today, although any sound produced is usually made by the beeper function on a modern digital voltmeter.

A popular design has the tester combined with a standard flashlight. A TRS connector or jack plug in the rear of the unit permits a set of test leads to be plugged in effecting a quick conversion between the two applications.

For situations where continuity testing must be done on high resistance circuits, or where delicate conductors and sensitive components that might be damaged by excessive current are present, a low voltage, low current device must be used. These typically use an op-amp and watch batteries to drive an LED as an indicator. These testers can be exquisitely sensitive; for example they will indicate if the test points are taken by both hands.

There are times when a simple continuity test fails to reveal the problem. For example, vibration-induced problems in automobile wiring can be extremely difficult to detect because a short or open is not maintained long enough for a standard tester to respond.

In these applications a latching continuity tester is used. A more complex device, it detects intermittent opens and shorts as well as steady-state conditions. These devices contain a fast acting electronic switch (generally a Schmitt trigger) forming a gated astable oscillator which detects and locks (latches) the indicator on an intermittent condition with a duration of less than a millisecond.

Question:What benefits are there for using standard devitaion, over the absolute deviation? The absolute deviation seems much more intuitive (taking the average of the deviation), but since standard deviation is much more common, I assume there are benefits of taking a root mean square deviation.

Answers:Here is a little introduction from a paper. Bottom line, you have a good question, and the common use of variance is due to historical reasons. But there are also theoretical reasons to do so. Revisiting a 90-year-old debate: the advantages of the mean deviation Stephen Gorard Department of Educational Studies, University of York, email: sg25@york.ac.uk Paper presented at the British Educational Research Association Annual Conference, University of Manchester, 16-18 September 2004 Introduction This paper discusses the reliance of numerical analysis on the concept of the standard deviation, and its close relative the variance. Such a consideration suggests several potentially important points. First, it acts as a reminder that even such a basic concept as standard deviation , with an apparently impeccable mathematical pedigree, is socially constructed and a product of history (Porter 1986). Second, therefore, there can be equally plausible alternatives of which this paper outlines one the mean absolute deviation. Third, we may be able to create from this a simpler introductory kind of statistics that is perfectly useable for many research purposes, and that will be far less intimidating for new researchers to learn (Gorard 2003a). We could reassure these new researchers that, although traditional statistical theory is often useful, the mere act of using numbers in research analyses does not mean that they have to accept or even know about that particular theory. for your question, see the paragraph " Why do we use the Standard Deviation?" http://www.leeds.ac.uk/educol/documents/00003759.htm

Question:A continuous random variable X has mean 60.0 and standard deviation 8. What value does the random variable have 2.5 standard deviations above the mean? 62.5; 70.5; 76.0; 80.0. Please explain? Thanks =)

Answers:80 2.5 standard deviations above the mean = 2.5 x 8 + 60 = 80

Question:the mean for body temperature in humans is 98.6 degrees and the standard deviation is 0.6 degrees what % of people have a body temp below 99.2? can you show any equations and how you got the answer? i never learned this but its on a test i am doing thanks! ive never learned anything at all about stats so i basic explanation would be super helpful! thanks again

Answers:This is a normal distribution problem: z = (99.2 - 98.6) / 0.6 = 1.0 So P(x < 99.2) = P(z < 1.0) = 0.5 + 0.3413 = 0.8413 So 84.13% of people have a body temp below 99.2

Question:How do I find a confidence interval for a sample standard deviation? this is the formula I learned butI cant get the right answe (e^x(ln(variance)) +/- sqrt((2/n-2)(ln(variance))

Answers:Check one of these 2 links below, and see if it helps: