Discipline and curriculum issues about statistics

Central to a consideration of teachers’ beliefs about statistics education are beliefs about statistics itself and its place in the curriculum. Are teachers’ beliefs about statistics congruent with the views of statisticians and statistics educators? In asking this question, however, it is important to identify the views of the latter group. Statistics tutor’ perceptions about Statistics help and statistics education may suggest a set of “desirable beliefs” that they believe teachers ought to have.

A strong theme of the ICMI/IASE conference presentations was that teachers must be helped to see that statistics is not defined by a set of procedural computations but rather by investigative processes given expression in the range of societal activity(e.g . Statistics questions and Statistics answers). Pfannkuch (2008) expresses concern that when it comes, for example, to statistical graphs, schools emphasize construction techniques for Statistics problems rather than the thinking needed for data-based decision-making. This highlights a possible mismatch between teachers’ beliefs about statistics and how statistics educators view it. free Statistics help is easily to find on the internet nowadays  .

Basic Differences Between AM and FM

We need to mention a couple of other things before we leave the discussion of how radio works.  We’ve talked about AM and FM radio, but we haven’t explained the real difference.

In fact, there is a lot of difference — and not just a difference in the station numbers on your radio dial.

The first type of radio service — the one we’ve been talking about in the last couple of modules — was AM radio.

The term modulation refers to how sound is encoded on a radio wave called a carrier wave; or, more accurately, how the sound affects the carrier wave so that the original sound can later be detected by a radio receiver.

In the top-left of this drawing the RF energy (carrier wave) is not modulated by any sound.  There would be silence on your radio receiver.

Sound transmitted by an AM radio station affects the carrier wave by changing the amplitude (height) of the carrier wave, as shown on the left.

Unfortunately, this type of modulation is subject to static interference from such things as household appliances — and especially from lightening storms.

AM also limits the loud-to-soft range of sounds that can be reproduced (called dynamic range) and the high-to-low sound frequency range (called frequency response, to be explained below).

FM radio, which came along in the 1930s, uses a different approach than AM. It’s virtually immune to any type of external interference, it has a greater dynamic range, and it can handle sounds of higher and lower frequencies. This is why music, with its much greater frequency range than the human voice, sounds better on FM radio.

Note on the left that when the carrier wave of FM radio is modulated with sound that the distance between the waves, or the frequency of the carrier wave, changes.

Thus, AM radio works by changing the amplitude of the carrier wave and FM radio works by changing the frequency of the carrier wave.

Frequency Response

Frequency relates to the basic pitch of a sound — how high or low it is. A frequency of 20 Hz would sound like an extremely low-pitched note on a pipe organ — almost a rumble.

At the other end of the scale, 20,000 Hz would be the highest pitched sound that can be imagined, even higher than the highest note on a violin or piccolo.

As we’ve noted, frequency is measured in Hertz (Hz) or cycles per second (CPS). A person with exceptionally good hearing will be able to hear sounds from 20-20,000 Hz.

Since both ends of the 20-20,000Hz range represent rather extreme limits, the more common range used for FM radio and TV is from 50 to 15,000 Hz. (A typical AM radio signal does not cover this entire range.)

Although the 50-15,000 Hz doesn’t quite cover the full range that can be heard by people with good hearing, it covers almost all naturally occurring sounds.  Note in the drawing above that the ear does not hear all frequencies of sound at the same loudness, but a good microphone does.

The sound level or amplitude of sound in radio and TV stations is monitored and adjusted with the help of a volume units meter (VU meter) meter. One model is shown on the left.  Audio levels must be carefully controlled in broadcasting to keep noise and distortion from reducing the quality of sound.

Algebra in electromagnetic waves

An important distinction between the optical and radio regions of the electromagnetic spectrum is the statistical one. As the wave length of radiation becomes shorter one has less and less detailed knowledge of the positions and phases of the radiating elements. In the radio region this knowledge is for all practical purposes absolute; in the optical region it is almost entirely statistical. The experimental techniques in the two regions are markedly different both as to mode of generation and mode of measurement of the radiation. For a long time it has appeared desirable to close the gap experimentally in the sense of producing effective millimeter wave generators. From a theoretical standpoint, the existence of a similar gap has not been so obvious although there are few who have studied the common brand of physical optics who have not felt a passing dissatisfaction with the ad hoc character of the treatment of many parts of it in terms of monochromatic plane waves. Symptomatic of this dissatisfaction has been the work of Gouy, Schuster, Stokes, Rayleigh, Mueller, and Wiener directed toward a proper description of the “white” and “partially polarized” aspects of radiation. Even in the microwave region the necessity for statistics makes itself felt when one is faced with the problem of scattering from sea waves, the leaves of trees, and other assemblages of scatterers.  Find any difficulties with Algebra 1 and Algebra 2 ? get Algebra 1 Help and Algebra 1 Answers also  Algebra 2 Help and Algebra 2 Answers

About Electromagnetic Pulse

Electromagnetic Pulse (EMP) is an instantaneous, intense energy field that can overload or disrupt at a

distance numerous electrical systems and high technology microcircuits, which are especially sensitive to power surges.  A large scale EMP effect can be produced by a single nuclear explosion detonated high in the atmosphere.  This method is referred to as High-Altitude EMP (HEMP).  A similar,smaller-scale EMP effect can be created using non-nuclear devices with powerful batteries or reactive chemicals.  This method is called High Power Microwave (HPM).  Several nations, including reported sponsors of terrorism, may currently have a capability to use EMP as a weapon for cyber warfare or cyber terrorism to disrupt communications and other parts of the U.S. critical infrastructure.  Also, some equipment and weapons used by the U.S. military may be vulnerable to the effects of EMP.

 The threat of an EMP attack against the United States is hard to assess, but some observers indicate that it is growing along with worldwide access to newer technologies and the proliferation of nuclear weapons.  In the past, the threat of mutually assured destruction provided a lasting deterrent against the exchange of multiple high-yield nuclear warheads.  However, now even a single, low-yield nuclear explosion high above the United States, or over a battlefield, can produce a large-scale EMP effect that could result in a widespread loss of electronics, but no direct fatalities, and may not necessarily evoke a large nuclear retaliatory strike by the U.S. military. This, coupled with published articles discussing the vulnerability of U.S. critical infrastructure control systems, and some U.S. military battlefield systems to the effects of EMP, may create a new incentive for other countries to rapidly develop or acquire a nuclear capability. Policy issues raised by this threat include (1) what is the United States doing to protect civilian critical infrastructure systems against the threat of EMP, (2) could the U.S. military be affected if an EMP attack is directed against the U.S. civilian infrastructure, (3) are other nations now encouraged by U.S. vulnerabilities to develop or acquire nuclear weapons, and (4) how likely are terrorist organizations to launch a smaller-scale EMP attack against the United States ?

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