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From Wikipedia

Frequency distribution

In statistics, a frequency distribution is a tabulation of the values that one or more variables take in a sample. Each entry in the table contains the frequency or count of the occurrences of values within a particular group or interval, and in this way the table summarizes the distribution of values in the sample.

Univariate frequency tables

Univariate frequency distributions are often presented as lists ordered by quantity showing the number of times each value appears. For example, if 100 people rate a five-point Likert scale assessing their agreement with a statement on a scale on which 1 denotes strong agreement and 5 strong disagreement, the frequency distribution of their responses might look like:

A different tabulation scheme aggregates values into bins such that each bin encompasses a range of values. For example, the heights of the students in a class could be organized into the following frequency table.

A Frequency Distribution shows us a summarized grouping of data divided into mutually exclusive classes and the number of occurrences in a class. It is a way of showing unorganized data e.g. to show results of an election, income of people for a certain region, sales of a product within a certain period, student loan amounts of graduates, etc. Some of the graphs that can be used with frequency distributions are histograms, line graphs, bar charts and pie charts. Frequency distributions are used for both qualitative and quantitative data..

Joint frequency distributions

Bivariate joint frequency distributions are often presented as (two-way) contingency tables:

The total row and total column report the marginal frequencies or marginal distribution, while the body of the table reports the joint frequencies.


Managing and operating on frequency tabulated data is much simpler than operation on raw data. There are simple algorithms to calculate median, mean, standard deviation etc. from these tables.

Statistical hypothesis testing is founded on the assessment of differences and similarities between frequency distributions. This assessment involves measures of central tendency or averages, such as the mean and median, and measures of variability or statistical dispersion, such as the standard deviation or variance.

A frequency distribution is said to be skewed when its mean and median are different. The kurtosis of a frequency distribution is the concentration of scores at the mean, or how peaked the distribution appears if depicted graphically—for example, in a histogram. If the distribution is more peaked than the normal distribution it is said to be leptokurtic; if less peaked it is said to be platykurtic.

Letter frequency distributions are also used in frequency analysis to crack codes and refer to the relative frequency of letters in different languages.

Letter frequency

The frequency of letters in text has often been studied for use in cryptography, and frequency analysis in particular. No exact letter frequency distribution underlies a given language, since all writers write slightly differently. Linotype machines sorted the letters' frequencies as etaoin shrdlu cmfwyp vbgkqj xz based on the experience and custom of manual compositors. Likewise,Modern International Morse code encodes the most frequent letters with the shortest symbols; arranging the Morse alphabet into groups of letters that require equal amounts of time to transmit, and then sorting these groups in increasing order, yields e it san hurdm wgvlfbk opjxcz yq. Similar ideas are used in modern data-compression techniques such as Huffman coding.

More recent analyses show that letter frequencies, like word frequencies, tend to vary, both by writer and by subject. One cannot write an essay about x-rays without using frequent Xs, and the essay will have an especially strange letter frequency if the essay is about the frequent use of x-rays to treat zebras in Qatar. Different authors have habits which can be reflected in their use of letters. Hemingway's writing style, for example, is visibly different from Faulkner's. Letter, bigram, trigram, word frequencies, word length, and sentence length can be calculated for specific authors, and used to prove or disprove authorship of texts, even for authors whose styles aren't so divergent.

Accurate average letter frequencies can only be gleaned by analyzing a large amount of representative text. With the availability of modern computing and collections of large text corpora, such calculations are easily made. This [http://deafandblind.com/word_frequency.htm Deafandblind link] details examples from a variety of sources, (press reporting, religious text, scientific text and general fiction) and there are differences especially for general fiction with the position of 'h' and 'i'. The example differs from the linotype 'etaoin shrdlu' to come out as 'etaoHn Isrdlu'. There is an unproven statement that conversation is similar in frequency to general fiction.

Herbert S. Zim, in his classic introductory cryptography text "Codes and Secret Writing", gives the English letter frequency sequence as "ETAON RISHD LFCMU GYPWB VKXJQ Z", the most common letter pairs as "TH HE AN RE ER IN ON AT ND ST ES EN OF TE ED OR TI HI AS TO", and the most common doubled letters as "LL EE SS OO TT FF RR NN PP CC".

The 'top twelve' letters comprise about 80% of the total usage. The 'top eight" letters comprise about 65% of the total usage. A spy using the VIC cipher or some other cipher based on a straddling checkerboard typically uses a mnemonic such as "a sin to err" (dropping the second "r") to remember the top 8 characters.

The use of letter frequencies and frequency analysis plays a fundamental role in several games, including hangman, Scrabble, Wheel of Fortune,Definition,Bananagrams, and cryptograms.

Letter frequencies had a strong effect on the design of some keyboard layouts. The most-frequent letters are on the bottom row of the Blickensderfer typewriter. The most-frequent letters are on the home row of the Dvorak Simplified Keyboard.

Relative frequencies of letters in the English language

The letter frequencies for English are listed below. However, this table differs slightly from others, such as Cornell University Math Explorer's Project, which produced [http://www.math.cornell.edu/~mec/2003-2004/cryptography/subs/frequencies.html this table] after measuring over 40,000 words.

In English, the space is slightly more frequent than the top letter (7% more frequent than, or 107% as frequent as, e), and the non-alphabetic characters (digits, punctuation, etc.) occupy the fourth position, between t and a.

Relative frequencies of the first letters of a word in the English language

First Letter of a word frequencies:

Relative frequencies of letters in other languages

*See Turkish dotted and dotless I

The figure below illustrates the frequency distributions of the 26 most common Latin letters across some languages.

Based on these tables, the 'etaoin shrdlu'-equivalent results for each language is as follows:

  • French: 'esait nrulo'; (Indo-European: Romance; traditionally, 'esartinulop' is used, in part for its ease of pronunciation)
  • Spanish: 'eaosr nidlc'; (Indo-European: Romance)
  • Portuguese: 'aeosr indmt' (Indo-European: Romance)
  • Italian: 'eaion lrtsc'; (Indo-European: Romance)
  • Esperanto: 'aieon lsrtk' (artificial language – influenced by Indo-European languages, Romance, Germanic mostly)
  • German: 'enisr atdhu'; (Indo-European: Germanic)
  • Swedish: 'eantr slido'; (Indo-European: Germanic)
  • Turkish: 'aeinr ldkmu'; (Turkic: a non Indo-European language)
  • Dutch: 'enati rodsl'; (Indo-European: Germanic)
  • Polish: 'aoiez nscwr'; (Indo-European: Slavic)

All these languages use a basically similar 25+ character alphabet.

High frequency

High frequency (HF)radio frequencies are between 3 and 30 MHz. Also known as the decameter band or decameter wave as the wavelengths range from one to ten decameters (ten to one hundred metres). Frequencies immediately below HF are denoted Medium-frequency (MF), and the next higher frequencies are known as Very high frequency (VHF). Shortwave (2.310 - 25.820 MHz) overlaps and is slightly lower than HF.

Propagation characteristics

Since the ionosphere often refracts HF radio waves quite well (a phenomenon known as skywave propagation), this range is extensively used for medium and long range radio communication. However, suitability of this portion of the spectrum for such communication varies greatly with a complex combination of factors:

These and other factors contribute, at each point in time for a given communication path, to a

Exploitation of, and limits imposed by, these characteristics

When all factors are at their optimum, worldwide communication is possible on HF. At many other times it is possible to make contact across and between continents or oceans. At worst, when a band is 'dead', no communication beyond the limited groundwave paths is possible no matter what powers, antennas or other technologies are brought to bear. When a transcontinental or worldwide path is open on a particular frequency, digital, SSB and CW communication is possible using surprisingly low transmission powers, often of the order of tens of watts, provided suitable antennas are in use at both ends and that there is little or no man-made or natural interference. On such an open band, interference originating over a wide area affects many potential users. These issues are significant to military, safety and amateur radio users of the HF bands.


The high frequency band is very popular with amateur radio operators, who can take advantage of direct, long-distance (often inter-continental) communications and the "thrill factor" resulting from making contacts in variable conditions. International shortwave broadcasting utilizes this set of frequencies, as well as a seemingly declining number of "utility" users (marine, aviation, military, and diplomatic interests), who have, in recent years, been swayed over to less volatile means of communication (for example, via satellites), but may maintain HF stations after switch-over for back-up purposes. However, the development of Automatic Link Establishment technology based on MIL-STD-188-141A and MIL-STD-188-141B for automated connectivity and frequency selection, along with the high costs of satellite usage, have led to a renaissance in HF usage among these communities. The development of higher speed modems such as those conforming to MIL-STD-188-110B which support data rates up to 9600 bit/s has also increased the usability of HF for data communications. Other standards development such as STANAG 5066 provides for error free data communications through the use of ARQ protocols.

CB radios operate in the higher portion of the range (around 27 MHz), as do some studio-to-transmitter (STL) radio links. Some modes of communication, such as continuous wavemorse code transmissions (especially by amateur radio operators) and single sideband voice transmissions are more common in the HF range than on other frequencies, because of their bandwidth-conserving nature, but broadband modes, such as TV transmissions, are generally prohibited by HF's relatively small chunk of electromagnetic spectrum space.

Noise, especially man-made interference from electronic devices, tends to have a great effect on the HF bands. In recent years, concerns have risen among certain users of the HF spectrum over "broadband over power lines" (BPL) Internet access, which is believed to have an almost destructive effect on HF communications. This is due to the frequencies on which BPL operates (typically corresponding with the HF band) and the tendency for the BPL "signal" to leak from power lines. Some BPL providers have installed "notch filters" to block out certain portions of the spectrum (namely the amateur radio bands), but a great amount of controversy over the deployment of this access method remains.

Some radio frequency identification (RFID) tags utilize HF. These tags are commonly known as HFID's or HighFID's (High Frequency Identification).

Frequency counter

A frequency counter is an electronicinstrument, or component of one, that is used for measuring frequency. Frequency is defined as the number of events of a particular sort occurring in a set period of time. Frequency counters usually measure the number of oscillations or pulses per second in a repetitive electronic signal.

Operating principle

Most frequency counters work by using a counter which accumulates the number of events occurring within a specific period of time. After a preset period (1 second, for example), the value in the counter is transferred to a display and the counter is reset to zero. If the event being measured repeats itself with sufficient stability and the frequency is considerably lower than that of the clock oscillator being used, the resolution of the measurement can be greatly improved by measuring the time required for an entire number of cycles, rather than counting the number of entire cycles observed for a pre-set duration (often referred to as the reciprocal technique). The internal oscillator which provides the time signals is called the timebase, and must be calibrated very accurately.

If the thing to be counted is already in electronic form, simple interfacing to the instrument is all that is required. More complex signals may need some conditioning to make them suitable for counting. Most general purpose frequency counters will include some form of amplifier, filtering and shaping circuitry at the input. DSP technology, sensitivity control and hysteresis are other techniques to improve performance. Other types of periodic events that are not inherently electronic in nature will need to be converted using some form of transducer. For example, a mechanical event could be arranged to interrupt a light beam, and the counter made to count the resulting pulses.

Frequency counters designed for radio frequencies (RF) are also common and operate on the same principles as lower frequency counters. Often, they have more range before they overflow. For very high (microwave) frequencies, many designs use a high-speed prescaler to bring the signal frequency down to a point where normal digital circuitry can operate. The displays on such instruments take this into account so they still display the correct value. Microwave frequency counters can currently measure frequencies up to almost 100 GHz. Above these frequencies the signal to be measured is combined in a mixer with the signal from a local oscillator, producing a signal at the difference frequency, which is low enough to be measured directly.


The accuracy of a frequency counter is strongly dependent on the stability of its timebase. Highly accurate circuits are used to generate this for instrumentation purposes, usually using a quartzcrystal oscillator within a sealed temperature-controlled chamber known as a crystal oven or OCXO (oven controlled crystal oscillator). For higher accuracy measurements, an external frequency reference tied to a very high stability oscillator such as a GPS disciplined rubidium oscillator may be used. Where the frequency does not need to be known to such a high degree of accuracy, simpler oscillators can be used. It is also possible to measure frequency using the same techniques in software in an embedded system. A CPU for example, can be arranged to measure its own frequency of operation provided it has some reference timebase to compare with.

I/O Interfaces

I/O interfaces allow the user to send information to the frequency counter and receive information from the frequency counter. Commonly-used interfaces include RS232, USB, GPIB and Ethernet. Besides sending measurement results, a counter can notify the user when user-defined measurement limits are exceeded. Common to many counters are the SCPI commands used to control them. A new development is built-in LAN-based control via Ethernet complete with GUI's. This allows one computer to control one or several instruments and eliminates the need to write SCPI commands. any time


Agilent's AN200: Fundamentals of electronic frequency counters is a very good resource [http://cp.literature.agilent.com/litweb/pdf/5965-7660E.pdf][http://cp.literature.agilent.com/litweb/pdf/5965-7661E.pdf]

  • [http://lea.hamradio.si/~s53mv/counter/history.html Counter history]
  • [http://www.hamradio.in/circuits/fcountlcd.php LCD Frequency Counter]
  • [http://www.ikalogic.com/freq_meter.php How to build your own Frequency Counter]
  • [http://www.aspisys.com/frqm.htm Panel Frequency Counter for RF systems]
  • [http://www.berkeleynucleonics.com/products/model_1105.html Example of control over Ethernet and GUI]

From Yahoo Answers

Question:Is a frequency diagram another term for a cumulative frequency diagram or is a frequency diagram a diagram that has 'Frequency' along the vertical axis and looks similar to a bar chart? Thanks in advance.

Answers:"What's the difference between a frequency polygon and a frequency diagram?" The term frequency diagram is used in the UK at GCSE level: it can be any chart that shows a frequency distribution, such as a bar chart, a histogram or a frequency polygon. A frequency polygon is a particular type of frequency diagram. "Is a frequency diagram another term for a cumulative frequency diagram?" No. The difference is that a cumulative frequency diagram plots cumulative frequency on the y-axis, unlike the frequency diagram that plots frequency or frequency density. Cumulative frequency is the frequencies added together. See the table below. For the first group (150-160), the frequency is 4 and the cumulative frequency is also 4. For the next group the frequency is 20. The cumulative frequency is the original 4 plus the 20. That makes 24, and so on. group frequency cumulative frequency <150 0 0 150-160 4 0+4=4 160-170 20 4+20=24 170-180 30 24+30=54 "Or is a frequency diagram a diagram that has 'Frequency' along the vertical axis and looks similar to a bar chart?" Correct it can be a bar chart, or a histogram (that looks similar to a bar chart) or it can be a frequency polygon, that looks like a line graph, not a bar chart.


Answers:A cumulative frequency polygon is actually just a line that joins all the midpoints of the "bars" on the cumulative frequency graph.

Question:This is about data communication or networking devices.. And I also want to know what are the devices that uses radio waves or radio frequency...

Answers:Radio frequency simply means frequencies that radio works at. It can apply to the electrical signals and components used in radio equipment or the radio waves themselves. Radio waves are electromagnetic waves at radio frequencies, that travel in similar ways to light waves. The frequency is the number of times per second that the signal goes through its cycle from positive to negative. It is measured in Hz, and usually radio is considered to be between 30kHz and 30GHz. Networking devices using radio are commonly WIFI or bluetooth. There are a lot of other types of radio networks, but those are probably what you are interested in. Bluetooth is used to connect accessories to computers and mobile phones etc, and only works over a few meters. WIFI is an equivalent of ethernet wired networks in some ways, and connects computers together, or to the internet. It can be used for point to point communications between a computer and another computer or device like a machine too. WIFI works around a frequency of 2.4GHz as well as 5.6 GHz.

Question:Help please 10 points to best answer!

Answers:basically they are the same thing except that in a histogram you are using bars (like in a bar chart) to show the frequency, while a polygon uses points connected by straight lines to show the frequencies. The way I have the students do it is to plot the x,y coordinates for your data ( x is the value of the random variable, y is the frequency ) then if you are doing a frequency polygon, you just connect the dots with straight lines (you need to start at zero to the left of your first point and to the right of your last point) if you are doing a histogram, just draw bars where the middle of each bar comes up to the x,y point

From Youtube

Frequency Modulation :Frequency ModulationAlong with the use of amplitude modulation for transmission of radio signals the so-called frequency modulation is widely used.Moreover, the frequency modulation is even more widespread.This is due to the fact that the frequency modulation allows you to transfer analog audio signals with higher quality than the amplitude modulation.In addition, it features high noise immunity, and is resistant to atmospheric and industrial interference.When frequency modulation is used, the modulating signal modulates not the power of the reference signal, but its frequency.We should also pay attention to the fact that frequency modulation changes the carrier frequency, while the amplitude remains unchanged.In principle, it's quite easy to get a frequency-modulated signal.For this purpose, it would be convenient to use a condenser microphone connected in parallel with the capacitor of a continuous oscillations circuit.The change in capacitance of the microphone under the influence of the sound wave will change the oscillator frequency.Thus, the generator will output a frequency-modulated signal which could be received by an ordinary FM receiver.One of the key parameters of frequency modulation is the frequency deviation.Frequency deviation represents the maximum deviation of the instantaneous frequency of a modulated signal from the value of its carrier frequency.Deviation equals half the frequency excursion value, ie it equals the difference between the maximum and ...

Interpolation between time and frequency domain :We analyse a signal that consists of three percussive sounds (sine waves in an exponential envelope). We correlate this signal with time-frequency-atoms (gaussian enveloped complex sine waves, aka Morlet wavelets) at certain time and frequency points. We show the correlation values in this two-dimensional pixel array, where the time axis is horizontal and the frequency axis is vertical. To put it differently: We have performed a windowed Fourier transform. Each pixel represents a complex value, where dark values have great absolute value and the color encodes the complex argument. That is, the darkness of a pixel encodes the amplitude of a time-frequency atom and its color encodes the phase. The width of the time-frequency-atoms is altered as the video progresses. We start with width zero, meaning that time resolution is perfect, but we cannot see any frequency information. Then we increase the atom's width. As the width grows, the frequency resolution becomes better and the time resolution becomes worse. In the end we reach an atom that has the width of the whole signal. Now frequency resolution is perfect, but we cannot see any structure with respect to time. This is the Heisenberg uncertainty principle in action: We cannot have arbitrarily high resolution in both time and frequency, because time and frequency are phenonema that depend on each other. It's a matter of taste, whether you want to see more frequency or more time structure in your signal. Actually, by the ...