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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.

## Applications

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&mdash;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.

Question:The carbonyl stretching frequency of aliphatic carboxylic acids in dilute solution is located near 1770 cm^-1. This frequency is much higher than the carbonyl frequency of these substances when measured neat (1720 cm^-1. Also, it is considerably higher than the corresponding simple aliphatic ester value (1745 cm^-1). Explain. I'm not sure what raises or decreases frequencies. Ideas? Does this have to do with electronegativity or hydrogen bonding?

Answers:Hydrogen bonds absorb some of energy.

Question:Ultrasound is mechanical energy and IR is electromagnetic energy that causes mechanical vibrations. So, if you used the mechanical energy of ultrasound on a molecule, using several of the peak frequency of absorption bands that are known from its IR spectra would that molecule be tuned in for absorption of the energy better than various other types of molecules with a different IR absorption spectra? Why do I ask? I was hoping that the above was true, so that ultrasound could be used to detect and destroy roadside bombs. That is, the plastic explosive molecule would absorb enough energy that it would fall apart (explode) well away from their targets.

Answers:I'm not sure that you've been correctly informed on what IR excitation generally does. It causes *bonds* to vibrate, but doesn't necessarily cause significant increase in the movement of the whole molecule (translational motion). EMR moves at the speed of light (which varies very slightly depending on the medium). Ultrasound moves at the speed of sound (which varies greatly depending on the medium). Since frequency is a function of wave speed, so you can't strictly use the IR absorption spectrum for a "tuned" excitation of a bond. That doesn't mean that you can't destroy compounds using Ultrasound and (I suppose) the IR spectrum can give you a hint about which molecules are more likely to break apart. I just don't think it'll won't work the way that you envision. There's been some research done to destroy contaminants in water via US - it results in incinerated compounds without raising the bulk water temp (you effectively get pockets of 5000K temps within 25 C water), but the process is cost prohibitive and still has alot of technical problems. Ultrasound needs a efficient tranmission medium. Soil (as opposed to water or oil) is full of voids and cracks that will rob your US wave of energy. If you have to put your US transmited within a few meters (much less a few centimeters) of a IED, I don't know that you've accomplished all that much. Keep at it, though.

Question:I have an Ir of of benzilic acid, which i synthesized in my organic lab, and as i was analyzing the finger print region of the graph i noticed that basicly all of the wavenumber matched my authentic published graph. however, there are a couple frequencies that vary by about 1-2 wave number. does that mean its not fully comfiremd what i have is really what i have( the sample)

Answers:One or two wavenumbers is a very tiny difference! You can have something vary as much as 5-10 wavenumbers sometimes; but anything less than 5 you can consider a sure match.

Question:how can i construct a grouped frequency distribution table from the following data? 41 32 67 44 46 47 36 53 56 45 31 43 25 33 25 38 48 57 42 49

Answers:I guess you could sort it into intervals. Intervals Frequency 1-10 0 11-20 0 21-30 2 31-40 5 41-50 9 51-60 3 61-70 1