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Encyclopedia > Frequency distribution

In statistics, a frequency distribution is a list of the values that a variable takes in a sample. It is usually a list, ordered by quantity, showing the number of times each value appears. For example, if 100 people rate a five-point attitude item 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: Statistics is a type of data analysis which practice includes the planning, summarizing, and interpreting of observations of a system possibly followed by predicting or forecasting of future events based on a mathematical model of the system being observed. ... Sampling is that part of statistical practice concerned with the selection of individual observations intended to yield some knowledge about a population of concern, especially for the purposes of statistical inference. ...

Rating Degree of agreement Number
1 Strongly agree 25
2 Agree somewhat 35
3 Not sure 20
4 Disagree somewhat 15
5 Strongly disagree 5

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. One may be faced with the problem of making a definite decision with respect to an uncertain hypothesis which is known only through its observable consequences. ... Central tendency is a term used in some fields of empirical research to refer to what statisticians sometimes call location. A measure of central tendency is either a location parameter or a statistic used to estimate a location parameter. ... In mathematics, there are numerous methods for calculating the average or central tendency of a list of n numbers. ... In statistics, mean has two related meanings: the average in ordinary English, which is more correctly called the arithmetic mean, to distinguish it from geometric mean or harmonic mean. ... In probability theory and statistics, the median is a number that separates the highest half of a sample, a population, or a probability distribution from the lowest half. ... In descriptive statistics, statistical dispersion (also called statistical variability) is quantifiable variation of measurements of differing members of a population within the scale on which they are measured. ... In probability and statistics, the standard deviation is the most commonly used measure of statistical dispersion. ... In probability theory and statistics, the variance of a random variable is a measure of its statistical dispersion, indicating how far from the expected value its values typically are. ...

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 graphicallyâ€”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. In probability theory and statistics, skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable. ... In probability theory and statistics, kurtosis is a measure of the peakedness of the probability distribution of a real-valued random variable. ... In statistics, a histogram is a graphical display of tabulated frequencies. ... The normal distribution, also called Gaussian distribution, is an extremely important probability distribution in many fields, especially in physics and engineering. ...

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

Results from FactBites:

 Learning Resources: Statistics: Power from Data! Frequency distribution tables (1706 words) The distribution of a variable is the pattern of frequencies of the observation. Frequency distributions are portrayed as frequency tables, histograms, or polygons. This relative frequency of a particular observation or class interval is found by dividing the frequency (f) by the number of observations (n): that is, (f ÷ n).
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