What is Frequency distribution?
{{complex|date=May 2012}} [[File:Angola population pyramid 2005.png|thumb|right|Example of an (absolute) frequency distribution. This is the [[population pyramid]] of [[Angola]], for the year 2005.]] [[File:China population pyramid 2005.png|thumb|right|This is the population pyramid of [[China]] for the year 2005.]] In [[statistics]], a '''frequency distribution''' is a list of the values that a [[variable]] takes in a [[Sampling (statistics)|sample]]. It is usually a list, ordered by quantity. It will show 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: {| border=1 cellspacing=0 cellpadding=2 ![[ranking|Rank]] !Degree of agreement !Number |- |1 |Strongly agree |25 |- |2 |Agree somewhat |35 |- |3 |Not sure |20 |- |4 |Disagree somewhat |15 |- |5 |Strongly disagree |5 |} This simple table has two drawbacks. When a variable can take continuous values instead of discrete values or when the number of possible values is too large, the table construction is difficult, if it is not impossible. A slightly different scheme based on the range of values is used in such cases. For example, if we consider the heights of the students in a class, the frequency table might look like below. {| border=1 cellspacing=0 cellpadding=2 !Height range !Number of students !Cumulative number |- | 4.5–5.0 feet |25 |25 |- |5.0–5.5 feet |35 |60 |- |5.5–6 feet |20 |80 |- |6.0–6.5 feet |20 |100 |- |} == Applications == Managing and operating on frequency tabulated data is much simpler than operation on raw data. There are simple [[algorithm]]s to calculate [[median]], [[mean (statistics)]], [[standard deviation]] etc. from these tables. [[Statistical hypothesis testing]] is based on the assessment of differences and similarities between frequency distributions. This assessment involves measures of [[Measures of