How To Find The Midpoint In A Frequency Table

Term in statistics

In statistics, a frequency distribution is a listing, table (i.e.: frequency table) or graph (i.e.: bar plot or histogram) that displays the frequency of various outcomes in a sample.^[1] Each entry in the tabular array contains the frequency or count of the occurrences of values within a particular grouping or interval.

Example [edit]

Here is an example of a univariate (=unmarried variable) frequency table. The frequency of each response to a survey question is depicted.

Rank	Caste of agreement	Number
i	Strongly agree	22
2	Concord somewhat	xxx
3	Not sure	20
four	Disagree somewhat	fifteen
v	Strongly disagree	fifteen

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 tabular array.

Height range	Number of students	Cumulative number
less than 5.0 feet	25	25
5.0–5.5 feet	35	60
5.v–vi.0 feet	20	80
6.0–6.5 feet	twenty	100

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

Structure [edit]

Determine the number of classes. Too many classes or too few classes might non reveal the basic shape of the data fix, also it will be difficult to interpret such frequency distribution. The ideal number of classes may be adamant or estimated by formula: ${\text{number of classes}}=C=1+3.3\log n$ (log base of operations 10), or by the foursquare-root selection formula $C={\sqrt {n}}$ where north is the total number of observations in the data. (The latter volition be much too large for large data sets such as population statistics.) However, these formulas are not a difficult rule and the resulting number of classes determined by formula may not always exist exactly suitable with the data being dealt with.
Calculate the range of the data (Range = Max – Min) by finding the minimum and maximum data values. Range will be used to make up one's mind the class interval or class width.
Decide the width of the classes, denoted by h and obtained past $h={\frac {\text{range}}{\text{number of classes}}}$ (assuming the class intervals are the aforementioned for all classes).

Generally the grade interval or class width is the aforementioned for all classes. The classes all taken together must cover at to the lowest degree the distance from the everyman value (minimum) in the data to the highest (maximum) value. Equal class intervals are preferred in frequency distribution, while diff form intervals (for example logarithmic intervals) may exist necessary in certain situations to produce a good spread of observations between the classes and avert a big number of empty, or almost empty classes.^[2]

Decide the individual class limits and select a suitable starting point of the outset course which is arbitrary; it may exist less than or equal to the minimum value. Unremarkably it is started before the minimum value in such a way that the midpoint (the average of lower and upper class limits of the first grade) is properly^{[ clarification needed ]} placed.
Take an observation and mark a vertical bar (|) for a class it belongs. A running tally is kept till the last observation.
Find the frequencies, relative frequency, cumulative frequency etc. equally required.

Articulation frequency distributions [edit]

Bivariate joint frequency distributions are often presented as (2-style) contingency tables:

*Two-way contingency table with marginal frequencies*
	Dance	Sports	Boob tube	Full
Men	2	10	8	20
Women	xvi	half-dozen	eight	30
Total	18	xvi	xvi	l

The total row and total column study the marginal frequencies or marginal distribution, while the body of the tabular array reports the articulation frequencies.^[3]

Applications [edit]

Managing and operating on frequency tabulated data is much simpler than operation on raw data. There are simple algorithms to calculate median, mean, standard departure 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 divergence or variance.

A frequency distribution is said to be skewed when its mean and median are significantly different, or more generally when it is disproportionate. The kurtosis of a frequency distribution is a measure of the proportion of extreme values (outliers), which appear at either end of the histogram. If the distribution is more outlier-prone than the normal distribution information technology is said to exist leptokurtic; if less outlier-prone it is said to be platykurtic.

Letter frequency distributions are also used in frequency analysis to crack ciphers, and are used to compare the relative frequencies of letters in dissimilar languages and other languages are often used like Greek, Latin, etc.

See as well [edit]

Count data
Cross tabulation
Cumulative frequency analysis
Cumulative distribution function
Empirical distribution office

Notes [edit]

^ Australian Bureau of Statistics, http://www.abs.gov.au/websitedbs/a3121120.nsf/dwelling/statistical+linguistic communication+-+frequency+distribution
^ Manikandan, Due south (1 January 2011). "Frequency distribution". Periodical of Pharmacology & Pharmacotherapeutics. 2 (1): 54–55. doi:x.4103/0976-500X.77120. ISSN 0976-500X. PMC3117575. PMID 21701652.
^ Stat Trek, Statistics and Probability Glossary, s.five. Joint frequency