How To Find The Estimated Mean Of A Frequency Table

In statistics, a frequency distribution is a listing, table (i.e.: frequency tabular array) or graph (i.east.: bar plot or histogram) that displays the frequency of various outcomes in a sample.^[i] Each entry in the table contains the frequency or count of the occurrences of values within a item group 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
1	Strongly agree	22
ii	Agree somewhat	thirty
3	Not sure	twenty
4	Disagree somewhat	15
5	Strongly disagree	15

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 course could be organized into the following frequency table.

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

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 notably to show results of an election, income of people for a certain region, sales of a product within a certain period, educatee loan amounts of graduates, etc. Some of the graphs that tin can be used with frequency distributions are histograms, line charts, bar charts and pie charts. Frequency distributions are used for both qualitative and quantitative data.

Construction [edit]

Decide the number of classes. As well many classes or too few classes might not reveal the basic shape of the data ready, also it volition be hard to interpret such frequency distribution. The ideal number of classes may exist determined or estimated past formula: ${\text{number of classes}}=C=1+3.three\log n$ (log base 10), or by the square-root choice formula $C={\sqrt {northward}}$ where n is the total number of observations in the data. (The latter volition be much too big for large data sets such every bit population statistics.) Nonetheless, these formulas are non a difficult rule and the resulting number of classes determined by formula may not e'er be exactly suitable with the data being dealt with.
Calculate the range of the data (Range = Max – Min) past finding the minimum and maximum data values. Range will be used to determine the grade 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 grade intervals are the same for all classes).

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

Make up one's mind the individual class limits and select a suitable starting bespeak of the kickoff class which is arbitrary; it may be less than or equal to the minimum value. Usually it is started before the minimum value in such a fashion that the midpoint (the average of lower and upper form limits of the first class) is properly^{[ description needed ]} placed.
Take an observation and marking 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. as required.

Articulation frequency distributions [edit]

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

*Ii-mode contingency tabular array with marginal frequencies*
	Dance	Sports	Television set	Full
Men	2	10	8	twenty
Women	xvi	half-dozen	8	30
Total	eighteen	16	sixteen	50

The total row and total column report 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 information. There are simple algorithms to summate 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 fundamental tendency or averages, such equally the hateful and median, and measures of variability or statistical dispersion, such equally the standard departure or variance.

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

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

Encounter also [edit]

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

Notes [edit]

^ Australian Bureau of Statistics, http://www.abs.gov.au/websitedbs/a3121120.nsf/dwelling house/statistical+language+-+frequency+distribution
^ Manikandan, S (one Jan 2011). "Frequency distribution". Journal of Pharmacology & Pharmacotherapeutics. 2 (1): 54–55. doi:10.4103/0976-500X.77120. ISSN 0976-500X. PMC3117575. PMID 21701652.
^ Stat Trek, Statistics and Probability Glossary, s.five. Articulation frequency