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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:

Answers:I am assuming you mean histogram versus frequency distribution graph. Most stats books use the terms interchangeably. Both illustrate the distribution of responses for a sample.

Answers:basically they are the same thing except that in a histogram you are using bars (like in a bar chart) to show the frequency, while a polygon uses points connected by straight lines to show the frequencies. The way I have the students do it is to plot the x,y coordinates for your data ( x is the value of the random variable, y is the frequency ) then if you are doing a frequency polygon, you just connect the dots with straight lines (you need to start at zero to the left of your first point and to the right of your last point) if you are doing a histogram, just draw bars where the middle of each bar comes up to the x,y point

Question:Is a frequency diagram another term for a cumulative frequency diagram or is a frequency diagram a diagram that has 'Frequency' along the vertical axis and looks similar to a bar chart? Thanks in advance.

Answers:"What's the difference between a frequency polygon and a frequency diagram?" The term frequency diagram is used in the UK at GCSE level: it can be any chart that shows a frequency distribution, such as a bar chart, a histogram or a frequency polygon. A frequency polygon is a particular type of frequency diagram. "Is a frequency diagram another term for a cumulative frequency diagram?" No. The difference is that a cumulative frequency diagram plots cumulative frequency on the y-axis, unlike the frequency diagram that plots frequency or frequency density. Cumulative frequency is the frequencies added together. See the table below. For the first group (150-160), the frequency is 4 and the cumulative frequency is also 4. For the next group the frequency is 20. The cumulative frequency is the original 4 plus the 20. That makes 24, and so on. group frequency cumulative frequency <150 0 0 150-160 4 0+4=4 160-170 20 4+20=24 170-180 30 24+30=54 "Or is a frequency diagram a diagram that has 'Frequency' along the vertical axis and looks similar to a bar chart?" Correct it can be a bar chart, or a histogram (that looks similar to a bar chart) or it can be a frequency polygon, that looks like a line graph, not a bar chart.

Question:Explain the difference between a frequency polygon and a histogram.

Answers:A frequency polygon shows the data in a line graph. A histogram shows the data in a bar graph. See links below.