#### Theory of Frequency Distributions and Graphs

Basic Definitions:

Raw Data: In this the data collected is in original form.

Frequency: A certain value or class of values takes place in a number of times is termed as frequency.

Frequency Distribution: The organization in tabular form of a raw data with classes and frequencies are termed as frequency distribution.

Categorical Frequency Distribution: In this type of distribution, the data is only nominal or ordinal.

Ungrouped Frequency Distribution: In Ungrouped frequency distribution, the raw data is not grouped. Basically it is a frequency distribution of the numerical data.

Grouped Frequency Distribution: In this several numbers are grouped into one class.

Class Limits: It separate grouped frequency distribution from one class to another. The limits could really appear in the data and contain gaps among the upper limit of one class and lower limit of the subsequent.

Class Boundaries: It separate one class of a grouped frequency distribution from the other. The boundaries encompass one more decimal place than the raw data and thus do not appear in data. The upper boundary of one class and the lower boundary of the next class consist of no gap. The lower class boundary is determined by subtracting 0.5 units from lower class limit and upper class boundary is determined by adding up 0.5 units to the upper class limit.

Class Width: It is basically the difference between lower and upper boundary of any class. The class width is as well the difference between the lower limits of two successive classes or the upper limits of two successive classes. However, it is not the difference between the lower and upper limits of similar class.

Class Mark: It is the number in middle of class. We can determine it by adding the lower and upper limit and then dividing it by two. We can also determine it by adding the upper and lower boundaries and then dividing it by two.

Cumulative Frequency: This is the running total of frequencies. It is the number of values less than the upper class boundary for current class.

Relative Frequency: The formula for determining the relative frequency is by dividing the frequency by the total frequency. The percent of values falling in that class is determined by the above formula.

Cumulative Relative Frequency: It can be computed by dividing the total running relative frequency or cumulative frequency by the total frequency. It provides the percent of the values that are less than the upper class boundary.

Histogram: The graph that displays the data by employing vertical bars of different heights to symbolize frequencies. The horizontal axis can be either class boundaries, class marks or the class limits.

Frequency Polygon: It is fundamentally a line graph. The frequency is placed all along the vertical axis and the class mid-points are put all along the horizontal axis. Such points are joined with lines.

Ogive: The ogive is a frequency polygon of the cumulative or relative cumulative frequency. Horizontal axis is the class boundaries and Vertical axis is the cumulative frequency or relative cumulative frequency. The graph always begins at zero at the lowest class boundary and will end up at net frequency (that is, for cumulative frequency) or 1.00 for the relative cumulative frequency.

Pareto Chart: In this bars are arranged according to frequency for qualitative data.

Pie Chart: It is the graphical representation of data as the slices of pie. The frequency recognizes the size of slice. The number of degrees in any slice is the relative frequency times of 360 degrees.

Pictograph: It is a graph which uses pictures to represent the data.

Stem and Leaf Plot: It is the data plot that uses part of data value as the stem and the rest of data value (that is the leaf) to make classes or groups. With the help of Stem and Leaf Plot we can quickly sort the data.

Grouped Frequency Distributions:

Guidelines for classes:

A) There must be between 5 to 20 classes.

B) The class width must be an odd number. This will assure that the class mid-points are integers rather than decimals.

C) The classes should be mutually exclusive. This signifies that no data value can drop into two distinct classes.

D) The classes should be all exhaustive or inclusive. This signifies that each and every data values should be involved.

E) It can be kept in mind that classes will be continuous. There are no gaps in the frequency distribution. The classes which have no values in them should be involved

F) The classes should be equivalent in width. The exception here is the initial or last class. This is possible to have a "below ..." or "... and above" class. This is frequently used with ages.

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