Revision: Statistics Mathematics (English Medium) ICSE Class 9 CISCE

Each group into which raw data is divided is called a class interval.

The two values that bound a class interval.

• Lower limit: Smallest value of the class

• Upper limit: Largest value of the class

Frequency:

The number of times a particular observation occurs.

Frequency Distribution:

A tabular arrangement of data showing the frequency of each observation or class.

• Inclusive form: Both lower and upper limits are included in the class.
  (Example: 1–10, 11–20)

• Exclusive form: Lower limit is included, but upper limit is excluded.
  (Example: 0–10, 10–20)

The difference between the highest and lowest observations.

Range = Highest value − Lowest value

Statistics is the area of study dealing with the collection, presentation, and analysis of data as well as drawing meaningful conclusions from the data.

A collection of given facts or figures, usually expressed in numerical form.

A variable is a symbol, usually a letter (like x, y, or z), representing an unknown or changeable numerical value in an equation or an algebraic expression.

A constant is a fixed value that does not change.

• Examples: 5, −7, 256

Frequency Distribution Table: When the number of observations in an experiment is large then we can convert it into the tabular form which is called a Frequency Distribution Table.

Ungrouped Frequency Distribution Table: When the frequency of each class interval is not arranged or organized in any manner.

Grouped Frequency Distribution Table: The frequencies of the corresponding class intervals are organised or arranged in a particular manner, either ascending or descending. 

Inclusive or discontinuous Frequency Distribution: A frequency distribution in which the upper limit of one class differs from the lower limit of the succeeding class is called an Inclusive or discontinuous Frequency Distribution.

Exclusive or continuous Frequency Distribution: A frequency distribution in which the upper limit of one class coincides from the lower limit of the succeeding class is called an exclusive or continuous Frequency Distribution.

Frequency Distribution Table: When the number of observations in an experiment is large then we can convert it into the tabular form which is called a Frequency Distribution Table.

Ungrouped Frequency Distribution Table: When the frequency of each class interval is not arranged or organized in any manner.

Grouped Frequency Distribution Table: The frequencies of the corresponding class intervals are organised or arranged in a particular manner, either ascending or descending. 

Inclusive or discontinuous Frequency Distribution: A frequency distribution in which the upper limit of one class differs from the lower limit of the succeeding class is called an Inclusive or discontinuous Frequency Distribution.

Exclusive or continuous Frequency Distribution: A frequency distribution in which the upper limit of one class coincides from the lower limit of the succeeding class is called an exclusive or continuous Frequency Distribution.

• Adjustment
• Class - Size
• Class - Mark

The cumulative frequency of a class interval is the sum of the frequencies of all the classes up to this class interval.

\[\text{Adjustment Factor}=\frac{1}{2}\text{(Lower limit of next class - Upper limit of previous class)}\]

\[\text{Frequency density}=\frac{\mathrm{Frequency}}{\text{Class width}}\]