Revision: Applied Mathematics >> Index Numbers and Time Based Data CUET (UG) Index Numbers and Time Based Data

1. Spiegel: “An index number is a statistical measure designed to show changes in a variable or a group of related variables with reference to time, geographical location and other characteristics such as income, profession etc.”
2. Croxton and Cowden: “Index Numbers are devices for measuring differences in the magnitude of a group of related variables.”

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

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

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

• 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)

Frequency:

The number of times a particular observation occurs.

Frequency Distribution:

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

The difference between the highest and lowest observations.

Range = Highest value − Lowest value

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

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