Meaning, Objectives and Requisites of a Good Average

An average (also called a measure of central tendency) is a single value that represents the general level of a whole mass of data — it summarises dozens or hundreds of individual figures into one number that speaks for the entire distribution. When a shop is said to have an average daily sale of ₹4,500, that single figure is standing in for every individual day's actual sale. The Odisha CHSE Std-11 Business Mathematics and Statistics syllabus draws on the same statistical principles found in any standard treatment of descriptive statistics, applied here specifically to business and commercial data — wages, sales, prices, profits and growth rates.

Objectives of studying averages:

• To obtain a single representative value that summarises an entire mass of data.
• To make comparison possible — e.g., comparing the average marks of two sections, or the average profit of two firms over a year.
• To provide a base for further statistical analysis, such as measures of dispersion, correlation and index numbers, all built on top of an average.
• To assist business decision-making — a reorder level, a target sales figure or a wage structure is usually fixed with reference to some average of past performance.

Requisites of a good average — the standard checklist examined under the Odisha CHSE +2 Commerce Business Mathematics and Statistics syllabus's treatment of averages:

1. It should be rigidly (precisely) defined, so that different persons computing it from the same data always arrive at the same figure.
2. It should be based on all the observations in the series, not just a few of them.
3. It should be easy to understand and simple to calculate, without elaborate mathematics.
4. It should be capable of further algebraic treatment — for example, combining two group averages into one combined average (§4).
5. It should not be unduly affected by extreme values (a few very small or very large figures).
6. It should be least affected by sampling fluctuations — a small change in the data should not swing it wildly.

No single average satisfies all six requisites at once — the arithmetic mean, for instance, is rigidly defined and algebraically treatable but is badly shaken by extreme values, while the median resists extreme values but cannot be combined algebraically. That trade-off is exactly why this chapter studies five different averages — arithmetic mean, median, mode, geometric mean and harmonic mean — instead of just one, and closes (§11) by comparing where each is strongest and weakest.