Fundamentals of Business Mathematics and Statistics · Measures of Central Tendency and Dispersion

Objectives and Requisites of Averages in Statistics

Updated 10 October 2026 · Fact-checked

A measure of central tendency, or average, is a single value that represents the centre of a whole data set. Its objectives are to summarise data and allow comparison. A good average is rigidly defined, easy to understand and calculate, based on all items, stable under sampling and suitable for further algebraic treatment.

Understand Objectives and Requisites of Averages

Imagine you have the marks of 500 students. Nobody can read 500 numbers and understand them. You need one number that tells you where the marks are centred. That number is an average, also called a measure of central tendency.

Data tends to cluster around a central value. The average points to that cluster. This is why it is called a measure of central tendency.

Averages have two main objectives. First, condensation: they reduce a large mass of data to one representative figure. Second, comparison: you can compare two groups, such as the average sales of two shops or the average wages in two factories, using one figure each. Averages also help in decision-making and in further statistical work such as dispersion and correlation.

The common averages are the arithmetic mean, median, mode, geometric mean and harmonic mean. The first three are the most used. The arithmetic mean, geometric mean and harmonic mean are mathematical averages, calculated from all the values. Median and mode are positional averages, because they depend on the position or frequency of values.

Not every average suits every situation. The requisites of a good average are the qualities you use to judge which average to choose. The exam tests these qualities, and also which average meets which quality.

Key formulas to remember

Requisites of a good average: Rigidly defined; easy to understand; easy to calculate; based on all observations; not unduly affected by extreme values; least affected by sampling fluctuations; suitable for further algebraic treatment; Learn this list. Questions ask which quality an average satisfies or fails.
Types of averages: Mathematical: AM, GM, HM. Positional: Median, Mode; Mean-type averages use all values. Median and mode are positional averages that depend on position or frequency.
Which averages are affected by extreme values: AM is greatly affected by extreme values. GM and HM also use all items, so they are affected too, but less than AM for large values. HM is affected most by very small values. Median and mode are not unduly affected by extreme values.; Mode resists extreme values but may be ill-defined or not unique. GM and HM are not suitable when any value is zero or negative.

How to solve Objectives and Requisites of Averages questions

Use this method for any question on the meaning, objectives or qualities of averages.

1Read the question and find whether it asks for a meaning, an objective, a quality or a comparison of averages.
2If it asks for a meaning, recall that an average is a single value representing the centre of the data.
3If it asks for a quality, match it to the list of requisites: rigid definition, simplicity, all items used, stability, extreme values, algebraic treatment.
4Decide whether the average named is mathematical (AM, GM, HM) or positional (median, mode).
5Check the data situation: extreme values, open-ended classes or qualitative data change which average is suitable.
6Eliminate options that overstate a property, such as saying median is based on all items.
7Pick the option that is true without exception for the average named.

Quickest way: Property grid recall

When to use it: Use this for any MCQ asking which average has or lacks a quality.

Remember: AM, GM and HM use all items and are rigidly defined. All three are affected by extreme values, AM the most for large values.
Remember: GM and HM cannot be used when values are zero or negative.
Remember: median and mode are positional averages. They do not use all values and are not unduly affected by extreme values.
Remember: AM is the one most used in further algebraic work.
Remember: mode may be not unique or may not exist, so it is not always rigidly defined.
Match the option to this grid and cross out contradictions.

Common mistakes in Objectives and Requisites of Averages

Saying the median is based on all observations.
Students know it is a central value and assume all items count.
Fix: Median is found from the position of the middle value. It does not use the size of every value.
Saying the arithmetic mean is not affected by extreme values.
Mixing up mean with median.
Fix: Every value enters the AM, so a very large or small value shifts it. Median is not unduly affected by this.
Calling mode a rigidly defined average.
Mode looks simple as the most frequent value.
Fix: A data set can have no mode or several modes, so it is not always rigidly defined.
Thinking an average must be one of the actual data values.
Students link average with the middle item.
Fix: AM often is not an observed value. The average of 2 and 3 is 2.5.
Confusing the objective of averages with that of dispersion.
Both appear in the same chapter.
Fix: Averages give the central value for condensation and comparison. Dispersion measures spread.

Worked examples

Example 1

Which of the following is NOT a requisite of a good average? (A) It should be rigidly defined (B) It should be based on all observations (C) It should be unduly affected by extreme values (D) It should be easy to calculate

Show the solution

List the requisites: rigidly defined, easy to understand and calculate, based on all items, not unduly affected by extreme values, stable, suitable for algebraic treatment.
Options A, B and D match requisites: rigid definition, use of all items, and ease of calculation.
Option C states the opposite of the requisite that an average should not be unduly affected by extreme values.

Answer: (C)

Example 2

The monthly incomes (₹) of five people are 20,000, 22,000, 24,000, 26,000 and 3,08,000. What is the median income? (A) ₹80,000 (B) ₹24,000 (C) ₹22,000 (D) ₹26,000

Show the solution

Arrange the incomes in order: 20,000, 22,000, 24,000, 26,000, 3,08,000.
There are 5 values, so the median is the (5 + 1) ÷ 2 = 3rd value.
The third value is ₹24,000.
Note that ₹80,000 is the mean (4,00,000 ÷ 5), pulled up by the extreme value 3,08,000. It is not the median.
The median is not affected by the size of the extreme value, only by its position, so it is more representative of a typical person here.

Answer: (B) ₹24,000

Exam tips

Memorise the requisites list and which average fails each one.
Questions often use phrases like 'not unduly affected by extreme values'. Link that phrase to median and mode.
With no negative marking, always attempt every property question. Eliminate the absolute statements first.
Remember AM is the most widely used average because it suits algebraic treatment.
Remember mode is not unduly affected by extreme values, but it may be ill-defined or not unique.
Watch for the word NOT in the question stem before choosing.

Practice questions from Measures of Central Tendency and Dispersion

Objectives and Requisites of Averages: frequently asked questions

What is a measure of central tendency?

It is a single value that represents the centre or typical value of a data set. Examples are mean, median and mode. It condenses data and helps comparison.

What are the requisites of a good average?

A good average should be rigidly defined, easy to understand and calculate, based on all observations, not unduly affected by extreme values, stable across samples and suitable for further algebraic treatment.

Which average is best?

No average is best in every case. The arithmetic mean satisfies most requisites, but median suits data with extreme values and mode suits the most common item.

What are the types of averages with examples?

The main types are arithmetic mean, median, mode, geometric mean and harmonic mean. For data 2, 4, 6 the arithmetic mean is 4 and the median is also 4.