# Measures of Central Tendency

• ### Average and Types of Averages

Average:   “A single value which can represent the whole set of data is called an average”. If the average tends to lie or indicating the center of the distribution is called measure of central tendency or sometimes they locate the general position of the data, so they are also called measure of location. Desirable […]

• ### Arithmetic Mean

It is the most commonly used average or measure of the central tendency applicable only in case of quantitative data. Arithmetic mean is also simply called “mean”. Arithmetic mean is defined as: “Arithmetic mean is quotient of sum of the given values and number of the given values”. The arithmetic mean can be computed for […]

• ### Examples of Arithmetic Mean

Example (4): The following data shows distance covered by persons to perform their routine jobs. Distance (Km) Number of Persons Calculate Arithmetic Mean by Step-Deviation Method; also explain why it is better than direct method in this particular case.  Solution: The given distribution belongs to a grouped data and the variable involved is ages of […]

• ### Merits and Demerits of Arithmetic Mean

Merits: It is rigidly defined. It is easy to calculate and simple to follow. It is based on all the abservations. It is determined for almost every kind of data. It is finite and not indefinite. It is readily put to algebraic treatment. It is least affected by fluctuations of sampling. Demerits: The arithmetic mean […]

• ### Weighted Arithmetic Mean

In calculation of arithmetic mean, the importance of all the items was considered to be equal. However, there may be situations in which all the items under considerations are not equal importance. For example, we want to find average number of marks per subject who appeared in different subjects like Mathematics, Statistics, Physics and Biology. […]

• ### Geometric Mean

It is another measure of central tendency based on mathematical footing like arithmetic mean. Geometric mean can be defined in the following terms: “Geometric mean is the nth positive root of the product of “n” positive given values” Hence, geometric mean for a value containing values such as is denoted by of and given as […]

• ### Merits and Demerits of Geometric Mean

Merits: It is rigidly defined and its value is a precise figure. It is based on all observations. It is capable of further algebraic treatment. It is not much affected by fluctuation of sampling. It is not affected by extreme values. Demerits: It cannot be calculated if any of the observation is zero or negative. […]

• ### Properties of Geometric Mean

The main properties of geometric mean are: The geometric mean is less than arithmetic mean, The product of the items remains unchanged if each item is replaced by the geometric mean. The geometric mean of the ratio of corresponding observations in two series is equal to the ratios their geometric means. The geometric mean of […]

• ### Harmonic Mean

Harmonic mean is another measure of central tendency and also based on mathematic footing like arithmetic mean and geometric mean. Like arithmetic mean and geometric mean, harmonic mean is also useful for quantitative data. Harmonic mean is defined in following terms: Harmonic mean is quotient of “number of the given values” and “sum of the […]

• ### Merits and Demerits of Harmonic Mean

Merits: It is based on all observations. It not much affected by the fluctuation of sampling. It is capable of algebraic treatment. It is an appropriate average for averaging ratios and rates. It does not give much weight to the large items Demerits: Its calculation is difficult. It gives high weight-age to the small items. […]

• ### Concept of Mode

Mode is the value which occurs the greatest number of times in the data. When each value occur the same numbers of times in the data, there is no mode. If two or more values occur the same numbers of time, then there are two or more modes and distribution is said to be multi-mode. […]

• ### Graphic Location of Mode

Graphic Location of Mode: Mode being a positional average so it can be located graphically by the following process. A histogram of the frequency distribution is drawn. In histogram, the highest rectangle represents the model class. The top left corner of the highest rectangle is joined with the top left corner of the following rectangle […]