Measures of Central Tendency (Averages)

Measures of Central Tendency, also called Averages, are representative of the entire distribution. It is the central value of a data set representing the whole data in a single number.

There are five commonly used measures of central tendency:

  1. Arithmetic mean
  2. Median
  3. Mode
  4. Geometric mean
  5. Harmonic Mean

Note: From the viewpoint of Econometrics, only Arithmetic Mean is important. Therefore, we will not talk in detail about these topics. A brief sketch is given below.

  1. Arithmetic Mean: Arithmetic Mean is a simple average of observations in a distribution. It can easily be calculated by dividing the summation of all observations by the number of observations. Symbolically: \[\bar X = \frac{{\sum {{X_i}} }}{n}\]
    Note: population mean is generally denoted by the symbol \(\mu\) and sample mean is generally denoted by \(\bar X\).
  2. Median: Median is one of the values in the data series which divides the data series into two equal parts.
  3. Mode: Mode is the value in a data series that occurs most frequently.
  4. Geometric Mean: Geometric Mean is the \(nth\) root of the product of \(n\) observations in a data series. Symbolically: \[G = {\left( {{X_1} \cdot {X_2},…,{X_n}} \right)^{\frac{1}{n}}}\]
  5. Harmonic Mean: Harmonic Mean is the reciprocal of summation of reciprocal of all observation divided by the number of observations. Symbolically: \[H = \frac{1}{{\frac{1}{n}\sum\limits_{i = i}^n {\left( {\frac{1}{{{X_i}}}} \right)} }}\]

Questions for practice will be updated soon on the website with solutions. To read more about these topics, you should consult Statistics for Economics, NCERT, Class – 11. For advanced reading, you should consult Fundamentals of Mathematical Statistics by S. C. Gupta and V. K. Kapoor. Here, only essential part of the topic has been discussed.

We will be using Arithmetic Mean frequently throughout the Statistics & Econometrics course.

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