Understanding Measures of Central Tendency in Statistics".
Learn about the concept of central tendency in statistics, including mean, median, and mode. Discover how these measures help to represent data accurately and efficiently. Explore the advantages and disadvantages of each measure and how to calculate them.
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U.G THIRD SEMESTER U.G THIRD SEMESTER UNIT UNIT- -1 1 TOPIC: MEASURE OF CENTRAL TENDENCY TOPIC: MEASURE OF CENTRAL TENDENCY NAME :MANOJ KUMAR DAS (Associate Professor in Commerce)
MEASURE OF CENTRAL TENDENCY 1. Concept and definition 2. Mean 3. Median 4. Mode Uses tendency Advantages measure Uses tendency. . Advantages and measure of of of different different measure measure of of central central and disadvantages of central disadvantages of central tendency of different different tendency . .
CONCEPT Data in nature has a tendency to cluster around a central value. That central value condenses the large mass of data into a single representative figure. The Central Value can be obtained from sample values called statistics and population observation called parameters.
DEFINITION A measure of central tendency is a typical value around which other figures congregate. Simpson and Kafka Simpson and Kafka Average is an attempt to find an single figure to describe a group of figure. Clark and Charade Clark and Charade
Mathematical Average o Arithmetic Mean o Geometric Mean o Harmonic Mean Positional Average o Median o Mode Mean ,Median,Mode arethe most commonly used measure of central tendency .
It is easy to understand and easy to calculate. It is rigidly defined, so that different persons may not interpret differently. It should be least affected by the sampling fluctuations. It should be based on all observation. It should not be unduly affected by the extreme values.
The Arithmetic Mean is the average of a set of numbers , calculated by adding up all the values and dividing the sum by the total number and values . Mean = X +X +X ..Xn n
MERITS It can be easily calculated. Its calculation is based on all observation. It is easy to understand. DEMERITS It is affected by extreme values. It can not be used for qualitative data . It can not be calculated if all the observation are not known
Median is defined as the middle most or the central value of the variable in a set of observation , when the observation are arranged either in ascending or descending order of their magnitudes. It is a positional average. It divides the series into two equal parts.
MERITS It can be used for qualitative data. It can be calculated graphically. It can be used for open ended distributions.
DEMERITS Not based on all observation . It is affected by sampling fluctuation. Not suitable for further mathematical treatment.
Mode is defined as the most frequently occurring measurement in a set of observation or a measurement of relatively great concentration , for some frequency distributions may have more than one such point of concentration ,even though these concentration might not contain precisely the same frequencies.
MERITS Mode is readily comprehensible and easy to calculate. Mode is not at all affected by extreme values. DEMERITS It is not based upon all observation. It is not amenable to further mathematical treatment.
