Measures of Central Tendancy

Central tendancy measures such as average, arithmetic mean, and methods for calculating mean in individual and discrete series are discussed in this content. Learn about the characteristics of a good average and different types of averages like arithmetic mean, geometric mean, harmonic mean, median, and mode. Explore direct and shortcut methods for finding arithmetic mean in various scenarios.

• Central Tendancy
• Average
• Arithmetic Mean
• Methods
• Individual Series

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Uploaded on Feb 26, 2025 | 0 Views

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Presentation Transcript

1. MEASURES OF CENTRAL TENDANCY

2. AVERAGE Average is a single value which is the representative of whole data i.e. the value which describe the whole figures of the observation It lies between the two extreme of the series. CHARACTERISTIC OF A GOOD AVERAGE : Must be rigidly defined . Should be based on all observation. * It should be easily understood. Should be capable of further algebraic calculations. * It should not affected by extreme values. It should have sampling stability. *

3. TYPES OF AVERAGES The following are the important types of averages : A)Mathematical Averages Arithmetic mean Geometric mean Harmonic mean B)Positional Averages Median Mode

4. ArithmeaticMean The arithmetic mean is defined as being equal to the sum of the numerical values of the observation divided by the total number of observation. CALCULATION OF ARITHMETIC MEAN (IN CASE OF INDIVIDUAL SERIES) Lets take an example: Calculate the arithmetic mean of the marks obtained by a group of 10 students. Individual marks obtained are as follows: Student 1 2 3 4 5 6 7 8 9 10 Marks 20 48 39 51 45 69 54 29 60 35

5. There are two methods for finding arithmetic mean in case of individual series DIRECT METHOD SHORT CUT METHOD Mean= X/N Mean= A+ d/N Where A is Assumed Mean and D= X-A In the above question: Let A =39 D or (X-A)= 60 =39 + 60/10 =39+6 =45 X X-A 20 -19 Where X is sum of all observation & N is number of observation. In the above question ; 20+48+39+51+45+69+54+29+60+35 10 =450/10 =45 48 9 39 0 51 12 45 6 69 30 54 15 29 -10 60 21 35 -4

6. Calculation of Arithmetic mean in case of discrete series Discrete series means where frequencies of a variable are given without giving class interval There are two methods of calculating mean; Direct Method Mean = f x / f Short cut Method Mean =A+ f d x / f Question: Calculate A.M. from the following data Marks Obtained 4 8 12 16 20 No.Of Students 6 12 18 15 9

7. Direct Method x f fx Dx(X-A) fdx 4 6 24 -8 -48 8 12 96 -4 -48 12 18 216 0 0 16 15 240 4 60 20 09 180 8 72 f=60 fx=756 dx=0 fdx=36

8. Direct Method : Mean= 756/60 =12.6 Short Cut Method: A+ fdx / f =12+36/60 (putting values in formula) =12+0.6 =12.6