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# Meanch3

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### Meanch3

1. 1. Measures of Central tendency Princy
2. 2. Measures of Central Tendency or (Measures of Location)   <ul><li>Enable us to locate the position of the distribution in the question   </li></ul><ul><li>Measures of central tendency are measures of the location of the middle or the center of a distribution. The mean is the most commonly used measure </li></ul>
3. 3. Summary Measures Central Tendency Mean Median Mode Quartile Geometric Mean Summary Measures Variation Variance Standard Deviation Coefficient of Variation Range Harmonic Mean Mean Deviation
4. 4. Various measures of central tendency are <ul><li>Arithmetic Mean </li></ul><ul><li>Harmonic Mean Mathematical Averages </li></ul><ul><li>Geometric Mean </li></ul><ul><li>Median </li></ul><ul><li>Mode Positional average </li></ul>
5. 5. Measures of Central Tendency Central Tendency Mean Median Mode Geometric Mean Harmonic Mean
6. 6. Mean (Arithmetic Mean) <ul><li>The Most Common Measure of Central Tendency </li></ul><ul><li>Affected by Extreme Values (Outliers) </li></ul>(continued) 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 12 14 Mean = 5 Mean = 6
7. 7. Mean (Arithmetic Mean) <ul><li>Mean (Arithmetic Mean) of Data Values </li></ul><ul><ul><li>Sample mean </li></ul></ul><ul><ul><li>Population mean </li></ul></ul>Sample Size Population Size
8. 8. Arithmetic mean <ul><li>The arithmetic mean is what is commonly called the average: </li></ul><ul><li>The mean of a numeric variable is calculated by </li></ul><ul><ul><ul><li>adding the values of all observations in a data set and then dividing that sum by the number of observations in the set. This provides the average value of all the data. </li></ul></ul></ul><ul><li>. It is a method representing whole data by one figure </li></ul>
9. 9. . Example <ul><li>Mount Rival hosts a soccer tournament each year. This season, in 10 games, the lead scorer for the home team scored 7, 5, 0, 7, 8, 5, 5, 4, 1 and 5 goals. What was the mean score? </li></ul><ul><li>Mean = sum of all the observed values ÷ number of observations            = (7 + 5 + 0 + 7 + 8 + 5 + 5 + 4 + 5 + 1) ÷ 10            = 47 ÷ 10            = 4.7// </li></ul><ul><li>  </li></ul>
10. 10. Individual Series Example <ul><li>The marks obtained by 11 students in Presidency College are </li></ul><ul><li>Roll no 1 2 3 4 5 6 7 8 9 10 11 </li></ul><ul><li>Marks 40 38 60 62 65 35 20 30 80 86 90 </li></ul><ul><li>Calculate the Arithmetic mean? </li></ul>
11. 11. ANSWER <ul><li>A.M x =  x/N </li></ul><ul><li>= 40+38+60+62+65+35+20+30+80+86+90 </li></ul><ul><li>11 = </li></ul><ul><ul><ul><ul><li>= 606 </li></ul></ul></ul></ul><ul><ul><ul><ul><ul><li>11 </li></ul></ul></ul></ul></ul><ul><li>= 55.09// </li></ul>
12. 12. Problem 2 <ul><li>The Mean weight of a student in a group of 6 students is 119 lbs.The individual weight of five of them are 115,109,129,117,114 lbs.What is the weight of the sixth student? </li></ul><ul><li>130 </li></ul>
13. 13. Discrete series <ul><li>Discrete series refer to a series when actual size of items(individual measurement) and corresponding frequencies are given </li></ul>
14. 14. For finding the mean of a discrete variable three Methods are there <ul><li>Direct Method </li></ul><ul><li>Short cut method </li></ul><ul><li>Step deviation Method </li></ul>
15. 15. Direct method <ul><li>The arithmetic mean is the sum of the products of the values of the items and corresponding frequencies divided by total frequencies </li></ul><ul><li>Formula  </li></ul>x =  fx /  f where  f =N (total no of frequency) Where x is the sample mean,  f is the sum of the frequencies in each class
16. 16. Example 1 <ul><li>Calculate the arithmetic mean from the following data (by direct method)? </li></ul><ul><li>5 15 25 35 45 55 65 75 </li></ul><ul><li>7 11 16 17 26 31 1 1 </li></ul>