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- 1. Measures of Central tendency Princy
- 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. 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. 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. Measures of Central Tendency Central Tendency Mean Median Mode Geometric Mean Harmonic Mean
- 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. 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. 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. . 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. 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. 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. 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. 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. 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. 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. 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>
- 17. Answer
- 18. 2.Short cut method <ul><li>Formula </li></ul><ul><li> </li></ul><ul><li> </li></ul><ul><li>Where A is the assumed mean , x is the actual mean, f or N is the sum of the frequencies in each class </li></ul>
- 19. Example 1 <ul><li>Calculate the arithmetic mean from the following data by shortcut 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>
- 20. Answers
- 21. Arithmetic Mean b y step Deviation Method <ul><li>The Formula is </li></ul><ul><li>i is the magnitude of the class interval </li></ul>
- 22. Example 1 <ul><li>Calculate the arithmetic mean from the following data by step deviation method 5 15 25 35 45 55 65 75 </li></ul><ul><li>7 11 16 17 26 31 1 1 </li></ul>
- 23. Answer
- 24. HW 1 <ul><li>Soccer tournament at Mount Rival I </li></ul><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>
- 25. Hw.2 The following table lists the number of people killed in traffic accidents over a 10 year period. During this time period, what was the average number of people killed per year? How many people died each day on average in traffic accidents during this time period? Table 1. Number of fatalities in traffic accidents Year Fatalities 1 959 2 1,037 3 960 4 797 5 663 6 652 7 560 8 619 9 623 10 583
- 26. HW 3 In an office there are 84 employees. Their salaries are given Below 1.Find the mean salary of the employees 2.What is the total salary of the employees
- 27. HW 4 <ul><li>The Calculate arithmetic mean of the weight of ten students in a class </li></ul>
- 28. HW 5 <ul><li>Find the missing frequency from the following data </li></ul><ul><li>The average mark is 16.82 </li></ul><ul><li>Ans: x = 18 </li></ul>
- 29. Hw 6 <ul><li>In the frequency distribution of 100 families given below the number of families corresponding to the expenditure groups and 60-80 are missing from the table.However the mean of the distribution is known to be 50.Find the missing frequencies </li></ul>
- 30. Thanks

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