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# Combined Mean & Weighted Mean

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### Combined Mean & Weighted Mean

1. 1. Combined Mean
2. 2. Combined Mean <ul><li>  </li></ul><ul><li>The arithmetic mean of several sets of data may be combined into a single arithmetic mean for the combined sets of data </li></ul>
3. 3. Formula <ul><li>For two sets of data the combined Mean is </li></ul><ul><li>  </li></ul><ul><li>  </li></ul><ul><ul><li>Where X1 is the no of items in the first group </li></ul></ul><ul><li>  </li></ul>
4. 4. Question No 1 <ul><li>If a sample size of 22 items has a mean of 15 and another sample size of 18 items has a mean of 20. Find the mean of the combined sample? </li></ul>
5. 5. Class work <ul><li>The mean annual salary paid to all employees of a company was Rs.5000. The mean annual salary paid to male and female employees were Rs.5200 and Rs.4200 respectively. Determine the percentage of males and females employed by the company </li></ul>
6. 6. HW <ul><li>The average salary of male employees in a firm was Rs.520 and that of females was Rs.420.The mean salary of all the employees was Rs.500 . Find the percentage of male and female employees. </li></ul>
7. 7. Weighted Mean
8. 8. Weighted Mean <ul><li>Let w 1 ,w 2 ,….. w n be the weights attached to a variable values X1,X2,X3…Xn respectively then the weighted A.M generally denoted by </li></ul><ul><li> WX /  w </li></ul>
9. 9. Question no 1 <ul><li>A candidate Obtains the following percentage of marks . English 60,Hindi 75,Mathematics 63, Physics 60,Chemistry 55. Find the weighted mean if weights are 1,1,2,3,3 respectively to allotted subjects. </li></ul>
10. 10. Question no 2 <ul><li>Comment upon the performance of the students of two colleges given below using the weighted average. </li></ul>Passed Appeared Passed Appeared 52 80 72 120 B.Com 70 100 150 200 B.A 90 120 45 50 M.Com 80 100 24 30 M.A B College A College Course
11. 11. Summary <ul><li>The mean is used in computing other statistics (such as the variance) and does not exist for open-ended grouped frequency distributions. It is often not the most appropriate measure for skewed (unbalanced) distributions such as salary information. </li></ul>
12. 12. Thanks