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# Median2

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### Median2

1. 1. Median Princy Thomas
2. 2. Median <ul><li>The median is the middle of a distribution: half the scores are above the median and half are below the median. The median is less sensitive to extreme scores than the mean and this makes it a better measure than the mean for highly skewed distributions. The median income is usually more informative than the mean income, of central tendency </li></ul>
3. 3. Summary Measures Central Tendency Mean Median Mode Quartile Geometric Mean Summary Measures Variation Variance Standard Deviation Coefficient of Variation Range
4. 4. Median <ul><li>Robust Measure of Central Tendency </li></ul><ul><li>Not Affected by Extreme Values </li></ul><ul><li>In an Ordered Array, the Median is the ‘Middle’ Number </li></ul><ul><ul><li>If n or N is odd, the median is the middle number </li></ul></ul><ul><ul><li>If n or N is even, the median is the average of the 2 middle numbers </li></ul></ul>0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 12 14 Median = 5 Median = 5
5. 5. Individual series or ungrouped data <ul><ul><ul><ul><ul><li>First arrange the values in increasing order. </li></ul></ul></ul></ul></ul><ul><li>Median = size of n+1 th item 2 </li></ul>
6. 6. Question no 1 <ul><li>Find the median from the following data </li></ul><ul><li>4,45,60,20,83,19,26,11,27,12,52 </li></ul>
7. 7. Question No2 <ul><li>Find the median from the following data </li></ul><ul><li>35,23,45,50,80,61,92,40,52,61 </li></ul>
8. 8. Median 2 Discrete series
9. 9. Discrete Series <ul><ul><li>Find the cumulative frequency </li></ul></ul><ul><ul><li>Then calculate the measure of (N+1)/2 th item . </li></ul></ul><ul><li>The value we can easily locate with the help of the table. Here the variable is an integral value. </li></ul>
10. 10. Question No 1 <ul><li>Find the median from the following data </li></ul><ul><li>Wages 10 12 15 18 20 25 30 </li></ul><ul><li>.F 3 5 8 12 13 8 7 </li></ul>
11. 11. Note 1 <ul><li>if the series is is an inclusive one we should change the inclusive series into exclusive one. </li></ul><ul><li>For eg. 11-15 16-20 </li></ul><ul><li>10.5-15.5 15.5-20.5 </li></ul>
12. 12. Note 2 <ul><li>If the classes are not equal, make the classes equal </li></ul><ul><li>Wrong Form Right Method </li></ul><ul><li>10-15 10-20 </li></ul><ul><li>15-17.5 20-30 </li></ul><ul><li>17.5-20 30-40 </li></ul><ul><li>20-30 </li></ul><ul><li>30-35 </li></ul><ul><li>35-37.5 </li></ul><ul><li>37.5-40 </li></ul>
13. 13. Continuous Frequency distribution <ul><li>Prepare less than cumulative frequency </li></ul><ul><li>Find N/2 </li></ul><ul><li>See cumulative frequency just greater than N/2 </li></ul><ul><li>The corresponding class contains the median value and is called the median class </li></ul>
14. 14. The formula for median Class <ul><li>c.f- is the cumulative frequency of the class just preceding the median class </li></ul><ul><ul><li>C-magnitude of the class interval </li></ul></ul><ul><ul><li>f- frequency of the median class </li></ul></ul>
15. 15. Note 3 <ul><li>Median is the best suitable measure for open ended classes </li></ul>
16. 16. Question 1 <ul><li>Compute the median </li></ul><ul><li>Class 0-10 10-20 20-30 30-40 40-50 50-60 60-70 </li></ul><ul><li>Freq 8 12 20 23 18 7 2 </li></ul>
17. 17. Question <ul><li>Draw a less than cumulative frequency curve for the following data and find the median </li></ul>10 13 17 20 20 30 65 35 28 12 No of Workers 900-1000 800-900 700-800 600-700 500-600 400-500 300-400 200-300 100-200 0-100 Monthly income
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