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- 1. 14-04-2012 Research Methodology Dr. Nimit Chowdhary, Professor Mean Arithmetic mean Geometric Mean Median Harmonic Mean Mode Trimmed mean© Dr. Nimit Chowdhary Research Methodology 2 Saturday, April 14, 2012 1
- 2. 14-04-2012 Measures of central There are hundred of tendency refer to the colleges in India summary measures Each college has used to describe the different tuition most "typical" value in Average college tuition a set of values. is Rs. 2000 Central tendency Mean MedianSaturday, April 14, 2012 © Dr. Nimit Chowdhary Research Methodology Workshop p. 3 Compute mean and median Explain pros and cons of each measure Describe how they change after: Adding a constant to each value in the data set Multiplying each value in the data set by a constantSaturday, April 14, 2012 © Dr. Nimit Chowdhary Research Methodology Workshop p. 4 2
- 3. 14-04-2012 Computing mean is a two step process 1. Find the sum of all values in a group of values 2. Divide the sum by the number of values in the group Sum of all values Mean Number of valuesSaturday, April 14, 2012 © Dr. Nimit Chowdhary Research Methodology Workshop p. 5POPULATION MEAN SAMPLE MEAN = Sum the following = Sum the following X = Sum all X values x = Sum all x values N = Number of X values n = Number of x values = Population mean x = sample mean X x x N nSaturday, April 14, 2012 © Dr. Nimit Chowdhary Research Methodology Workshop p. 6 3
- 4. 14-04-2012BOWLING SCORE Game Score X / N 1 100 2 170 X 100 170 130 140 540 3 130 N 4 4 140 X / N 540/ 4 135 Mean bowling scoreSaturday, April 14, 2012 © Dr. Nimit Chowdhary Research Methodology Workshop p. 7The median is the midpoint in a set of data List scores from smallest to largest With an odd number of scores, the median is the middle score With an even number of scores, the median is the sum of the middle two scores divided by 2 Median= Sum of middle two scores / 2Saturday, April 14, 2012 © Dr. Nimit Chowdhary Research Methodology Workshop p. 8 4
- 5. 14-04-2012BOWLING SCORE Game Score List the scores in ascending order 1 100 100 130 140 160 170 2 170 3 130 With an odd number of scores, identify the middle 4 140 score 5 160 100 130 140 160 170BOWLING SCORE List the scores in ascending order Game Score 100 130 140 170 1 100 With an even number of scores, identify the two 2 170 middle scores 3 130 100 130 140 170 The median is the sum of 4 140 the middle scores divided by two 130 140 Median 135 2 5
- 6. 14-04-2012 MEAN MEDIAN The mean is better if a The median is better if a large set of scores does not small set of scores has an have an outlier outlierRs. 60,000/- Rs. 70,000/- Rs. 80,000/- Rs. 90,000/- Rs. 10,000,000/- Mean: = X/ N = (60,000 + 70,000 + 80,000 + 90,000 + 10,000,000) = Rs. 2,060,000 Median: Rs. 80,000/- Saturday, April 14, 2012 © Dr. Nimit Chowdhary Research Methodology Workshop p. 12 6
- 7. 14-04-2012Marks obtained by 30 students of class X of acertain school in a mathematics text consistingof 100 marks are as follows: Marks Number of Marks Number of obtained students obtained students 10 1 70 4 20 1 72 1 36 3 80 1 40 4 88 2 50 3 92 3 56 2 95 1 60 4Saturday, April 14, 2012 © Dr. Nimit Chowdhary Research Methodology Workshop p. 13 Marks obtained (xi) No. of students (fi) f ix i 10 1 10 20 1 20 36 3 108 40 4 160 50 3 150 56 2 112 60 4 240 70 4 280 72 1 72 80 1 80 88 2 176 92 3 276 95 1 95 Total fi=30 fixi = 1779 7
- 8. 14-04-2012 Mean fx i i 1779 59.3 f i 30 Class interval No. of students Class mark (xi) f ix i (fi) 10-25 2 17.5 35.0 25-40 3 32.5 97.5 40-55 7 47.5 332.5 55-70 6 62.5 375.0 70-85 6 77.5 465.0 85-100 6 92.5 555.0 fi= 30 fixi =1860.0 Mean fx i i 1860 62 f i 30Saturday, April 14, 2012 © Dr. Nimit Chowdhary Research Methodology Workshop p. 16 8
- 9. 14-04-2012Suppose we have to find the median of thefollowing data which gives the marks, out of50, obtained by 100 students in a test. Marks obtained 20 29 28 33 42 38 43 25 No. of students 6 28 24 15 2 4 1 20Saturday, April 14, 2012 © Dr. Nimit Chowdhary Research Methodology Workshop p. 17 No. of data points is even, 100 The median is the middle-most value, that is, the value between 50th and 51st points Median will therefore be the average of 50th and 51st pointSaturday, April 14, 2012 © Dr. Nimit Chowdhary Research Methodology Workshop p. 18 9
- 10. 14-04-2012 Marks obtained No. of students Cumulative frequency 20 6 6 25 20 26 28 24 50 29 28 78 33 15 93 38 4 97 42 2 99 43 1 100Saturday, April 14, 2012 © Dr. Nimit Chowdhary Research Methodology Workshop p. 19 n/2 th value is 50th, that is 28 (n/2 + 1)th value is 51st , that is 29 So the median is 28 29 Median 28.5 2Saturday, April 14, 2012 © Dr. Nimit Chowdhary Research Methodology Workshop p. 20 10
- 11. 14-04-2012 n 2 cf Median l h f Where, l = Lower limit of median class n = Number of observations cf = Cumulative frequency of class preceding median class f = Frequency of median class h = Class size Saturday, April 14, 2012 © Dr. Nimit Chowdhary Research Methodology Workshop p. 21A survey of heights (in cm) of 51 girls of class Xof a school was conducted and the followingdata was obtained Height in cms No. of girls Less than 140 4 Less than 145 11 Less than 150 29 Less than 155 40 Less than 160 46 Less than 165 51Saturday, April 14, 2012 © Dr. Nimit Chowdhary Research Methodology Workshop p. 22 11
- 12. 14-04-2012 Create a frequency table Class intervals Frequency Cumm. frequency Below 140 4 4 140-145 7 11 145-150 18 29 150-155 11 40 155-160 6 46 160-165 5 51Saturday, April 14, 2012 © Dr. Nimit Chowdhary Research Methodology Workshop p. 23 n= 51, therefore n/2 n =25.5; this means cf Median l 2 h 145-150 is the median f class l= 145 25.5 11 cf= 11 Median 145 5 18 f= 18, and h= 5 72.5 145 18 149.03Saturday, April 14, 2012 © Dr. Nimit Chowdhary Research Methodology Workshop p. 24 12
- 13. 14-04-2012 Two important measures of central tendency- mean and median Grouped and ungrouped data How to calculate mean How to calculate median When to use mean and when to use medianSaturday, April 14, 2012 © Dr. Nimit Chowdhary Research Methodology Workshop p. 25 13

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