BS_2Harmonic Mean.pptx

Business Statistics- II B.Com.

1. Harmonic Mean Dr. RMKV SBKC

2. Harmonic Mean Is based on the reciprocals of numbers Is defined as the reciprocal of the arithmetic mean Individual observation H.M. = Discrete series H.M. = Continuous series H.M. =  

3. Illustration – Individual Observation 1. Find the Harmonic Mean from the following : 2574,475,75,5, 0.8,0.08, 0.005, 0.0009 2. Calculate Harmonic mean from the following data: 3834,382,63,8,0.4,0.03,0.009,0.0005

4. Solution – individual observation X 2574 0.0004 475 0.0021 75 0.0133 5 0.2000 0.8 1.2500 0.08 12.500 0.005 200.000 0.0009 1111.1111 N= 8 1325.0769 X 2574 0.0004 475 0.0021 75 0.0133 5 0.2000 0.8 1.2500 0.08 12.500 0.005 200.000 0.0009 1111.1111 N= 8 1325.0769 H.M. = = = 0.006 H.M = 0.006  

5. Solution – individual observation X 3834 0.0003 382 0.0027 63 0.0159 8 0.1250 0.4 2.5000 0.03 33.3333 0.009 111.1111 0.0005 2000.0000 2147.0883 X 3834 0.0003 382 0.0027 63 0.0159 8 0.1250 0.4 2.5000 0.03 33.3333 0.009 111.1111 0.0005 2000.0000 2147.0883 H.M. = = = 0.003726 H.M =0.003726  

6. Illustration – Discrete Series 1. From the following data compute the value of harmonic mean 2. The OT wage earned by workers of a factory are given below. Calculate the harmonic mean. Marks 10 20 30 40 50 No. of Students 20 30 50 15 5 OT wage 20 30 40 50 60 70 No. of Workers 40 20 70 10 30 10

7. Solution – Discrete series X f 10 20 2.000 20 30 1.500 30 50 1.667 40 15 0.375 50 5 0.100 120 5.642 X f 10 20 2.000 20 30 1.500 30 50 1.667 40 15 0.375 50 5 0.100 120 5.642 H.M. = = = 21.269 H.M =21.27  

8. Solution – Discrete series X f 20 40 2.000 30 20 0.667 40 70 1.750 50 10 0.200 60 30 0.500 70 10 0.143 180 5.26 X f 20 40 2.000 30 20 0.667 40 70 1.750 50 10 0.200 60 30 0.500 70 10 0.143 180 5.26 H.M. = = = 34.22 H.M =34.22  

9. Illustration – Continuous series From the following data compute the value of H.M. Compute the H.M. X 10-20 20-30 30-40 40-50 50-60 f 4 6 10 7 3 X 0-20 20-40 40-60 60-80 80-100 f 3 17 27 20 9

10. Solution – continuous series X m f 10-20 15 4 0.267 20-30 25 6 0.240 30-40 35 10 0.286 40-50 45 7 0.156 50-60 55 3 0.055 30 1.004 X m f 10-20 15 4 0.267 20-30 25 6 0.240 30-40 35 10 0.286 40-50 45 7 0.156 50-60 55 3 0.055 30 1.004 H.M. = = = 29.88 H.M =29.88  

11. Solution – continuous series X m f 0-20 10 3 0.300 20-40 30 17 0.567 40-60 50 27 0.540 60-80 70 20 0.286 80-100 90 9 0.100 76 1.793 X m f 0-20 10 3 0.300 20-40 30 17 0.567 40-60 50 27 0.540 60-80 70 20 0.286 80-100 90 9 0.100 76 1.793 H.M. = = = 42.387 H.M =42.39