Includes Solved practical problem of Harmonic mean step by step in individual, discrete and continuous series.

1. HARMONIC MEAN
INDIVIDUAL SERIES
1. 2475,475,75,5,0.5,0.05,0.005,0.0005
X 1/X
2475 1/2475=0.0004
475 1/475=0.0021
75 1/75=0.0133
5 1/5=0.2
0.5 1/0.5=2
0.05 1/0.05=20
0.005 1/0.005=200
0.0005 1/0.0005=2000
N=8 ∑1/x =2222.2158
H.M. = N
∑1/x
= 8/2222.2158
=0.0036
2. Discrete Series
X 10 20 40 60 120
f 1 3 6 5 4
X f f/x
10 1 1/10=.1000
20 3 3/20=.1500
40 6 6/40=.1500
60 5 5/60=.0833
120 4 4/120=.0333
N=19 ∑f/x =0.5166
H.M= N
∑f/x
= 19/0.5166
= 36.77

2. 3. Continuous Series
X 0-10 10-20 20-30 30-40 40-50
f 2 7 13 5 3
x f m f/m
0-10 10/2 2 5 2/5=0.400
10-20 30/2 7 15 7/15=0.467
20-30 50/2 13 25 13/25=0.520
30-40 70/2 5 35 5/35=0.143
40-50 90/2 3 45 3/45=0.067
N= 30 ∑f/m = 1.597
H.M.= N
∑f/m
= 30/1.597
= 18.79
Do it yourself
1. 10,20,30,40,60.
2.
X 10 20 25 40 50
f 20 30 50 15 5
3.
X 0-10 10-20 20-30 30-40 40-50
f 4 6 10 7 3
E-notes by
Asst. Prof. Harpreet Kaur
Sri Guru Granth Sahib World University,
Fatehgarh Sahib