
Measures of Central Tendency
121
Chapter 3
PB
Harmonic mean for discrete and continuous frequency distributions
H =
N
f
x
i
i
i
n
1
1
⎛
⎝
⎜
⎞
⎠
⎟
=
∑
where
i
i
n
=
=
∑
1
where x
1
, x
2
, x
3
, …, x
n
are the items of a data series and f
1
, f
2
, f
3
, …, f
n
are their corresponding frequencies. N = f
1
+ f
2
+ f
3
+
…
+ f
n
Weighted harmonic mean
w
where x is the value of the item, and w the weights attached to corresponding items.
Relationship between AM, GM, and HM
AM ≥ GM ≥ HM
When all the observations are same, the equality sign holds, that is,
AM = GM = HM (When all the observations are equal)
For any two observations
()()
()
GM AM HM
GM AM HM
2
=×
⇒= ×
Median for individual frequency ...