Agriculture Reference
In-Depth Information
Solution. Let the monthly expenditure on fuel
be Rs “
F
” and the prices of fuel of “
K
” for the
consecutive months be
n
i¼
1
f
i
P
n
P
5
i¼
1
f
i
P
HM
¼
¼
p
k
, respectively.
Then, average monthly consumption of fuel is
given by
p
1
,
p
2
,
...
,
5
i¼
1
f
i
=x
i
1
f
i
=x
i
i¼
5
þ
4
þ
3
þ
4
þ
4
20
¼
16
¼
149
¼
17
:
406
:
5
4
3
4
4
15
þ
20
þ
18
þ
12
þ
1
:
KF
¼
p
1
þ
F
F
p
2
þþ
F
Properties
1. It is rigidly defined.
2. It is easier to calculate than geometric mean.
3. It is easy to understand and calculate on the
basis of all observations.
4. The harmonic mean of the “
n
” number of
constants is the constant.
5. If any of the observation is zero, then the
harmonic mean cannot be defined.
p
K
KF
¼
1
p
1
þ
1
p
2
þþ
1
p
K
F
K
¼
¼
Harmonic mean of price of fuel
:
K
1
=
p
i
i¼
1
The relationship of Arithmetic Mean, Geo-
metric Mean, and Harmonic Mean:
Let
Use of the Different Types of Means
:
One has to be selective while choosing the type
of means to be used in different situations.
Arithmetic mean
x
1
,
x
2
,
x
3,
...
,
x
n
be the
n
positive values of
variable
“
X
”;
then,
for
arithmetic mean,
1
=n
,
P
n
is widely used in most of the
situations where the data generally do not follow
any definite pattern.
Geometric mean
is generally
used in a series of observations, both discrete and
continuous data, where the values are changing
in geometric progression (observation changes
in a definite ratio). The average rate of deprecia-
tion, compound rate of interest, etc. are some
examples where geometric mean can effectively
be used. GM is useful in the construction of index
numbers. As GM gives greater weights to smaller
items, it is useful in economic and socioeco-
nomic data. The
n
i¼
1
x
i
1
n
A ¼
1
x
i
, geometric mean,
G ¼ Π
i¼
n
P
n
and harmonic mean,
H ¼
;
A G H
.
1
x
i
i¼
1
Thus, for a given set of data which is meant to
be used must be decided based on the nature of
the data and its purpose of use.
Example 8.10.
Four different blends of teas at
Rs 200, Rs 250, Rs 400, and Rs 150 per kilogram.
He/she then mixed these four types of teas that
are to be sold. What could be the minimum
selling price (per kilogram) of tea?
use is very
restricted though it has ample uses in practical
fields particularly under changing scenario.
harmonic mean
Solution. Let a shopkeeper spend Rs(
) for
each quality of tea; then, he has spent altogether
4
X
the amount of his/her money. In the process,
he/she has bought
x
Example 8.9.
The price of petrol/diesel/kero-
sene oil changes frequently, particularly over
the growing seasons, and let us assume that a
farmer has a fixed amount of money on fuel
expenses for running pumps, etc., from his/her
monthly farm budget. So, the use of fuel is to be
organized in such a way that the above two
conditions are satisfied (the monthly expenditure
on fuel remains constant and the prices of fuel
changes over themonths); that is, the objective is to
get an average price of fuel per unit which suggests
the amount of average consumption of fuel.
X
X
X
/200,
/250,
/400, and
X
/150 kg of tea, respectively, for four different
qualities of tea. So the average purchasing price
of tea is 4
/150);
this is nothing but the harmonic mean of the
individual prices. Thus, the average purchasing
price is
X
/(
X
/200 +
X
/250 +
X
/400 +
X
¼
4
=
ð
1
=
200
þ
1
=
250
þ
1
=
400
þ
1
=
150
Þ
¼
4
=
ð
0
:
005
þ
0
:
004
þ
0
:
0025
þ
0
:
006
Þ
¼
4
=
0
:
0175
¼
228
:
57 per kilogram of tea
:
