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4
= Size of 39th item
=5 Q2 Q3 N + 1 th
= Median = Size of item
2 155 + 1 = Size of th item
2
= Size of 78th item
=6 N + 1 th
= Size of 3 item
4 155 + 1 th
= Size of 3 item
4
= Size of 117th item = 6.5
181 Bowley’ s Coefficient Skewness = Q 3 + Q1 − 2 Median
Q 3 − Q1 6.5 + 5 − 2 × 6
6.5 − 5
11.5 − 12
0.5
=
=
1.5
1.5
= − 0.33
= Example 23:
Calculate the value of the Bowley’ s coefficient of skewness from
the following series.
Wages : 1020 2030
(Rs)
No.of
Persons : 1
3
Solution:
Wages(Rs)
1020
2030
3040
4050
5060
6070
7080 3040 4050 5060 6070 7080 11 21 43 32 9 F
1
3
11
21
43
32
9
N=120 N
− m1
4
Q1 = l1 +
× c1
f1
N 120
=
= 30
4
4
Q1class = 4050
l1= 40, m1=15, f1=21, c1=10
182 c.f
1
4
15
36
79
111
120 30 − 15
× 10
21
150
= 40 +
21
= 40 + 7.14
= 47.14
N
−m
2
Q2 = Median = l +
×c
f
N 120
=
= 60
2
2 ∴Q1 = 40 + Medianal class = 50 − 60
l= 50 , m=36, f = 43, c=10
60 − 36
median
= 50 +
× 10
43
240
= 50 +
43
= 50 + 5.58
= 55.58
N
− m3
Q3 = l3 + 4
× c3
f3
N
120
3 = 3×
= 90
4
4
Q3 class = 60 −70
l3=60, m3=79, f3=32, c3=10
90 − 79
∴Q3 = 60 +
× 10
32
110
= 60 +
32
= 60 +3.44
= 63.44
183
3 Bowley’ s Coefficient of skewness Q 3 + Q1 − 2 Median
Q 3 − Q1
63.44 + 47.14 − 2 × 55.58
=
63.44 − 47.14 = 110.58 − 111.16
16.30
− 0.58
=
16.30
= − 0.0356
7.10.3 Measure of skewness based on moments:
The measure of skewness based on moments is denoted by
β1 and is given by:
= If µ3 is negative, then β1 is negative
7.11 Kurtosis:
The expression ‘ Kurtosis’ is used to describe the
peakedness of a curve.
The three measures – central tendency, dispersion and
skewness describe the characteristics of frequency distributions.
But these studies will not give us a clear picture of the
characteristics of a distribution.
As far as the measurement of shape is concerned, we have
two characteristics – skewness which refers to asymmetry of a
series and kurtosis which measures the peakedness of a normal
curve. All the frequency curves expose different degrees of flatness
or peakedness. This characteristic of...
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This note was uploaded on 01/18/2014 for the course BUS 100 taught by Professor Moshiri during the Winter '08 term at UC Riverside.
 Winter '08
 Moshiri
 Business

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