Upload
jorie-roco
View
49
Download
0
Embed Size (px)
DESCRIPTION
statistics
Citation preview
Measure of Skewness andKurtosis
Dr. Romario Bhong P. Ybaez
Research Director
St. Paul University Dumaguete
Measure of Skewness and Kurtosis
Types of Skewness1. Skewed to the right distribution tapers more to the right longer tail to the rightmore concentration of values below than above more concentration of values below than above
the meanMean > Md > Momost skewed curves encountered in the social
sciences are skewed to the right
Monthly Income of Households in Barangay Maligaya, 2003
6
8
10
12
14
16
18
Nu
mb
er
of
Ho
useh
old
s
0
2
4
6
2.0 an d below
2.1 - 7 .0
7.1 - 12.0
12.1 - 17.0
17.1 - 22.0
22.1 - 27.0
27.1 - 32.0
Monthly Income (in 10,000 Pesos)
Nu
mb
er
of
Ho
useh
old
s
Examples: frequency distributions ofwages or salaries, use of electricity,weights of adult male human beings,family income
2. Skewed to the leftAges at Death of Inventors in Makulay Barangay
6
8
10
12
Nu
mb
er o
f In
v en
tors
0
2
4
45 1nd b elow
46 - 5051 - 55
56 - 6061 - 65
66 - 7071 and ab ove
Age at Death (in years)
Nu
mb
er o
f In
v en
tors
Formulas
1.
s
MoXSK
2.
s
MdxSK
)(3
Interpretation of SK: SK>0: positively skewed since the
mean > mode SK < 0: negatively skewed since the SK < 0: negatively skewed since the
mean < mode SK=0: symmetric since the mean =
mode
Example
Given the following scores: 80,92,85, 87, 94, 83, 88, 91, 92, and80.
Solution:Solution:
Mean =87.2, Median = 87.5, s= 5.09
SK=3(87.287.5)/5.09 = -0.18
Kurtosis
Measures of kurtosis look at how sharply the distribution rises to a peak and then drops away
MEASURE OF KURTOSIS Peakedness or flatness
1. Leptokurtic
2. Platykurtic2. Platykurtic
3. Mesokurtic
Formulas:
1
dataungroupedfor)(
1
41
4
4 S
XXn
n
n
ii
datagroupedfor
)(1
4
1
4
4 S
fXXf
n
iii
i
Computational formula
1090
13
2)(PP
Kkurtosis
Interpretation:K=3: mesokurticK>3: leptokurticK
Example:
Q3 = 91.75 Q1 = 83.5
P90 = 92.2 P10 = 80
5.8375.91 34.0
802.922
5.8375.91
)(
K