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Tablas estadísticas Medidas estadísticas Variable Bidimensional Probabilidad Variable Aleatoria Inferencia estadística Gráficas Gestión de alumnos
 
Statistics

Central Tendency Measures
Geometric Mean
Measures of Location
Measures of Position
Medidas de Forma

Kurtosis
Kurtosis is the statistical measure that tells us when a distribution is more or less peaked tahn a normal distribution.
  • A distribution that is less peaked than normal is called platykurtic.
  • A distribution identical to the normal distribution is called mesokurtic.
  • A distribution that is more peaked than normal is called leptokurtic.

platykurtic

mesokurtic

leptokurtic


Different formulae for measuring kurtosis are:

i) Moment coefficient of kurtosis

One measure of kurtosis uses the fourth moment about the mean expresses in dimensionless form:

which is often denoted as b2

ii) Excess kurtosis:

Kurtosis is more commonly defined as the fourth cumulant divided by the square of the second cumulant, which is equal to the fourth moment around the mean divided by the square of the variance minus 3,

  • means leptokurtic distribution.
  • means mesokurtic distribution.
  •  means platikurtic distribution.

iii) Percentile coefficient of kurtosis

Another measure of kurtosis is based on both quartiles and percentiles and is given by:

where is the semi-interquartile range.


The following frequency distribution indicates the test scores of 40 students in Educational Measurement and Evaluation. Calculate the coefficient of kurtosis.

C.I.
fi
65-69
2
60-64
2
55-59
3
50-54
1
45-49
6
40-44
11
35-39
8
30-34
3
25-29
2
20-24
2

Solution:

C.I.
fi
Xi

65-69
2
67
24.125
338742.188
677484.375
60-64
2
62
19.125
133784.492
267568.985
55-59
3
57
14.125
39806.4846
119419.454
50-54
1
52
9.125
6933.16431
6933.16431
45-49
6
47
4.125
289.531494
1737.18896
40-44
11
42
-0.875
0.58618164
6.44799805
35-39
8
37
-5.875
1191.32837
9530.62695
30-34
3
32
-10.875
13986.7581
41960.2742
25-29
2
27
-15.875
63511.8752
127023.75
20-24
2
22
-20.875
189891.68
379783.36
 
40
     
16311447.63

Where:

SD = 7.22

(leptokurtic)