Titel_SS06

01.0102.01

03.01

04.0105.01

06.01

07.01

08.0109.01

10.01

11.0112.01

13.01

14.01

15.0116.01

17.01

18.0119.01

20.01

21.0122.01

23.01

24.01

25.0126.01

27.01

28.0129.01

30.01

(^30874664)
4164
(^37104029)
4323
4041
(^37374103)
5457
(^45633906)
4419
4359
(^46675098)
6551
(^43713578)
4366
(^43684588)
5001
7118
(^47274085)
4741
(^47395193)
5892
31.01 7974
(^30873578)
3710
(^37373906)
4029
4041
(^40854103)
4164
(^43234359)
4366
4368
(^43714419)
4563
(^45884664)
4667
(^47274739)
4741
5001
(^50985193)
5457
(^58926551)
7118
7974
(^36777357)
9323
11748
(^102564453)
4815
(^47574672)
5401
(^56886308)
4946
4635
(^51004791)
5235
(^45605729)
5005
(^44804880)
4928
5398
(^46486183)
5220
(^50135281)
5318
5679
3677
4453
4480
(^45604635)
4648
4672
(^47574791)
4815
(^48804928)
4946
5005
(^50135100)
5220
(^52355281)
5318
(^53985401)
5679
5688
(^57296183)
6308
(^73579323)
10256
11748
1
2
(^34)
5
6
(^78)
9
(^1011)
12
13
(^1415)
16
(^1718)
19
(^2021)
22
23
(^2425)
26
(^2728)
29
30
31
i Date
Direction 1 Direction 2
xi xiO
Unordered Ordered
xi xOi
Unordered Ordered
01.01
02.01
03.0104.01
05.01
06.01
07.0108.01
09.01
10.0111.01
12.01
13.0114.01
15.01
16.01
17.0118.01
19.01
20.0121.01
22.01
23.01
24.0125.01
26.01
27.0128.01
29.01
30.0131.01
Date
Table 2.3: Daily traffic flow through the Gotthard tunnel, January 1997.
Other Measures
Whereas the sample mean, mode and median are central measures of a data set, and the
sample variance is a measure of the dispersion around the sample mean it is also useful to
have some characteristic indicating the degree of symmetry of the data set. To this end the
sample coefficient of skewness, which is a simple logical extension of the sample variance is
suitable. The sample coefficient of skewness  is defined as:
3
1
3

(-)

1

n

i

i

x x

ns

 



(2.15)

This coefficient is positive if the mode of the data set is less than its mean value (skewed to
the right) and negative if the mode is larger than the mean value (skewed to the left). For the
concrete cube compressive strength data (Table 2.2) the sample coefficient of skewness is –
0.12. For the traffic flow data (Table 2.3) the observations in direction 1 and 2 have a
skewness coefficient of 1.54 and 2.25 respectively. The coefficients are positive and that
shows that both distributions are skewed to the right.

In a similar way the sample coefficient of kurtosis  is defined as:

4

1

4

(-)

1

n

i

i

x x

ns

 



(2.16)

which is a measure of how closely the data are distributed around the mode (peakedness).
Typically one would compare the sample coefficient of kurtosis to that of a Normal