Ugrás a tartalomhoz

SOCIAL STATISTICS

Renáta Németh, Dávid Simon

ELTE

Again about percentiles

Again about percentiles

  • we have seen: the nth percentile is the value of a variable below which n percent of observations fall

  • the median is the 50th percentile

  • percentiles are also appropriate for ordinal variables

  • deciles are the 10th percentiles, the 25th percentile is the lower quartile, while the 75th percentile is the upper quartile

Example. ISSP 2006, Subjective social status measured on a 10-grade scale. Cumulative percentage distribution

Taiwan

Hungary

Denmark

Lowest, 01

10.7

3.8

1.4

 

02

17.0

11.9

3.1

 

03

28.7

30.5

6.9

 

04

38.8

51.8

11.4

 

05

73.8

80.6

29.9

 

06

91.2

93.2

58.1

 

07

97.0

98.5

81.6

 

08

98.9

99.7

95.4

 

09

99.5

100.0

98.6

 

Highest, 10

100.0

100.0

 

What are the country-specific third, fifth and seventh deciles?

Conclusions, for example:

  • „Only 3 out of 10 Danish position themselves in the lowest half of the scale.” (third decile)

  •  “However, only 30 percents of Taiwanese people perceive themselves to be of high status (higher than 5-grade ranking).” (7th decile)

  • Note that in the latter case we cumulated the percentages “upward”: quantiles can be interpreted in this way as well.

Example. Subjective health status on a 100-grade scale separately for people in bad / good or very good financial status.

(Source: Hungarian National Health Interview Survey 2000)

Find and compare the lower and upper quartiles and the median.

In bad financial status

Score

Frequency

%

Cumulative %

0

5

1.79

1.79

1

1

0.36

2.14

3

1

0.36

2.50

10

6

2.14

4.64

15

3

1.07

5.71

19

1

0.36

6.07

20

11

3.93

10.00

23

1

0.36

10.36

25

3

1.07

11.43

28

2

0.71

12.14

30

13

4.64

16.79

34

1

0.36

17.14

35

3

1.07

18.21

39

1

0.36

18.57

40

17

6.07

24.64

42

1

0.36

25.00

43

1

0.36

25.36

45

3

1.07

26.43

46

1

0.36

26.79

48

1

0.36

27.14

49

3

1.07

28.21

50

55

19.64

47.86

51

1

0.36

48.21

55

6

2.14

50.36

60

22

7.86

58.21

62

3

1.07

59.64

65

9

3.21

62.86

67

1

0.36

63.21

68

1

0.36

63.57

70

25

8.93

72.50

73

1

0.36

72.86

75

7

2.50

75.36

76

1

0.36

75.71

79

2

0.71

76.43

80

29

10.36

86.79

81

1

0.36

87.14

83

1

0.36

87.50

84

1

0.36

87.86

85

2

0.71

88.57

89

1

0.36

88.93

90

17

6.07

95.00

92

1

0.36

95.36

95

3

1.07

96.43

97

1

0.36

96.79

98

1

0.36

97.14

100

8

2.86

100.00

Total

280

100.00

In good or very good financial status

Score

Frequency

%

Cumulative %

0

1

0.15

0.15

10

1

0.15

0.31

15

1

0.15

0.46

20

1

0.15

0.62

29

1

0.15

0.77

30

4

0.62

1.39

35

1

0.15

1.54

40

8

1.23

2.78

50

39

6.02

8.80

55

6

0.93

9.72

58

2

0.31

10.03

60

26

4.01

14.04

61

1

0.15

14.20

62

1

0.15

14.35

64

1

0.15

14.51

65

6

0.93

15.43

67

1

0.15

15.59

69

1

0.15

15.74

70

50

7.72

23.46

71

1

0.15

23.61

73

1

0.15

23.77

75

31

4.78

28.55

77

1

0.15

28.70

78

1

0.15

28.86

79

6

0.93

29.78

80

115

17.75

47.53

81

1

0.15

47.69

83

1

0.15

47.84

84

1

0.15

47.99

85

69

10.65

58.64

86

2

0.31

58.95

87

2

0.31

59.26

88

3

0.46

59.72

89

3

0.46

60.19

90

122

18.83

79.01

91

1

0.15

79.17

92

7

1.08

80.25

93

5

0.77

81.02

94

1

0.15

81.17

95

51

7.87

89.04

96

1

0.15

89.20

97

1

0.15

89.35

98

5

0.77

90.12

99

3

0.46

90.59

100

61

9.41

100.00

Total

648

100.00