Statistics

Practical Uses of Data Interpretation

In our example, there will be three different parties interested in making use of the data for making decisions. These three parties are:

  • The school principal

  • A women's organization

  • The parents of one of the students

And each will use a different manner of data interpretation.

The School Principal

The school principal wishes to avoid gaps in grades between the two classes. If gaps exist, then he will act in various ways to narrow them. First, however, he must verify that such gaps exist. He will need the average grade of each class on each date, and the average annual grade for each class.

The school statistician gave the principal the following table:

The principal sees that according to the exams, and also in terms of the annual grade, the average scores of students in class 11-1 are better than those of students in class 11-2.

He considers the necessary steps that will raise the grades of students in class 11-2, so they will be equal to those of the students in class 11-1.

In order to obtain this table, the crude data must be organized in the following manner (by classes):


Class 11-1

Class 11-2

Average class grade on January exam

76.55

71.36

Average class grade on April exam

82.86

71.5

Average class grade on June exam

77

75.91

Average annual class grade

78.8

72.92

If we calculate the average of every column, and the annual average for each class, we will obtain the numbers that the statistician presented to the school principal.

Class 11-1

Class 11-2

Name

January

April

June

Name

January

April

June

James

78

99

80

George

94

50

53

Becky

62

55

80

Benny

92

91

72

Craig

97

72

99

Tony

77

56

78

Grace

85

85

100

Dan

66

81

67

Ronnie

61

83

72

Christiana

71

74

95

Shown

51

90

95

Elizabeth

49

61

87

Dennis

99

70

77

Christian

85

62

55

Benjamin

63

86

81

Freddie

95

86

84

John

60

98

58

Hillary

67

95

71

Ben

65

87

80

Carlos

50

62

93

Britney

77

86

70

Carl

51

88

79

Mel

66

96

81

Leonard

88

56

93

Michael

98

80

92

Dave

58

92

79

Sara

55

86

90

William

86

52

65

Robbie

75

96

76

Morgan

69

71

94

Allen

87

81

100

Alex

88

66

65

Tommy

84

61

51

Paul

50

61

93

Ralph

89

90

85

Zippy

78

54

78

Maria

57

95

55

Samuel

81

82

89

Bruce

85

99

55

Rachel

67

77

87

David

98

58

50

Matt

60

93

49

Tom

91

70

67

Todd

48

63

57


The Women’s Organization

The women’s organization wishes to monitor how girls fare in this prestigious subject (physics), and their degree of success. What is needed in this case is the average grade for each gender separately on each date, and the average annual grade, as follows:

Boys

Girls

Number of students

32

12

Average class grade on January exam

75.48

69.36

Average class grade on April exam

77.03

77.63

Average class grade on June exam

74.76

81.55

Average annual class grade

75.76

76.18

The women’s organization concluded that the girls were as successful as the boys in physics, and perhaps even a little more so. At the same time, the number of girls choosing to study this subject remains far less than the number of boys (i.e., 10 girls, as compared to 30 boys). The organization is considering a publicity campaign to encourage girls to study physics.

In order to reach this table, the crude data must be organized in the following manner (according to gender).

Boys

Girls

Name

January

April

June

Name

January

April

June

James

78

99

80

Becky

62

55

80

Craig

97

72

99

Grace

85

85

100

Ronnie

61

83

72

Britney

77

86

70

Shown

51

90

95

Sara

55

86

90

Dennis

99

70

77

Maria

57

95

55

Benjamin

63

86

81

Christina

71

74

95

John

60

98

58

Elizabeth

49

61

87

Ben

65

87

80

Freddie

95

86

84

Mel

66

96

81

Hillary

67

95

71

Michael

98

80

92

Zippy

78

54

78

Robbie

75

96

76

Rachel

67

77

87

Allen

87

81

100

Tommy

84

61

51

Ralph

89

90

85

Bruce

85

99

55

David

99

58

50

Tom

91

70

67

George

94

50

53

Benny

92

91

72

Tony

77

56

78

Dan

66

81

67

Christian

85

62

55

Carlos

50

62

93

Carl

51

88

79

Leonard

88

56

90

Dave

58

92

79

William

86

52

65

Morgan

69

71

94

Alex

88

66

65

Paul

50

61

83

Samuel

81

82

89

Matt

60

93

49

Todd

48

63

57


Tom’s Parents

Tom’s parents wish to get an idea of how Tom is progressing in his studies. They look at Tom’s grades on each date. Tom’s mother is a statistician, and she presented her son’s grades in a diagram.

Three Different Perspectives of the Same Data-1

 

The diagram shows that Tom’s grades fell during the year.

The drop in Tom’s grades worried his parents, and they decided to send him to a private physics tutor, so that his command over the subject will improve by the time he takes his matriculation exam next year.

Summary

Three parties were involved in the above example of data interpretation.

Each party sorted the data in a way that suited them, analyzed the data and drew conclusions according to their interests.

Practical Uses of Data Interpretation536Practical Uses of Data Interpretation