# 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.

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 Interpretation536