Social Networking Website And The Academic Performances Commerce Essay

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Today the time an individual spends on a social networking website it considerably high and it is claimed that this is the reason for their poor scores in their academics. The inquisitiveness within me to verify the validity of this claim set the foundation for this mathematical project which is to explore the co-relation between the time that an individual actively spends on a social networking website and the ultimate performance shown in his/her term examinations. The main concept here that would be used is of statistics and functions, to be precise mathematical tools such as Pearson's co-relation coefficient, the χ2 test, etc. shall be used to compare any relation, if it exists.

Research Plan

The methodology used for data collection involved personal interrogation of the IBDP students. The students were not asked for the number of hours that they daily spend on a social networking website, this was not done because often students tend to round off their answers which could be a source of error while interpreting the results and drawing a conclusion. So the students were asked to precisely mention from what time to what time they access social networking websites which serves as the raw data. Then this raw data processed using the addition operator to get the total time spent on a social networking website on a regular basis. Along with this the students were even asked for their previous semester. As different boards have diverse evaluation methods, all the grades, points, etc, hence only IBDP students were chosen from various schools to have uniformity in the data being collected.

Data Collection and Processing

The total number of hours were initially recorded in hours and minutes but for calculation purposes the time spent on Social Networking Website was converted into hours and the minutes were also converted into decimals i.e. hours, hence using one single unit - hours. The raw data columns include the columns - Time Spent on Social Networking Website and Points Scored in Previous Semester. The raw data is tabulated and a new column labelled "Total Hours" has been added to the table which is a column for the processed data. Time Spent on Social Networking Website is a column containing fragmented data which has been processed i.e. added up in the "Total Hours" column.

Name

Time Spent on Social

Networking Website

Points Scored in

Previous Semester

Total Hours

Akshay Balwani

06 00 - 07 30 h

23 00 - 23 30 h

30

2 h

Devyani Ghoda

07 00 - 07 30 h

15 00 - 16 00 h

23 00 - 00 30 h

27

3 h

Aadam Mamaji

06 00 - 06 15 h

12 00 - 12 30 h

17 00 - 18 00 h

00 15 - 02 00 h

26

3.5 h

Sakshi Bhoolabhai

16 00 - 18 00 h

19 00 - 19 10 h

21 00 - 21 45 h

27

2.92 h

Pooja Siraj

15 20 - 16 00 h

19 00 - 19 20 h

22 25 - 23 00 h

32

1.58 h

Eshita Parekh

06 55 - 07 00 h

21 00 - 22 00 h

34

1.08 h

Isha Punjabi

05 00 - 05 10 h

16 00 - 19 00 h

27

3.17 h

Carina Xavier

16 00 - 21 00 h

00 00 - 00 15 h

21

5.25 h

Brandon Desouza

21 00 - 01 00 h

25

4 h

Saloni Shah

08 00 - 08 25 h

22 50 - 23 00 h

38

0.58 h

Akshita Arora

06 30 - 07 00 h

13 00 - 14 00 h

16 00 - 17 00 h

23 30 - 01 00 h

25

4 h

Columbus Marquis

15 30 - 17 00 h

23 30 - 12 30 h

29

2.5 h

Natasha Pereira

08 00 - 08 20 h

16 00 - 16 20 h

23 50 - 00 00 h

35

0.83 h

Sneha Kabra

05 00 - 06 00 h

18 00 - 21 00 h

00 00 - 01 30 h

20

5.5 h

Shaunak Bararia

12 00 - 13 00 h

16 00 - 16 45 h

21 30 - 22 15 h

23 45 - 00 00 h

28

2.75 h

Naomi Salot

17 00 - 20 00 h

22 30 - 00 00 h

24

4.5 h

Twisha Zaveri

23 00 - 01 30 h

24

4.33 h

Varun Kasturia

07 40 - 08 00 h

16 00 - 16 45 h

23 45 - 01 00 h

29

2.33 h

Rahul Vora

06 00 - 08 00 h

13 00 - 13 50 h

18 00 - 23 00 h

00 30 - 01 30 h

16

6.83 h

Mohit Tandon

07 45 - 08 00 h

13 30 - 14 00 h

22 00 - 01 00 h

26

3.75 h

Juhi Ajmera

08 00 - 08 10 h

21 30 - 22 00 h

36

0.67 h

Luv Seth

09 00 - 10 00 h

13 45 - 14 15 h

19 00 - 20 00 h

29

2.5 h

Karan Ravi

07 45 - 08 30 h

13 30 - 14 30 h

17 00 - 19 00 h

21 00 - 23 00 h

00 30 - 01 30 h

17

6.75 h

Gautam Lamba

16 00 - 20 00 h

23 00 - 00 45 h

20

5.75 h

Aditya Mehendale

-

40

0 h

Karan Choksi

07 00 - 07 35 h

16 00 - 16 20 h

35

0.92 h

Priyal Lodaria

06 00 - 06 30 h

15 45 - 16 00 h

22 00 - 23 00 h

30

1.75 h

Prashant Rayaprolu

16 00 - 18 00 h

22 00 - 02 00 h

20

6 h

Nikita Mehta

07 35 - 08 00 h

13 30 - 14 00 h

16 00 - 17 00 h

19 00 - 21 00 h

23 45 - 00 45 h

23

4.92 h

Priyanka Desai

06 30 - 08 00 h

15 30 - 17 00 h

21 15 - 22 15 h

26

4 h

Aadit Doshi

17 00 - 19 45 h

00 40 - 01 00 h

30

2.08 h

Ashna Ajmera

15 00 - 17 00 h

21 00 - 00 00 h

22

5 h

Yash Ajmera

16 30 - 17 30 h

19 50 - 20 00 h

00 15 - 01 15 h

30

2.17 h

Amrutha Sivakumar

08 10 - 08 30 h

14 00 - 14 45 h

22 00 - 01 00 h

25

4.08 h

Bahar Dhowan

-

41

0 h

Zoey Shain

09 00 - 09 10 h

17 00 - 20 00 h

25

3.75 h

Taylor Fernandez

06 00 - 07 20 h

16 00 - 17 00 h

29

2.33 h

Ali Contractor

20 40 - 21 00 h

37

0.33 h

Rhea Rane

06 05 - 07 00 h

20 00 - 22 00 h

27

2.92 h

Dhaval Dhrona

06 20 - 07 00 h

23 00 - 02 00 h

26

3.67 h

Tarique Patel

20 50 - 21 00 h

39

0.17 h

Dhruv Malhotra

13 15 - 17 15 h

21 20 - 22 00 h

23

4.67 h

Ayesha Malhotra

06 50 - 07 00 h

07 45 - 08 45 h

17 00 - 21 00 h

19

6.17 h

Neha Puri

07 50 - 08 30 h

15 00 - 15 30 h

21 00 - 01 00 h

25

4.17 h

Tanya Mansotra

08 00 - 08 30 h

16 00 - 16 30 h

21 30 - 23 00 h

29

2.5 h

Rohan Kukreja

15 10 - 16 00 h

35

0.83 h

Anushka Prabhu

10 55 - 11 30 h

13 00 - 13 30 h

19 00 - 21 00 h

23 00 - 01 00 h

22

5.08 h

Kaashish Madhani

07 45 - 08 00 h

16 00 - 16 30 h

23 00 - 00 00 h

28

1.75 h

Naman Parekh

11 45 - 12 00 h

14 00 - 14 45 h

15 45 - 16 00 h

34

1.25 h

Sasha Merchant

10 00 - 10 30 h

15 00 - 15 20 h

16 00 - 17 00 h

19 00 - 21 00 h

26

3.83 h

Priyal Parekh

21 45 - 22 00 h

37

0.25 h

Aastha Singhania

13 15 - 13 45 h

11 45 - 00 15 h

35

1 h

Shruti Shastri

05 00 - 05 50 h

06 30 - 07 30 h

16 00 - 20 00 h

21

5.83 h

Levina Robin

08 00 - 08 30 h

15 25 - 17 00 h

22 20 - 11 20 h

27

3.08 h

Pradnya Sharma

09 50 - 10 00 h

22 00 - 01 00 h

27

3.33 h

Jessica Turakhia

07 35 - 08 30 h

15 35 - 16 15 h

17 40 - 18 00 h

22 15 - 00 15 h

25

3.92 h

Tanvi Mehta

09 55 - 10 30 h

13 45 - 14 00 h

15 15 - 15 30 h

35

1.08 h

Saloni Atal

15 00 - 17 00 h

19 00 - 21 00 h

22 30 - 00 30 h

20

6 h

Aarushi Magan

06 55 - 08 00 h

15 55 - 17 00 h

18 35 - 19 00 h

21 00 - 22 00 h

00 00 - 01 00 h

26

3.58 h

Abhishek Tayal

09 50 - 10 10 h

38

0.33 h

Anmol Patel

15 15 - 16 15 h

21 40 - 01 00 h

24

4.33 h

Aman Parekh

07 30 - 09 00 h

15 30 - 17 00 h

18 30 - 19 00 h

20 00 - 22 00 h

23 45 - 00 45 h

18

6.5 h

Diya Nair

07 45 - 08 00 h

15 30 - 16 00 h

36

0.75 h

Faiz Kader

09 40 - 10 00 h

13 15 - 14 15 h

31

1.83 h

Jay Shah

10 00 - 11 00 h

14 00 - 15 00 h

21 00 - 01 00 h

19

6 h

Krupa Kapadia

22 30 - 00 00 h

32

1.5 h

Kunal Dhir

07 05 - 08 00 h

20 00 - 01 00 h

20

5.92 h

Nidhi Lakhani

08 25 - 09 00 h

15 30 - 16 00 h

20 00 - 21 00 h

30

2.08 h

Nikita Vispute

15 00 - 16 00 h

36

1 h

Mathematical Analysis

Scatter Plot

After the raw data had been collected and processed, using Microsoft Excel a scatter plot of the processed data was constructed to study the co-relation between the two variables - the Points scored i.e. their academic performances in the previous semester versus the Total hours spent on a social networking website.

Scale

x-axis: 1 unit = 1 hour

y-axis: 1 unit = 5 points

After plotting the scatter plot it can be studied that the co-relation between the total hours and points scored if a negative co-relation because with an increase in the value of x i.e. Total Hours, the value of y decreases i.e. Points.

The co-relation is a very strong one and this can be concluded as there aren't any outliers and most of the points are clustered closely above or below the line of best fit.

Pearson's Co-relation Coefficient

Pearson's co-relation coefficient is most commonly used method to determine the strength associated with a set of variables.

To verify the visual results of the scatter plot graph, Pearson's correlation coefficient (r) is calculated using the formula:

http://www.tnstate.edu/ganter/BIO311-Ch12-Eq8.gif ; where is the mean of all the x-values and is the mean of all the y-values. xi and yi are simply the x and the y values respectively.

After the value of 'r' has been calculated, it is squared to get the coefficient of determination (r2) which will help us understand the strength of association or the strength of the co-relation between the two variables. The link between the value of the coefficient of determination and the strength of association can be studied by the following table:

Calculating the value of 'r':

x = Total number of hours spent on a social networking website

y = Points scored in the International Baccalaureate Diploma Programme

x

y

xy

x2

y2

20

5.50

110

400

30.3

16

6.83

109

256

46.6

17

6.75

115

289

45.6

20

6.00

120

400

36.0

19

6.17

117

361

38.1

20

6.00

120

400

36.0

18

6.50

117

324

42.3

19

6.00

114

361

36.0

20

5.92

118

400

35.0

21

5.25

110

441

27.6

25

4.00

100

625

16.0

25

4.00

100

625

16.0

24

4.50

108

576

20.3

24

4.33

104

576

18.7

20

5.75

115

400

33.1

23

4.92

113

529

24.0

22

5.00

110

484

25.0

23

4.67

114

529

21.8

25

4.17

104

625

17.4

22

5.08

112

484

25.8

21

5.53

116

441

30.6

25

3.92

98

625

15.4

24

4.33

104

576

18.7

30

2.00

60

900

4.00

27

3.00

81

729

9.00

26

3.50

91

676

12.3

27

2.92

78.8

729

8.54

27

3.17

85.6

729

10.0

28

2.75

77

784

7.56

26

4.00

104

676

16.0

29

2.50

72.5

841

6.25

29

2.50

72.5

841

6.25

29

2.33

67.6

841

5.43

29

2.50

72.5

841

6.25

26

3.75

97.5

676

14.1

30

2.08

62.4

900

4.33

25

4.08

102

625

16.6

25

3.75

93.8

625

14.0

29

2.33

67.6

841

5.43

27

2.92

78.8

729

8.53

26

3.67

95.4

676

13.5

29

2.50

72.5

841

6.25

28

1.75

49

784

3.06

26

3.83

99.6

676

14.7

27

3.08

83.2

729

9.49

26

3.58

93.1

676

12.8

30

2.08

62.4

900

4.33

32

1.58

50.6

1024

2.50

34

1.08

36.7

1156

1.17

35

0.83

29.1

1125

0.69

35

0.92

32.2

1225

0.85

30

1.75

52.5

900

3.06

30

2.17

65.1

900

4.71

35

0.83

29.1

1225

0.69

34

1.25

42.5

1156

1.56

35

1.00

35

1225

1.00

35

1.08

37.8

1225

1.17

31

1.83

56.7

961

3.35

32

1.50

48

1024

2.25

38

0.58

22.0

1444

0.34

36

0.67

24.1

1296

0.45

40

0.00

0

1600

0

41

0.00

0

1681

0

37

0.33

12.2

1369

0.11

39

0.17

6.63

1521

0.03

37

0.25

6.25

1369

0.06

38

0.33

12.5

1444

0.11

36

0.75

27

1296

0.56

36

1.00

36

1296

1

Calculated value of r = -0.98347765662726 i.e. -0.983 (correct to 3 significant figures).

A TI-nspire Graphing Display Calculator operating at OS 2.1 was used and tools like spreadsheets were used to cross check the value of 'r'.

When this value of the Pearson's coefficient (r) is squared to find the coefficient of determination (r2):

(-0.983)2, the value of r2 is obtained to be 0.967 (correct to 3 significant figures).

We can conclude using the coefficient of determination (r2) that the value of r2 fits in the 0.90≤ r2 <1 band in the strength of association table which represents a very strong co-relation between the total number of hours spent on a social networking website and the points scored in the International Baccalaureate Diploma Programme. And hence our visual interpretations made earlier are also ratified.

Two-Variable Statistics

Two- variable statistics tools like the χ2 test was used to study the co-relation between the points scored in the Diploma Programme and the time spend on a social networking website on a daily basis. The χ2 test is used to determine whether there is a significant difference between the expected frequencies and the observed frequencies in one or more categories.

Let Ho be the null hypothesis and H1 be the alternative hypothesis.

Ho: The points scored in International Baccalaureate Diploma Programme are independent of the time spent on a social networking website by a Diploma Programme student on a daily basis.

H1: The points scored in International Baccalaureate Diploma Programme depend on the time a Diploma Programme student spends on a social networking website on a daily basis.

Time Spent on a Social Networking Website = t

Points Scored in Previous Semester = p

Experimental Values:

t ≤ 1

(Less)

1 < t ≤ 3

(Moderate)

3 < t ≤ 7

(A lot)

Total

p ≤ 21

(Poor)

0

0

12

12

21 < p ≤ 31

(Average)

0

16

22

38

31 < p ≤42

(Good)

14

5

0

19

Total

14

21

34

70

Expected Values:

The expected values were calculated by multiplying the row total by the column total and then divided by the sum total of the total values.

For example the first value of the expected values was calculated in the following method:

= 2.43

Thus applying the same method for all the other cells, the expected values of all the cells were calculated.

t ≤ 1

(Less)

1 < t ≤ 3

(Moderate)

3 < t ≤ 7

(A lot)

p ≤ 21

2.43

3.65

5.91

21 < p ≤ 31

7.71

11.7

18.7

31 < p ≤42

3.86

5.78

9.36

Degrees of Freedom:

d.o.f. = (r - 1) (c - 1) = (3 - 1) (3 - 1) = 4

Level of Significance: 5%

[The probability of a false rejection of the null hypothesis in a statistical test. This is also called as, significance level.]

χ2critical Value: 9.488

χ2calculated Value:

http://www.scielo.br/img/revistas/sa/v62n2/23488x1.gif

fo = Observed or experimental values

fe = Expected values

fo

fe

fo - fe

(fo - fe)2

(fo - fe)2

_________

fe

0

2.43

-2.43

5.90

2.43

0

7.71

-7.71

59.4

7.71

14

3.86

10.1

103

26.6

0

3.65

-3.65

13.3

3.65

16

11.7

4.30

18.5

1.58

5

5.78

-0.78

0.61

0.11

12

5.91

6.09

37.1

6.28

22

18.7

3.30

10.9

0.58

0

9.36

-9.36

87.6

9.36

(fo - fe)2

_________ = 58.502

fe

χ2calculated value: 58.5

After χ2 value was calculated manually, TI-nspire Graphing Display Calculator operating at OS 2.1 was used and tools like statistics tests were used to verify the χ2 calculated value.

Since, χ2critical < χ2calculated;

We reject the null hypothesis, H0 and accept the alternate hypothesis, H1.

H1: The points scored in International Baccalaureate Diploma Programme depend on the time a Diploma Programme student spends on a social networking website on a daily basis.

Function

Using graphing software named "Graphmatica" the processed data i.e. the total number of hours spent on a social networking website were plotted against the point scored in the previous semester. After the points were plotted a linear curve was introduced.

Scale

x-axis: 1 unit = 0.5 hour

y-axis: 1 unit = 5 points

For further analysis, equation for the curve was calculated i.e. an equation to show the relation between the number of hours spent on a social networking website and the points scored by an IBDP student in the previous semester. The equation of the line gives us an insight into how the points scored vary with the changes in the number of hours spent on a social networking website.

To find the equation of the line, the y-intercept and the gradient of the curve was found first.

Y-intercept: When x = 0, y = 37.6

Gradient(m) = = = -3.13

y = -3.13x + 37.6

Conclusion

After using various mathematical tools and with prior knowledge of the impact of social networking websites on academics, I'd like to conclude that these websites have shown a negative impact on a student's academics. Firstly from the scatter plot graph plotted using all raw data available, it is visibly evident that the two variables i.e. the time spent on a social networking website and the points scored in the International Baccalaureate Diploma Programme have shown a negative correlation. This conclusion can be further fortified by the results of the Pearson's co-relation coefficient(r) = -0.983. Since the value of "r" is very close to -1, it can be said that the two variables show almost a perfect negative co-relation. And when this value is used to calculate the coefficient of determination (r2) we saw that it fits the 0.90≤ r2 <1 band which also represents a very strong co-relation between the two variables.

The dependence between the two variables was further studied using the χ2 test. Since the null hypothesis is rejected, it is evident that the time spent on a social networking website and the points scored in the diploma programme are indeed not independent of each other. Additionally when we analyze the experimental values table, it is surprising to observe so many 0 values. We can conclude that the number of students scoring less than poor points and spending and spending less time on a social networking website is zero; similarly there are zero students scoring high points and spending a lot of time on a social networking website. This itself makes it evident that the relation between the two variables is a negative one.

This observable conclusion can be further strengthened when the best fit curve is plotted and the function of the best fit curve is calculated. The negativity and the strength of the co-relation can once again be seen to be reiterating by the magnitude of the slope of the best fit curve being -3.13.

Validation

Despite the fact that the conclusions exactly verify my prior interpretations, still the conclusions cannot be perfectly accurate for several reasons. For instance, the inherent problem of the raw data collected is that the time that a student of the International Baccalaureate Diploma Programme spends on a social networking website is rounded off to 3 significant figures and is not exact. Also the time specified by the students is an approximation and not timed accurately using any timing equipment like a stop watch. Yet the conclusions are quite precise and to a great degree even accurate as this the time spent on a social networking website is approximately on a daily basis and hence it can be used as one of the most important factors affecting the academic scores.

The conclusions can be highly valid as the sample size is quite large and the samples were chosen from a range of schools, hence exposing a larger variety of samples. The validity of the conclusions can be increased by considering a sample which includes students from several other boards and from different parts of the world but this would lead to another problem of reaching a single uniform unit (percentage, grades, points, etc) to measure the academic performances. These conclusions can then also be used and applied to a larger population to study the overall impact of social networking websites on academics.

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