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# Statistics project. Comparing and analyzing the correlation of the number of novels read per week and the modal grade of T.I.S students

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Introduction

Name: Benjamin Eyison

Date: 7th April 2008

Subject: Mathematical studies

Comparing and analyzing the correlation of the number of novels read per week and the modal grade of T.I.S students

This project investigates the number of story books read per week correlated with the modal grades of 30 girls and 30 boys of T.I.S. As mentioned, 30 girls and 30 boys will be surveyed, all from grade 9. Data on the number of books and genres read per week, as well as their modal grades earned last semester. This data is then compared and analyzed to yield necessary results

Statistics

In this section, the mean, mode and median are found. These were done 4 times in

• Number of book genres girls often read
• Number of book genres boys often read

Person’s Correlation coefficient (PCL)

The PCL was used to find out how and if the amount of books read on the modal grades of students. Both girls and boys data were done separately

Chi-squared test for independence (CST)

The CST was used to test if the modal grade and number of books read are dependent on one another, as well as modal grade and type of books.

Middle

MARK AVERAGES (GIRLS)

 Modal mark% Frequency Fx Below 40 0 0 40-60 9 450 61-80 17 1190 81-100 4 360

Total                                30                                  2000

Mean=∑fx  =  2000 =  66.7,  thus average achieved by the female body was from 61-80.

N         30

Mode= 61-80, meaning that the largest number of girls gained marks within that range

Median: = 15.5th value: 40-60.

median value shows that midway modal mark % of the girls was lower, showing poorer academic status of the girls

 Number of books Frequency Fx 1 6 6 2 8 16 3 6 18 4 3 12 5 1 5 6 2 12

Total                                26                                  69

\

Mean==∑fx =69

N       26

Mode: 2, which shows that most girls preferred a lower amount of books to read

Median:  3.5th value: 1. This shows that the middle amount of books read was 1, which is even lesser than the median number of books by boys. As shown, there is no correlation between number of books read and modal mark for girls

Step 2

The next step was to do the chi squared test. It was necessary to see which were dependent and which were independent. This will show if there is relationship between no of book genres read and modal grade marks. Modal mark groups were made into below and above 61-80. This is because calculations made previously for girls and boys generally lay round 61-80. Those with the exact average were added to the above group.

Phase 1:  Mark & gender

Ho = Modal mark and gender are independent

H1= Modal mark and gender are dependent

Observed Values

 Modal mark < 61-80 Modal mark > 61-80 Total Boys 19 11 30 Girls 21 9 30 Total 40 20 60 The expected values were calculated using the GDC:

Expected Values Using the GDC we can find the value of X² calc using the GDC. The following results are shown From above, the following was deduced

X² calc: 0.3

P: 1.0

Using the P value at 5%, decision taking was made

Since P >0.05,

Thus accept Ho

Therefore modal mark and gender are independent

The same test was used for the number of books read and gender. The groups were the number of books<3 and >3

Phase 2: Number of books read & Gender

Ho: Number of books read and gender are independent

H1: Number of books read and gender are dependent

Observed values

 Number of books <3 Number of books >3 Total Boys 9 21 30 Girls 14 16 30 Total 23 37 60 Expected Values  So X²= 1.8

P=0.8

Since P>0.05, at 5% expectancy level, we accept Ho

Therefore number of books read and gender are independent

Phase 3: Type of books read & Gender

This phase focused on the different type of books read against the gender

Observed values

 Horror Science fiction Adventure Comedy Romance Action Total Boys 5 6 5 3 1 10 30 Girls 2 2 3 4 18 1 30 Total 7 8 8 7 19 11 60

Conclusion

Reliability and Validity

There are a few factors which influence the reliability of this experiment.

Only 30 girls and 30 boys were chosen, as there was the need to use a an equal amount of people for each gender in order to gain fairer results

A specific grade was chosen: grade 9 as it has the largest class population, thus more data gained

There is a chance that those who filled in the questionnaire may have not been honest and wrote false marks or number of books they read per week

Students seemed to have more of higher marks than lower, showing the unreliability of their answers in the questionnaire, as well as lower amount of books read per week. This may be the reason why there is little or no correlation at all for the girls, and a string negative correlation for the boys. In fact, it is plausible to say that from the results gained, the girls who have positive, but low correlation seem more trustworthy than that of the boys’

In the modal grade, the only categories given were that of below 40 to 100. This is because as confirmed with the English Language teacher, no student gained below 40 very often. Thus values of 10-30 were summarized into that of “below 40”

This student written piece of work is one of many that can be found in our International Baccalaureate Maths section.

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