Are the Average IB points achieved by a school’s sixth form proportional to the fees of the school?
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Are the Average IB points achieved by a school’s 6th signifier proportional to the fees of the school?
Introduction
The International Baccalaureate Program is a strict class of survey designed to run into the demands of extremely motivated secondary pupils and to advance international apprehension. The effectivity of the IB plan is due non merely to the deepness of the single classs, but besides to the comprehensive nature of the plan. Unlike other awards plans, the IB Program requires each pupil to take advanced classs in six countries ( English, History, Science, Math, World Language, and an IB Elective ) . To measure up for the International Baccalaureate Diploma, pupils must take appraisals in the six capable countries, complete activities in the Creativity, Action, and Service ( CAS ) plan, and compose a 4000 word Extended Essay during the 12th and 13th twelvemonth. The pupil must besides take a alone class known as the Theory of Knowledge which explores how we think and learn, how we make connexions between capable countries, and how we justify the truth of cognition. [ 1 ]
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There are many schools across the universe that offer the IB and each a overplus of different topics. There are besides a batch of schools that range in school fees. Many schools claim that the highest quality instruction can be achieved by to a great extent funded installations amongst other things, and in bend the highest concluding classs. The intent of this this undertaking is to see if it really is true and that more paid for a high school instruction will ensue in higher classs.
Statement of undertaking
The intent of this probe is to find whether there is a relationship between the mean IB points a school earns and its fees between several British schools. The type of information I will be roll uping is the mean IB points and the fees in British lbs that have been voluntarily submitted to a nose count online by the schools themselves. This comparing will demo if the more a household pays for schooling, will they have a better instruction and higher concluding classs. I predict that there is a modest correlativity between the two, as it is believed that the money will be put into the schools learning resources, which should better the manner pupils learn.
( H0 ) : IB points and school fees are independent from each other.
( H1 ) : IB points and school fees are non independent from each other.
Probe Plan
I am look intoing whether there is a relationship between the mean IB points achieved in a school and the school’s fees. I have collected informations utilizing online resources that was provided by a school informations web site which has surveyed several Secondary schools in the UK. Several mathematical procedures will be conducted to analyse the information. First, some simple methods like ciphering the norms ( i.e. Mean, Mode, Median, Range ) every bit good as a spread graph with a line of best tantrum will be used. Then, some more sophisticated trials will be conducted which will happen out the PPMC and the least squares arrested development. Finally a chisquared trial will be conducted to prove the dependance of the IB tonss and school fees. The variables that will be measured are the mean overall IB points achieved by a 6th from one school and that school’s fees. Fifty different schools will be recorded to give a larger grade of truth when carry oning the mathematical procedure. This is besides reduces the opportunity of random mistake mostly impacting the consequences.
Mathematical Procedures
Table
Datas in this tabular array was collected from a nose count conducted across multiple schools in the UK and published online. A lower limit of 50 pieces of informations were collected
Avg. IB points 
School fees ( ? ) 
“ Avg. IB points 
“ School fees ( ? ) 
41.0 
22461 
34.4 
19710 
40.9 
15540 
34.0 
20890 
40.1 
18210 
34.0 
21860 
39.7 
14100 
34.0 
11388 
39.5 
15990 
34.0 
19810 
39.4 
20970 
33.9 
15960 
39.3 
21285 
33.8 
14061 
39.2 
15291 
33.0 
11902 
37.8 
16227 
33.0 
20370 
37.8 
17100 
32.5 
16230 
37.7 
23610 
32.3 
13350 
37.7 
21105 
31.9 
18990 
37.1 
21075 
31.7 
14055 
36.7 
10926 
31.0 
13350 
36.5 
20235 
30.9 
18474 
36.1 
19480 
30.7 
14700 
36.0 
24681 
29.6 
16050 
35.9 
18996 
29.5 
15975 
35.5 
21720 
28.4 
11700 
35.2 
26640 
28.3 
18294 
35.1 
16838 
27.8 
17801 
35.1 
13500 
27.6 
24464 
35.0 
21315 
27.6 
12693 
35.0 
12666 
27.3 
23903 
34.6 
24150 
27 
21508 
[ 2 ]
Simple Procedures
Some simple norms are calculated from the tabular array like mean, manner, average and scope.
To cipher mean of the information all the values have to be added up, so divided by the entire figure there are.
( ? IB Points ) /50 = 34.2 ( ? School Fees ) /50 = 18031
These are all the consequences:
Mean = 
34.2 
18031 
Mode = 
34.0 
13350 
Median = 
34.5 
18252 
Range = 
14.0 
15714 
These values were calculated utilizing a reckoner and the average norm will be used subsequently in the sophisticated mathematical procedures.
Graph
Graph shows the mean IB points versus the school fees ( lbs ) . At this point the graph seems to demo a weak positive correlativity. The mean IB points do non look to travel up every bit fees addition. ( This graph was generated utilizing Omnigraph )
Least Squares Regression
Linear arrested development is an attack to patterning the relationship between one or more independent variable. In the instance of this survey there is merely one independent variable every bit good as one dependant value.
The undermentioned expression is used:
andare found by utilizing the undermentioned equations:
To cipher the least squares arrested development. Datas from the tabular array will necessitate to be processed to acquire some needed values. I will necessitate to happen the ten and Y values multiplied together every bit good as the squared value of x. The amounts and norms of all the information must besides be conducted.
The deliberate values are as follows:
ten 
Y 
XY 
ten^{2} 
? = 1712 
? = 901599 
? = 30948987 
? = 59367 
= 32.4 
= 18032 
= 617451 
= 1172 
,
Calculation of PMCC
Pearson’s merchandise minute correlativity shows the strength of the relationship between two variables, in this instance the norm IB points and the school fees.
This is the most of import trial for this survey which will find whether there is in fact a correlativity between these two values.
The manner that this works is it is a figure between 1 and 1. The farther off from 0 the value is the closer they are to the gradient that means provinces that there is a strong correlativity.
The equation used to happen out this value is:
Where,and
ten 
Y 

? = 1712 
? = 901599 
? = 476.4 
? = 674829637 
= 32.4 
= 18032 
andwill be carried down from the old computation where the additive arrested development was found.
The value calculated seems to be really near to 0. When comparing it to the tabular array of coefficient of findings it achieves virtually no correlativity.
Chi Squared Test
Null ( H0 ) Hypothesis: IB points and school fees are independent from each other.
Alternative ( H1 ) Hypothesis: IB points and school fees are non independent each other.
Observed 

B1 
B2 
Entire 

A1 
A 
Bacillus 
A+B 
A2 
C 
Calciferol 
C+D 
A+C 
B+D 
Nitrogen 

Expected Calculated 

B1 
B2 
Entire 

A1 
( A+B ) ( A+C ) /N 
( A+B ) ( B+D ) /N 
A+B 
A2 
( A+C ) ( C+D ) /N 
( B+D ) ( C+D ) /N 
C+D 
A+C 
B+D 

Observed 

28.4 
34.7 
Entire 

1092618783 
13 
11 
24 
1878426640 
7 
12 
19 
20 
23 
50 

Expected Calculated 

28.4 
34.7 
Entire 

1092618783 
10.9 
12.5 
23.4 
1878426640 
8.6 
9.9 
18.5 
19.5 
22.4 
75 

[ 3 ]
Thecritical values at 10 % significance with 1 grade of freedom is 2.706. As thevalue is less than the critical value, 1.328 & A ; lt ; 3.841, the alternate hypothesis is rejected and Average IB points are assumed to be independent from school fees.
Validity and Restrictions
There can be several jobs that could originate of the informations collected.
One restriction is the sum of IB pupils in that school. A 6th signifier with around 20 people will give a much different norm than a school of 80.
Another restriction is that the tabular array of expected values in the^{2}trial contains values that are less than 5, which reduces its cogency.
IB schools greatly vary when it comes to capable picks, so a school that offers tougher topics may hold a lower norm than those that teach some topics, which are considered easier.
This research undertaking can be improved by trying a larger sum of schools. In some states, fundss are monitored more purely and criterions are higher so there could really be a much larger distance in Finland for illustration.
Decision
Despite of the antecedently mentioned restrictions, the found???’^{2}value, 2.706, rejects the alternate hypothesis that IB points are dependent from school fees and accepts the void hypothesis that IB points are independent from school fees. Furthermore, the probe clearly shows that there is an highly weak and positive correlativity between IB points and school fees as it can be an false independency from each other. Given the informations and consequences it is proven that because a school has really high school fees does non intend that the concluding consequences achieved by the pupils will be higher.
Appendixs
hypertext transfer protocol: //www.bestschools.co.uk/leaguetables/ibschools.aspx
hypertext transfer protocol: //math.hws.edu/javamath/ryan/ChiSquare.html
Raw Data
Avg. IB points 
School fees ( ? ) 
“ Avg. IB points 
“ School fees ( ? ) 
41.0 
22461 
34.4 
19710 
40.9 
15540 
34.0 
20890 
40.1 
18210 
34.0 
21860 
39.7 
14100 
34.0 
11388 
39.5 
15990 
34.0 
19810 
39.4 
20970 
33.9 
15960 
39.3 
21285 
33.8 
14061 
39.2 
15291 
33.0 
11902 
37.8 
16227 
33.0 
20370 
37.8 
17100 
32.5 
16230 
37.7 
23610 
32.3 
13350 
37.7 
21105 
31.9 
18990 
37.1 
21075 
31.7 
14055 
36.7 
10926 
31.0 
13350 
36.5 
20235 
30.9 
18474 
36.1 
19480 
30.7 
14700 
36.0 
24681 
29.6 
16050 
35.9 
18996 
29.5 
15975 
35.5 
21720 
28.4 
11700 
35.2 
26640 
28.3 
18294 
35.1 
16838 
27.8 
17801 
35.1 
13500 
27.6 
24464 
35.0 
21315 
27.6 
12693 
35.0 
12666 
27.3 
23903 
34.6 
24150 
27 
21508 
1