Investigating the Relationship Between English and Math Scores of Students
Task: To investigate the relationship between the results in Maths and
English of the students in Key Stage 4 at Mayfield High School
Plan: To investigate two questions related to the relationship between
the results in the key stage
and English Sats of students in
KS4 at Mayfield high school
1. Do students who do well in Maths also do well in English
2. Do girls do better than boys in maths and English
I am going to take a large sample, 60 (5-10 % of the total) of the
students in MayfieldHigh School. The larger the sample the more
accurate the reading will be
When all the data has been collected and recorded I am going to
represent it by using graphs of various types:
Q1 - Scatter diagram (positive correlation)
Q2 - Cumulative frequency diagram
Once I have drawn my mathematics graphs and diagrams I will analyse
the data to see whether I can draw any conclusions.
My hypotheses are
1. Children who do well in Maths will generally do well in English.
2. Girls do better than boys in maths but boys do better in English.
Results: I have taken a random sample of students from the Mayfield
database. I have decided to take a sample of 60 students as this is
between 5 and 10 % of the total number. I have taken random names so
am unsure how many girls or boys there will be, but I am assuming they
are near equal.
To take the random sample I picked 1 in every 10 student and then to
make up numbers I thought of any random number and inserted that in
Question 1: To answer this question I will need to make a scatter
diagram with the English and maths results of all the people chosen to
do this piece with. This will enable me to: compare maths and English
results for all students. If I see any correlation in the scatter
diagram I will draw a line of best fit.
Question 2: To answer this question I will need a cumulative frequency
diagram, to check whether girls do better than boys in English.
As you can see from the scatter diagram most students results were on
the diagonal in the middle of the graph on the line x = y. Hence this
is an ideal place to measure the line of best fit from.
Out of all the 60 students, 38 student got the same level of English
and maths results, also 9 out of 60 did better in English, so it is
possible to say that if a student does well in math
, he/she will also
do well in English.
2. for the girls results 19 out of 32 got the same in both, 7 did
better in English, and 6 did better in math.
For the boy's results 20 out of 28 got the same in both, 3 did better
in English, and 5 did better in math.
This may give a small suggestion as to what will happen in Question 2
In order to be able to fully show the English and maths results. I am
going to represent the data several cumulative frequency diagrams. I
can then calculate the median. By doing this I will be able to see
whether girls do better than boys in English and Maths.
Level (up to and including) English Math
3 20 21
4 48 48
5 59 58
6 60 60
Level English Math
3 11 13
4 27 26
5 32 32
6 32 32
Level English Math
3 8 7
4 20 21
5 27 26
6 28 28
The median is the next thing to be calculated
Low median Up
60E 3 3.91 6
60M 3 3.88 6
32GE 3 3.31 5
32GM 3 3.78 5
28BE 3 4.04 6
28BM 3 4.07 6
The cumulative frequency diagrams for the whole sample show quiet a
small but significant difference. The median is similar in all of the
Girls: For the girls there is a surprisingly large difference between
English and math, for both subjects the median is smaller than all the
results as a whole, but this is particular in English where the
results are extremely low.
Boys: The maths results are fractionally higher than the English. In
both subjects the median is higher than the total median which
suggests that boys do better than girls.
All of this shows that achieving boys and boys in general do better
than achieving girls and their total, in both subjects but
particularly in English.
But I could improve my results and their accuracy more by using a
bigger sample and making sure that there is a same number off girls as
there are boys.
Analysis of hypothesis:
Q1. The answer is appears to be yes in both cases, as shown by the
scatter diagram. My hypothesis was correct in this case
Q2. It is clear that my hypothesis was incorrect because, as shown by
the scatter diagram, boys do considerably better than girls in both