:Bryan Yip 10R

Maths Coursework

Are left-handed people more intelligent and creative than the right-handed in Mayfield High School?

In my coursework, I am going to focus on the IQ, Key Stage 2 results, favourite colour, favourite subject and height of students in Mayfield High School.

Specify, I will concentrate on the Year 7,8 and 9 boys and girls because these year groups have closer relationship with the Key Stage 2 results.

In the following coursework I am going to investigate:

- Do left-handed people have a higher IQ than the right-handed?
- There is a correlation between the IQ and the Key Stage 2 results for the left-handed and the right handed.
- Red colour always gives people the feeling of aggressive. Creative people often have new ideas and are willing to try, so more left-handed people like “red” than right-handed.
- The subjects “ Design & Technology”, “Art” and “Music” always require

creativity. More left-handed people like these subjects.

Before selecting the data, I will stratify the data. Stratifying data can reflect all of the data in Mayfield College,

Stratifying the number of right-handed in Year 7, 8 and 9

I will take about 16% of the people in from Mayfield. 8% of the left-handed and 8% of the right-handed. Having the same amount of data can have fair results.

For the right-handed, I will have 38% of them from Year 7 and 21% from boys and 17% from the girls. That means for my collected data, I should have 60x 21% from boys and 60x 17% from girls. I will take 32% from Year 8, 17% are from the boys and 15% from the girls. In my collected data, I should have 60x 17% boys and 60x 15% from girls. In Year 9, I will take 15% from boys and 15% from girls, so

In the following table, I am going to calculate what the actual number of data that I am going to get

In total there be 60 data from the right-handed.

Stratifying the left-handed people in year 7,8 and 9

I will take 60 data from the left-handed people

In Total, there will be 60 left-handed data

I will have to collect to collect the following information

Aim 1: 60 IQ of the left-handed and 60 IQ of the right-handed

in Year 7,8 and 9.

## Aim 2: 60 people of the IQ of the left-handed and 60 people of the IQ of the right-handed.

Key Stage results [English] [Maths] [Science] of the left-handed and the

right-handed in Year 7, 8 and 9.

Aim 3: Collect 60 people who likes red in Year 7, 8 and 9.

Aim 4: Collect 20 people who like Design & Technology

20 people who like Art

20 people who like Music

## I know this data s reliable because

Before choosing the data, I have already excluded the missing data and the extreme data. All of these data are randomly chosen.

For all data, I chose Year 7, 8 and 9 because these years are closer to their KS2 results.

This can make the KS2 results more reliable, so in Aim 2 the answer might be more accurate.

## I will use a sample of size

Aim 1: 60 people of the IQ of the left-handed and 60 people of the IQ of the right-handed.

## Aim 2: 60 people of the IQ of the left-handed and 60 people of the IQ of the right-handed. Key Stage results [English] [Maths] [Science] of the left-handed and the right-handed in Year 7, 8 and 9.

Aim 3: 60 people who likes red in Year 7, 8 and 9.

Aim 4: 20 of people who like Design & Technology

20 of people who like Art

20 of people who like Music

## I will make sure that my sample is fair

-Exclude all the missing and anonymous data before choosing them.

-By having the same amount of data of the left-handed and the right-handed.

## I will use this data to compare

Aim 1: Comparing the mean of the IQ of the left-handed people and the IQ of the right-handed people. As if the IQ of the left-handed people has a higher IQ then I can say they are more intelligent.

Aim 2: Comparing the correlation of the IQ and the Key Stage 2 results of the left-handed and the right-handed.

Aim 3: Calculating the percentages of left-handed and right-handed who likes red and find out the answer.

Aim 4: Comparing in the “Creative Subjects”, do more left-handed people take these subjects than the right-handed? By calculating the percentage of left-handed and right-handed people who take these subjects, we can find out the answer.

I will perform the following calculations:

Aim 1: Do a Cumulative Frequency table and divide data into groups

Calculate the median of the IQ of the left-handed and the median of the IQ

of the right-handed

Calculate the Upper Quartile and the Lower Quartile of the Data.

Calculate the IQR of both left-handed and right-handed

Compare the IQR of the IQ of the left-handed and the right-handed, to see how their data is spread and to see how much the data is concentrated about the median.

Do another table for left-handed. Calculate the frequency density. In this table, the class interval will be different.

Calculate the mean and standard deviation, to find out the average of the IQ of the left-handed and the right-handed, see who is clever and by calculating the Standard deviation, we can find whether the data is concentrated with the mean or not.

Aim 2: By Calculating the PMCC of the English result and the IQ

the PMCC of the Maths result and the IQ

the PMCC of the Science result and the IQ

to see if these results are high, low, positive or negative correlated.

Aim 3: Get 60 data of students who like “red”

Then work out how many of them is left-handed and right-handed. Find the percentage of the left-handed and right-handed that likes red.

Aim 4: Get 60 data of students who like studying “creative subjects”

Then find out how many students who like these subjects are left-handed and right-handed. Work out the percentage of how many of them is left-handed or right-handed.

These calculations will be useful because:

Aim 1: In this aim, I calculated the IQR because it can tell me clearly about how much the data is spread about the median. IQR is not affected by extreme data, so it won’t affect the accuracy of the range.

Except for IQR, I calculated S.D. and mean. Standard Deviation shows how the data is spread from the mean. We can show that left-handed is cleverer than the right-handed directly by mean and the S.D. can help to show how the data is spread away from the mean.

Aim 2: PMCC can show the data if it’s high/low, positive/negative correlated. It shows if there’s a relationship between the KS2 results and the IQ.

Aim 3 & 4: In these two aims, I calculate things in percentage. It can show results clearly.

I will check that the calculations make sense by:

Calculating the answer twice, to see if I get the same answer. If the answer is correct, that means I am right

In the Aim 2, the answers of PMCC must lie between 1 and –1, so if the answers of the PMCC lie between 1 and -1, it means the answers are correct.

I will show the information in the following types of diagrams:

Aim 1: Cumulative Frequency Curve will be used.

Then I can find the median, Upper Quartile Range and Lower Quartile Range

Box & Whisker diagram will be used. In comparing two data, we use the same scale in the Box & Whisker diagram and it can help to express how the data is spread.

Draw histogram for the IQ of the left-handed and right-handed. Then compare the diagrams

Aim 2: scatter diagram can be used to show if the data is high/low, positive/negative correlated.

Aim 3&4: Pie Charts are efficient to show the percentage of left-handed people and right-handed people who like “red” or “creative subjects”

As a result of the calculations and diagrams I will be able to compare:

Aim 1: Compare the IQR and median

S.D. and mean of the left-handed and the right-handed

Aim 2: Compare the PMCC and correlation of the left-handed and the right-handed, calculate which one has a higher correlation. high/low, positive/negative correlated.

Aim 3: Compare the percentage of people who like “red”

Aim 4: Compare the percentage of people who like studying “creative subjects”

#### Calculation

Aim 1:

First I will plot a table and divide all the IQ of the left-handed and right-handed into different group and I can calculate the Cumulative Frequency.

In the first graph, Cumulative Frequency Curve of the IQ of the Right-handed

I found the Lower Quartile

the Upper Quartile

the Interquartile Range

the Median of the right-handed

Lower Quartile: In total, there are 60 data. To find the LQ, we must calculate 60 x 25%=15, then cross the y-axis from 15 till it meets the curve. When it meets the curve, vertical down till it meets the x-axis. Read the x-intercept, and that’s the LQ.