# Statistics Coursework

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Introduction

Laura Clark Page 8/3/2008

Statistics Coursework

## Aim:

We have been given data about the different aspects of life of students from Mayfield High School. The data includes information such as the height and weights of the students, and educational stats such as KS2 results.

My aim is to investigate the relationship between two or more of these pieces of information.

Hypothesis:

My main hypothesis is that:

“As IQ increases, the total KS2result also increases”.

I chose this as my main hypothesis because I think that as IQ is natural intelligence, having a higher IQ would mean that a student could easily obtain higher KS2 results.

Related Hypotheses:

I have chosen to investigate two related hypothesis, these being:

1. “Year 7’s have higher total KS2 results than Year11’s”

- “Girls obtain higher percentage of results of a 4 or above in each KS2 test than boys”

I have chosen these as my related hypotheses as they allow me to look more closely at my main

hypothesis. I have chosen the first one specifically because I have heard that exams were getting easier, and I wanted to investigate this to see what I heard was correct. I have chosen the second one because I believe it to be true; in general boys spend a greater amount of time outdoors and so less time studying than girls do.

## Preliminary Studies:

I have carried out a small scale preliminary study for my main hypothesis, to check if there is any basic correlation, and therefore ensuring I can see if it is worth investigating.

Middle

15

Year 9 Female

14

Year 9 Male

12

Year 10 Female

9

Year 10 Male

11

Year 11 Female

9

Year 11 Male

8

Total:

118

After finding out the number of records required from each category of student, I used a Random Number Generator on a calculator to obtain the student numbers that I needed for the sample.

This involved finding out the total number of student in each category and inputting this number into the calculator, then using the Ran# key. I did this separately for each category to obtain the numbers, and as the data was in an Excel spreadsheet it was easy to see which records the generator would be referring to.

Investigating the Main Hypothesis:

After obtaining my sample, I used Excel to create a scatter graph comparing the two sets of information: IQ and total KS2 results obtained. To find the total KS2 result for each student I used the SUM “=Sum(number1,number2,number3)” formula in Excel which calculates the total if the numbers are inputted or the cells with the information in are clicked on.

This is the scatter graph I obtained from my results:

From looking at this graph I can see that the correlation between the two sets of data is positive and strong. This supports my hypothesis that “As IQ increases, the total KS2 result also increases”. However, to calculate the correlation more accurately I used the Correl formula in Excel “=correl(array1,array2)”. This gives a value for the correlation of the data. The correlation for this graph was 0.900607, which is extremely strong and shows that IQ has a direct effect on the KS2 results obtained.

Investigating the Related Hypotheses:

To investigate my first related hypothesis, I found the median, range, lower quartile and upper quartile values from both sets of data. To calculate this data, I used various formulas in Excel. To calculate the median for the data, I used the MEDIAN formula “=MEDIAN(array)”. This calculates the median of a highlighted selection of data, which is the “array” part of the formula. To calculate the upper and lower quartiles of the data, I used the QUARTILE formula, “=QUARTILE(array, quart)”. This calculates the value of the chosen quartile for the data highlighted, and the “quart” part of the formula is where the chosen quartile is inputted. For the lower quartile, the value is 1 and for the upper quartile the value is 3. I also calculated the range of the data. Once I had finished these calculations for both year groups, I put the data into a table so it could be displayed.

Year Group | Median | Lower Quartile | Upper Quartile | Range |

7 | 13 | 12 | 14 | 10 - 16 |

11 | 13 | 11.5 | 15 | 10 - 15 |

Conclusion

With regards to the findings from my investigation, although they are relevant to my investigation, they would not necessarily be relevant and accurate for our whole school population, or the population of the country. However it would probably be quite relevant to the school as the basic principles would be the same, however because Kendrick is a grammar school all results and IQs should be relatively high, making it hard to distinguish between different results. In terms of the whole country the investigation is not overly relevant as it was a small scale investigation looking at only one school, one type of school in one town. This means that to make it relevant and accurate for the whole population, samples would have had to be taken from all over the country at different types of school to get an accurate representation to generalise the study. Another factor that makes it less relevant is that I did not compare the KS2 results to all ages throughout the school, just the two extremes of year group in the school, Year 7 and Year 11. Therefore, any conclusions I obtained for my investigation are valid for this particular school, they cannot however be applied to any other school in any other area of the country, or the country as a whole.

This student written piece of work is one of many that can be found in our GCSE Height and Weight of Pupils and other Mayfield High School investigations section.

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