Mathematics coursework

Introduction

My second coursework for my Mathematics GCSE course is based on statistics. I have been provided with data from Mayfield High school. Mayfield is a fictional school. Mayfield School has 1183 students from year’s group 7 to 11. The data that is provided on each student includes, name, age, year group, IQ, weight, height, hair colour, eye colour, distance from home to school, usual method of travel to school, number of brothers and sisters, key stage 2 results in English, Mathematics and Science.

Hypothesis – The right-handed girls have an IQ number higher than the left-handed girls. I am going to investigate this hypothesis showing graphs and tables.

The next table shows how many students have in each year group.

The following table show the right and left-handed girls on school.

Right hand

I have collected 100 IQ number from the Mayfield High School based on right hand girls. The data is from different ages and year’s group.

I collected the following IQ numbers:

116, 105, 98, 69, 102, 101, 100, 104,103, 104,100, 99,100, 91, 122, 87, 90, 88,101, 100, 101, 103, 94, 94,105,100,102,102,100,103, 102, 90,107, 107, 106, 79, 99, 101, 106, 108,85,106, 100,93,107, 116, 100, 116, 112, 105, 108, 103, 90, 97, 95,102,102,100,99,102, 100, 90, 94, 103, 116, 106, 91, 91, 113, 105, 101, 107, 100, 90, 100, 103, 110, 104, 116, 113, 117, 101, 83, 106, 94, 92, 101, 112, 116, 104, 110, 117, 100, 114, 119, 112, 104, 104, 101, 108

75

80 < x ≤ 90

9

85

765

90 < x ≤ 100

29

95

2755

100 < x ≤ 110

44

105

4620

110 < x ≤ 120

15

115

1725

120 < x ≤ 130

1

125

125

Totals

100

―

10 130

Mean = 10130 ∕ 100 = 101.30

Girls left handed

Mean = 10150 ∕ 100 = 101.50

The median on right handed is lower than left handed. The mean of the left-handed girls is slightly higher than right-handed girls. These show us that the hypothesis is wrong. The girls left-handed have an IQ number higher than the girls right handed.

Now, I am going to investigate the right and left-handed boys IQ number and relate them to the girls IQ number.

For explore the right and left-handed boys IQ number I am going to use a hypothesis.

Hypothesis – The right-handed boys have an IQ number higher than the left-handed boys.

The following table show the right and left-handed boys in the school.

Right hand

I have collected 100 IQ number from the Mayfield High School based on right hand boys. The data is from different ages and year’s group.

I collected the following IQ numbers:

101, 116, 101, 90, 97, 107, 101, 99, 109, 101, 100, 97, 112, 92, 103, 100, 100, 100, 101, 116, 103, 105, 99, 90, 108, 100, 71, 100, 97, 102, 100, 100, 98, 98, 103, 91, 104, 104, 97, 103, 72, 97, 106, 107, 108, 117, 74, 97, 92, 102, 89, 103, 91, 106, 103, 116, 100, 121

102, 89, 119, 106, 88, 90, 103, 80, 76, 106, 102, 84, 117, 100, 103, 91, 110, 115, 98, 98, 78, 83, 108, 112, 109, 100, 100, 78, 86, 91, 107, 102, 102, 101, 100, 103, 101, 104, 81, 104, 106, 104

Then, I draw a stem and leaf diagram to group the data.

Stem and leaf diagram

Key: 8/9 = 80

      10/3 = 103

Cumulative Frequency

The cumulative frequency graph showing the above table is on a separate paper.

Left hand

I have collected 100 IQ number from the Mayfield High School based on left handed boys. The data is from different ages and year’s group.

I collected the following IQ numbers:

91, 103, 102, 103, 98, 100, 108, 100, 102, 107, 106, 103, 100, 98, 100, 106, 94, 102, 100, 88, 100, 101, 109, 100, 112, 116, 74, 100, 92, 103, 107, 112, 92, 98, 103, 100, 126, 103, 98, 99, 78, 100, 116, 89, 86, 100, 102, 90, 109, 103, 94, 116, 113, 105, 101, 88, 101, 116, 110, 90, 112, 131, 96, 110, 87, 74, 96, 102, 90, 109, 101, 112, 100, 91, 103, 113, 104, 106, 110, 90, 86, 127, 97, 112, 102, 99, 110, 117, 106, 102, 100, 92, 100, 111, 117, 99, 90, 87, 108, 124

Steam and Leaf diagram

Overall conclusions

In this section I am going to relate the results of the girls and boys IQ number. I am going to say which gender has higher IQ number. The first hypothesis demonstrated that the girls left-handed have a higher IQ number than right-handed girls. The second hypothesis showed that the boys left-handed have a higher IQ number than the right handed boys. For each hypothesis I have collected 200 IQ numbers from Mayfield High School database based on right and left hand students.

What the results prove?

The results prove that the girls have a superior average of IQ number. But in comparison of boys and girls Descriptive Classifications of Intelligence Quotients, the girls left-handed with a mean of 101.50 have a elevated average of IQ number than the boys left handed with 100.90.

Incorrect data displayed on the Mayfield High School datasheet

In this section I am going to look at the Mayfield school datasheet and try to find data that does not makes any sense.

I found the following incorrect data:

• Height – 4.65 m
• Average number of hours TV watched per week – 1000000 hours, 170 hours and 190 hours

Maximum possible = 24 × 7 = 168 hours

• IQ – 240 which is impossible
• No of siblings – 17 - It can be possible but I don’t believe