GCSE Mathematics course work
Guestimate
1. Collect relevant data
I asked a sample of people to estimate:
- The length of this line
- The size of this angle
*Note: The data collected from this investigation is located in the Appendix of this assignment
2. Extract a sample of 30 items
I have chosen to extract two random samples of 30 people wearing spectacles and 30 people with out. The reason for this is one of hypotheses 2 involves comparing peoples estimates with spectacles and without and I wanted to make sure it is
Hypotheses 1: Boys are more likely to estimate the length of the line and the given angle correctly as opposed to the girls
Hypotheses 2: People who wear spectacles are less likely to guess the length and the angle correctly than people who do not wear spectacles
Random sample of 30 people (15 boys and 15 girls) for hypothesis 1
Sample data 1:
*Note: Sample data 1: is a collection of data that was compiled as a result of randomly selecting data from both the data collection sheet (which I have enclosed in the Appendix)
Random sample of 30 people wearing spectacles for hypotheses 2
Sample data 2:
*Note: Sample data 2: is a collection of data that was compiled as a result of randomly selecting data from both the data collection sheet (which I have enclosed in the Appendix)
Random sample of 30 students who are not wearing spectacles
Sample data 3:
*Note: Sample data 3: is a collection of data that was compiled as a result of randomly selecting data from both the data collection sheet (which I have enclosed in the Appendix)
3. Write down two hypotheses to test using your data:
- Boys are more likely to estimate the length of the line and the given angle correctly as opposed to the girls
- People who wear spectacles are less likely to guess the length and the angle correctly than people who do not wear spectacles
4.2 Frequency tables for Hypotheses 1
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*Note: Sample data 3: is a collection of data that was compiled as a result of randomly selecting data from both the data collection sheet (which I have enclosed in the Appendix)
3. Write down two hypotheses to test using your data:
- Boys are more likely to estimate the length of the line and the given angle correctly as opposed to the girls
- People who wear spectacles are less likely to guess the length and the angle correctly than people who do not wear spectacles
4.2 Frequency tables for Hypotheses 1
Hypotheses 1: Boys are more likely to estimate the length of the line and the given angle correctly as opposed to the girls
Frequency table of estimated lengths taken from sample data 1
Frequency table of estimated lengths of the Boys (15)
Frequency table of estimated lengths of the Girls (15)
Selecting classes to organize data from sample data 1 (boys estimates of the angle)
The 30 estimated angles are as follows ( oC):
30, 30, 37, 38, 40, 40, 42, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 49, 50, 50, 52, 60, 62, 65
As the data has a range of: (65-30) = 30 I have decided to group the data into classes. A class width of 5 degrees gives 8 classes and will help to present the data in a useful way.
The class intervals are shown in the table below:
Frequency table of estimated angles taken from sample data 1
Frequency table of estimated angles taken from sample data 1
Frequency table of estimated angles taken from sample data 1
5.1 Calculate the range, median, mode and mean of your data for hypotheses 1
The 30 estimated lengths (in cm) are as follows (taken from sample 1):
2, 2, 2, 2.5, 3, 3, 3, 3, 3.5, 3.5, 4, 4, 4, 4, 4, 4, 4.5, 4.5, 4.5, 5, 5, 5.5, 6, 7, 7, 7, 7, 7, 9, 10
The range of sample 1’s estimates of the length = 10-2= 8
The Median = half the total estimates + 1 / 2 4+4 /2 =4
The Mode = 4
The Mean = cumulative estimates (130.8) divided by total number of estimates (30)
= 4.36 = 4.5
15 of the estimated lengths where boys their results where as follows:
2, 3, 3, 3.5, 4, 4.5, 4.5, 4.5, 5.5, 6, 7, 7, 7, 9, 10
The range of the boy’s estimates of the length = 10-2= 8
The median of the boys results = 4.5
The Mode = 4.5 and 7
The Mean = 2+3+3+4+4.5+4.5+4.5+5.5+6+7+7+7+9++10 / 15 = 5.36 = 5.5
15 of the estimated lengths where girls their results where as follows:
2, 2, 2.5, 3, 3, 3.5, 4, 4, 4, 4, 4, 5, 5, 7, 7
The range of the girls’s estimates of the length = 7-2= 5
The median of the girls results = 4
The Mode = = 4
The Mean = 2+2+2.5++3+3+3.5+4+4+4+4+4+5+5+7+7 / 15 = 5.36 = 5.5
The 30 estimated angles ( oC) are as follows (taken from sample 1):
30, 30, 37, 38, 40, 40, 42, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 49, 50, 50, 52, 60, 62, 65
The range of sample 1’s estimates of the angle = 65-30 = 30
The Median angle = =45+45 / 2 =45
The Mode angle = 45
The Mean = cumulative estimates (130.8) divided by total number of estimates (30)
= 4.36 = 4.5
15 of the estimated lengths where boys their results where as follows:
30, 37, 38, 40, 40, 45, 45, 45, 45, 45, 45, 45, 52, 60, 62
The range of the boy’s estimates of the length = 62-30 = 32
The median of the boys results = 45
The Mode = 45
The Mean = 30+37+38+40+40+45+45+45+45+45+45+45+52+60+62 / 15 = 44.9 = 45
15 of the estimated lengths where girls their results where as follows:
30, 42, 45, 45, 45, 45, 45, 45, 45, 45, 45, 49, 50, 50, 65
The range of the girl’s estimates of the length = 65-30 = 35
The median of the girls results = 45
The Mode = = 45
The Mean = 30+42+45+45+45+45+45+45+45+45+45+49+50+50+65 / 15 = 5.36 = 5.5
6.1 Pie charts
These pie charts, which are not drawn to scale, show the distribution of estimates by people who part of the investigation.
Pie chart representing percentages of Boys estimates of the length
*Note: Any estimates with a value of zero are not represented in this chart
The mode estimate for the both these pie charts are represented by the largest portion
Pie chart representing percentages of girls estimates of the length
*Note: Any estimates with a value of zero are not represented in this chart
The mode estimate for the girls is represented by the largest portion
I have decided to create a class representing the nearest estimates of the length of the line. As the line is 4.5 cm I have decided that the nearest answers are any estimates between 4cm and 5cm
- 4 – 5 cm
The sections of the pies representing estimates from 4 to 5 cm add up as shown below:
- Boys = 7% + 19% = 26%
- Girls = 34% + 13% = 47%
These pie charts clearly show that a greater percent of girls where closer to the correct answer.
So far my hypotheses seem to be negative. In fact from sample 1 used for these hypotheses girls seem to be more accurate in their estimates of the angle
Pie chart representing percentages of Boys estimates of the Angle
Pie chart representing percentages of girls estimates of the Angle
The two class intervals 40-44 and 45-49 are nearest to the correct answer (45 degrees)
- Boys = 13% + 47% = 60%
- Girls = 7% + 66% = 74%
These pie charts clearly show that a greater percent of girls where closer to the correct answer.
Bar charts comparing boys with girl’s estimates of the line
* Note: This bar chart clearly demonstrates that no girls estimated the correct answer. However the girls appear to be more consistently closer to the correct length of the line, where as the boys estimates are spread out.
*Note: The longest bar represents the mode frequency or mode class interval of the boys (in Blue) and the girls estimates (in Red)
Bar charts comparing boys with girl’s estimates of the angle
The boys estimates (in Blue) seem to be more evenly spread out. Meaning their estimates of the angle are all over the place. The Girls seem to be mostly concentrated around the 45-49 and 50-54 class which is as close to the correct answer as you are going to get.
Both these bar charts re-enforce the accuracy of the girl’s estimates when compared with the boys estimates
Frequency table for angle estimates
This frequency table shows the estimates of 15 boys and 15 girls of a 45 degree angle
Cumulative frequency table shows 15 boys and 15 girls estimates of a 45 0c angle
Cumulative frequency graph
Upper quartile of boys = 48.5
Interquartile of boys = 46.75
Lower quartile of boys = 41.5
Interquartile range (of cumulative frequency) of boys = 48.5-41.5 = 7
*Note: As you can see the results shown by this cumulative frequency graph show that the boys and girls estimates do not vary that much which leads to think that either sex does not seem to effect the estimation of angle or that the number of boys and girls used in this test data is not large enough to prove anything
4.2 Frequency tables for Hypotheses 2
Hypotheses 2: People who wear spectacles are less likely to guess the length and the angle correctly than people who do not wear spectacles
Frequency table of estimated lengths of students wearing spectacles (extracted from sample 2)
Frequency table of estimated lengths of students not wearing spectacles (extracted from sample 3)
Selecting classes to organize data from sample data 2 people who wear spectacles
The 30 estimated angles from sample 2 (people wearing spectacles) are as follows ( oC):
30, 30, 37, 38, 39, 40, 42, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 50, 55, 55, 60, 62, 65, 65
As the data has a range of: (65-30) = 30 I have decided to group the data into classes. A class width of 5 degrees gives 8 classes and will help to present the data in a useful way.
The class intervals are shown in the table below:
Selecting classes to organize data from sample data 3 people who do not wear spectacles
The 30 estimated angles from sample 3 (people not wearing spectacles) are as follows ( oC):
20, 26, 30, 30, 35, 40, 43, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 46, 49, 50, 52, 55
As the data has a range of: (69-29) = 40. As the data from sample 3 has a greater range I have decided to extended the amount of class intervals so I can record all the data.. A class width of 5 degrees gives 10 classes and will help to present the data in a useful manor.
The class intervals are shown in the table below:
Frequency table of estimated angles taken from sample data 2 people who wear spectacles
Frequency table of estimated angles taken from sample data 3 people who do not wear spectacles
5.2 Calculate the range, median, mode and mean of your data for hypotheses 2
The 30 estimated lengths (in cm) are as follows (taken from sample 2-people who wear spectacles):
2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4.5, 4.5, 5, 5, 5, 5, 5, 5, 5.5, 6, 6, 6, 7 ,7, 8, 8, 9, 10, 10, 10
The range of sample 2’s estimates of the length = 10-2= 8
The Median = 5+5 /2 =5
The Mode = 5
The Mean = cumulative estimates (163.5) divided by total number of estimates (30)
= 5.45 = 6
The 30 estimated lengths (in cm) are as follows (taken from sample 3-people who do not wear spectacles):
2, 2, 2.5, 3, 3, 3, 3, 3, 3.5, 3.5, 4, 4, 4, 4, 4, 4, 4.5, 4.5, 5, 5, 5, 5, 6, 6, 6, 7, 7, 7, 7, 9
The range of sample 3’s estimates of the length = 10-2= 8
The Median = 4+4 /2 =4
The Mode = 4
The Mean = cumulative estimates (136.5) divided by total number of estimates (30)
= 4.55 = 5
The 30 estimated angles ( oC) are as follows (taken from sample 2 -people who wear spectacles):
30, 30, 35, 35, 37, 38, 39, 40, 40, 42, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 50, 50, 55, 55, 60, 62, 65, 65
The range of sample 1’s estimates of the angle = 65-30 = 30
The Median angle = =45+45 / 2 =45
The Mode angle = 45
The Mean = cumulative estimates (1303) divided by total number of estimates (30)
= 43.43 = 43
The 30 estimated angles ( oC) are as follows (taken from sample 3-people who do not wear spectacles):
20, 26, 30, 30, 35, 40, 43, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 46, 49, 50, 52, 55
The range of sample 1’s estimates of the angle = 55-20 = 35
The Median angle = =45+45 / 2 =45
The Mode angle = 45
The Mean = cumulative estimates (1286) divided by total number of estimates (30)
= 42.86 = 43
6.2 Pie charts
These pie charts, which are not drawn to scale, show the distribution of estimates by people who part of the investigation.
Pie chart representing percentages of 30 people’s (wearing spectacles) estimates of the length
*Note: Any estimates with a value of zero are not represented in this chart
The mode estimate for the both these pie charts are represented by the largest portion
Pie chart representing percentages of 30 people’s ( not wearing spectacles) estimates of the length
Pie chart representing percentages of 30 people’s (wearing spectacles) estimates of the Angle
*Note: The mode estimate for the both these pie charts are represented by the largest portion
Pie chart representing percentages of 30 people’s (not wearing spectacles) estimates of the angle
This frequency diagram shows the distribution of estimates of the length
This frequency diagram shows the distribution of estimates of the angle
