20 students ÷ 60 students х 30 students = 10 students . from each . class.
Since I know that I need 10 students from each class, I obtained a list of students in each class and selected every 2nd student. To ensure that I survey an equal number of boys and girls, I arranged the class list so every 3rd name on the list is a different gender from the one before.
The survey shall, politely, ask the student to estimate the length of a 6.9 cm line and a 137 o angle. The angle had a 0 o , 90o and an 180o guideline to help the weaker side of the survey. I chose the measurements, as they seem to be of moderate length, none too big nor too small. This is also because the measurements escape the norm of 5cm, 10cm, etc. and 45o and 90o, which will ensure the student is required to think a bit harder.
The recording sheet will ensure that data collection will be fast and efficient, to content the subjects to the utmost.
To analyse the data, I shall be using a spreadsheet program. Microsoft Excel was chosen, as it ideally calculates and processes data more effectively than any other software, as well as by hand. I will use its vast range of graphical factors, ensuring that the information that I want to convey will be conveyed. It will also ensure easy and accurate graphs.
Hypothesis 1: The difference in angle estimation shall be more than inaccurate than then length estimation. I believe this because the awareness upon lengths is more common than the familiarity of angles, within the everyday context.
A staged table will enable me to steadily calculate and prove my hypothesis. To prove my hypothesis, the difference in results is to be calculated into a percentage of the actual answer This is because of the two different units of measurement, as the degree and the centimeter do not combine. To start, I shall calculate the average difference in the entire line estimate collection. I have placed the results in descending order, keeping in mind that the mean should be 13.9cm ideally.
The average difference in estimation from the real answer (13.9cm) is apparent to calculate the accuracy or inaccuracy of the estimations. The difference was calculated by subtracting the estimate from the answer, or subtracting the answer from the estimate, depending on whether the student over estimated or under estimated.
The average difference was calculated by the total difference (35.5cm) divided by the number of subjects (30 students). The outcome was 1.18333, meaning the average difference of estimate from the actual answer was 1.18cm.
To calculate the percentage of inaccuracy, the mean difference (1.18cm) is divided by the real answer (13.9cm) and multiplied by 100 to make it a percentage.
Calculation:
1.18 ÷ 13.9cm x 100% = 8.48%
This means that the percentage of inaccuracy for the line estimation was 8.5% from the actual answer.
Next, I am to compare this result with the percentage from the angle estimation.
As the gradient of the angle was 69o, my difference was calculated by subtracting the estimate from the real answer, or vice versa. Either way would have the same difference, yet I preferred all of the differences in the positive side to ensure accurate calculating.
To calculate the average angle estimation in degrees, I divided the total difference (198.5o) by the number of subjects surveyed (30 students). The answer was 6.62o. This meant that the average level of inaccuracy was 6.6o from the actually answer.
Yet this figure could still not be compared with the line inaccuracy figure, as that is in percentage. To convert this into a percentage, it should be divided by the actual answer (69o) and multiplied by 100 percent.
Calculations:
6.62o ÷ 69o x 100% = 5.97%
This means that the percentage of inaccuracy of both genders estimating the gradient of an angle is approximately 6% off of the actual answer.
From these statistics, we can derive the fact that the level of inaccuracy in angles was, in fact, lower than those from the estimation of the length.
Conclusion for Hypothesis 1:
The difference in angle estimation shall be more than inaccurate than then length estimation. I believe this because the awareness upon lengths is more common than the familiarity of angles, within the everyday context.
My investigation concluded that the first hypothesis was wrong. The inaccuracy of the angle estimation (6%) turned out to be lower than the length estimation error (8.5%). This shows that the level of accuracy for angle estimation was higher than the accuracy level for length estimation, which was my exact anticipation. The difference between the two inaccuracy percentages was 2.5%, causing me to reject my first hypothesis into a final statement.
The level of inaccuracy for estimating angles in Year 10 is lower than the level of inaccuracy for the length estimation.
A possibility for my inaccurate prediction could have been the because of the angled guidelines. The more familiar 90 and 180-degree angles could have really helped the subject in altering these answers slightly. Therefore equal guidelines should have been based within the length-estimating context, to encourage accurate answers for both units.
To receive the exact figures, which mine were not, the entire Year 10 should have been surveyed, yet due to the time period, this was impossible. The figures may have come from only a less intelligent range of students, but this could not have been determined too easily.
Hypothesis 2: In correspondence to the first hypothesis, male angle estimation shall be more closely populated towards the correct answer than the female estimation.
For this prediction to be proven or disproven, the measure of spread needs to be calculated. The table is to be analysis down into the equation of standard deviation: = Standard Deviation
is worked out through the averaging of the 15 different estimation errors.
= total inaccuracy ÷ number of candidates
For Male: = 93.5 ÷ 15 = 6.233
For Female: = 105 ÷ 15 = 7
To understand the calculations more closely, a standard deviation graph was constructed.
The graphs shows that the male estimation was more closely packed than the female estimation. This is because the standard deviation for boys was smaller., therefore my prediction was correct.
Conclusion for Hypothesis 1: In correspondence to the first hypothesis, male angle estimation shall be twice as close populated towards the correct answer than the female estimation. This means that the measure of spread will be grouped twice as close to the actual answer than the female.
The measure of spread explains how closely ranged the data is. The lower the standard deviation means the tighter the estimates are clustered together. The boys did estimate closer together than the girls, yet they did not cut the girls standard deviation in half. This is because the girls only obtained a 0.6 disadvantage, whereas as I predicted that it would have been 10. The difference may have lied within a single subject. If a single subject has an anomaly (abnormal estimate), the entire standard deviation figure will be changed. This could have been Subject 30 (on Table 1), which had an inaccuracy difference of nearly four times the average inaccuracy level. This proves that my investigation was all-but-perfect.
Conclusion: Overall, I have concluded that the genders and the angle/length have been well matched in both of their estimations. This has been deduced from few figures of calculations, yet more will simply continue to prove my findings. Within the gradient/length context, the difference in estimation was a mere 2.5% difference. That shows that either skill was neither too good nor too bad. The same can be said for the gender standard deviation. This means that genders generally stuck to a single figure and evolved upon that. They all consist of the average answer, yet from further investigation, the boys of Year 10 stood out as being more precise. Though they did not stand out too much as its was only 2/3 of a percentage difference.
My hypothesis emerged, as half right half wrong, as I predicted the first hypothesis incorrectly, yet my second hypothesis was rather accurate.
I hope to further my investigation with newer hypothesis and more graphical data.
