Guestimate The line and the angle Essay Example

Guestimate The line and the angle Essay Example Guestimate The line and the angle Essay Guestimate The line and the angle Essay Essay Topic: The Guest 1- I predict that if people are good at guessing the length of a line they will be good at guessing the degrees of an angle. 2- I predict that the higher the schooling year the better the estimate. Target population I have decided to investigate within the schooling ages of 7 and 9 firstly because these are easily available to collect due to having timetables and knowing where all the students will be when needed to guestimate. Another reason for picking students between these ages is that it is a big enough variety to draw conclusions from, and decide whether the amount of school really does improve the ability to guess the size of a line or angle. I will not be asking every year group as this will take up too much time and will not be necessary. I will be asking years 7, 9 and 11 this gives a big enough range of the amount of school experienced without asking every year. : Study Population I have chosen to get a list of the students in years 7, 9 and 11 and then ask every fourth person on the list this will the give a quarter of each year being asked which is enough to draw conclusions from. I am not going to ask everyone in the three selected years because this would take to long and it is not compulsory to get the information I need. Aims I will prove my hypothesis true or false by asking the selected people to guess the length of a line or size of an angle and then find the mean median mode for each year and draw graphs. I will also draw a graph relating their guess of the size of an angle to their guess of the length of a line. To gain fairly accurate results we will not let the pupils take the sheets away whilst guessing we will stay with them so there is no chance of using a rule or protractor. Possible things that may go wrong is that after we have asked one person they may go back and explain to the other people their opinion of the sizes that may give bias results to prevent this we will not tell them the actual answer. Results Year 7 Estimate of line Estimate (cms) 2 4? 4 6 ? 6 8 ? 8 10 ? 10 12 ? 12 14 ? 14 16 ? 16 18 ? 18 20 ? Totals Frequency 17 15 6 5 1 2 46 Mid-interval value 3 5 7 9 11 13 15 17 19 Frequency x mid-interval value 51 75 42 45 11 0 0 0 38 262 Mean = 262/46 = 5.70 Modal group = 2 4? Median is approximately 5cms Estimate (?) 10 20 20 30 30 40 40 50 50 60 60 70 70 80 80 90 90 100 Totals Frequency 3 10 12 12 1 1 2 4 1 46 Mid-interval value 15 25 35 45 55 65 75 85 95 Frequency x mid-interval value 45 250 420 540 55 65 150 340 95 1960 Range = 2-20 = 18 Estimate of angle Mean = 1960/46 = 42.61 Modal group = 30 50? Median is approximately 38? Range = 10-100 = 90 Year 9 Estimate of line Estimate 2 4 4 6 6 8 8 10 10 12 12 14 14 16 16 18 18 20 Totals Frequency 6 23 6 5 0 0 0 0 0 40 Mid-interval value 3 5 7 9 11 13 15 17 19 Frequency x mid-interval value 18 115 42 45 0 0 0 0 0 220 Mean = 220/40 = 5.50 Modal group = 4 6? Median is approximately 5cms Range = 2 10 =8 Estimate of angle Estimate 10 20 20 30 30 40 40 50 50 60 60 70 70 80 80 90 90 100 Totals Frequency 0 3 10 23 1 1 0 0 2 40 Mid-interval value 15 25 35 45 55 65 75 85 95 Frequency x mid-interval value 0 75 350 1035 55 65 0 0 190 1770 Mean = 1770/40 = 44.25 Modal group = 40 50? Median is approximately 43? Range = 20 100 =80 Year 11 Estimate of line Estimate 2 4 4 6 6 8 8 10 10 12 12 14 14 16 16 18 18 20 Totals Frequency 3 29 2 0 0 0 0 0 0 34 Mid-interval value 3 5 7 9 11 13 15 17 19 Frequency x mid-interval value 9 145 14 0 0 0 0 0 0 168 Mean = 168/34 = 4.94 Modal group = 4 6? Median is approximately 4.5cms Range = 2-8 = 6 Estimate of angle Estimate 10 20 20 30 30 40 40 50 50 60 60 70 70 80 80 90 90 100 Totals Frequency 0 6 11 16 1 0 0 0 0 34 Mid-interval value 15 25 35 45 55 65 75 85 95 Frequency x mid-interval value 0 150 385 720 55 0 0 0 0 1310 Mean = 1310/34 = 38.53 Modal group = 40 50? Median is approximately 40? Range = 20 60 = 40 To find if my first hypothesis is true I will draw a scatter graph of all the estimates of year 7. 9 and 11 students. I will have boundaries on the graph, from 3 6cms this will be classed as a good estimate of the line, 30 45? this will be a good estimate of the angle. I will shade these areas to investigate if students who are good at estimating the line are good at estimating the angle. I drew Cumulative frequency graphs of the results above this will show how consistent the estimates were. I will see how close to the actual the median is, and the smaller the inter-quartile range the more consistent the estimates will be. If my second hypothesis is correct the inter-quartile range should be larger for year 7 students and should be slightly smaller for year 9 students but year 11 students should have the smallest inter-quartile range. Under the cumulative frequency graphs I will draw box and whisker charts these will give a better picture of the size of the upper and lower quartiles of the graph and will show more how consistent the estimates were. Standard deviation Year 7 line 3.54cm Year 9 line 1.72cm Year 11 line 0.71cm Year 7 angle 16.40? Year 9 angle 13.85? Year 11 angle 8.00? This proves my hypothesis correct that the higher the academic year the better the estimate. With standard deviation the closer to 1 the result is the less spread out the results and the more consistent they are, showing a more educated estimates in the higher years. The higher the year in both angle and line the standard deviation becomes closer to 1. Whilst investigating my first two hypothesis 1: I predict that if people are good at guessing the length of a line they will be good at guessing the degrees of an angle. 2: I predict that the higher the year the better the estimate. I noticed a difference in the results from different sets so I have prepared a new hypothesis 3: I predict that the higher the set the better the estimate of the length of a line and the degrees of an angle. To investigate this hypothesis I will work out the Mean median mode and range for set 1, 3 and 5 students in years 7, 9 and 11 I will then compare and draw conclusions from this information Set 1 Estimate of the line Estimate 2 4 4 6 6 8 8 10 10 12 12 14 14 16 16 18 18 20 Totals Frequency 5 9 3 0 0 0 0 0 0 17 Mid-interval value 3 5 7 9 11 13 15 17 19 Frequency x mid-interval value 15 45 21 0 0 0 0 0 0 81 Mean = 4.76 Modal group = 4 6? Median is approximately 4.5 Range =2 8 Estimate of angle Estimate 10 20 20 30 30 40 40 50 50 60 60 70 70 80 80 90 90 100 Totals Frequency 1 4 3 9 0 0 0 0 0 17 Mid-interval value 15 25 35 45 55 65 75 85 95 Frequency x mid-interval value 15 100 105 405 0 0 0 0 0 625 Mean = 36.76 Modal group = 40 50? Median is approximately 40? Range = 10 50? Set 3 Estimate of line Estimate 2 4 4 6 6 8 8 10 10 12 12 14 14 16 16 18 18 20 Totals Frequency 0 13 4 1 1 0 0 0 0 19 Mid-interval value 3 5 7 9 11 13 15 17 19 Frequency x mid-interval value 0 65 28 9 11 0 0 0 0 113 Mean = 5.95 Modal group = 2 4? Median is approximately 5.5 Range = 4 12 Estimate of angle Estimate 10 20 20 30 30 40 40 50 50 60 60 70 70 80 80 90 90 100 Totals Frequency 0 3 4 10 1 0 0 1 0 19 Mid-interval value 15 25 35 45 55 65 75 85 95 Frequency x mid-interval value 0 75 140 450 55 0 0 85 0 805 Mean = 42.37 Modal group = 40 50? Median is approximately 43? Range = 20 90? Set 5 Estimate of line Estimate 2 4 4 6 6 8 8 10 10 12 12 14 14 16 16 18 18 20 Totals Frequency 5 7 0 6 0 0 0 0 0 18 Mid-interval value 3 5 7 9 11 13 15 17 19 Frequency x mid-interval value 15 35 0 54 0 0 0 0 0 104 Mean = 5.78 Modal group = 4 6? Median is approximately 5cm Range = 2 10cm Estimate of an angle Estimate 10 20 20 30 30 40 40 50 50 60 60 70 70 80 80 90 90 100 Totals Frequency 0 4 3 8 0 0 1 1 1 18 Mid-interval value 15 25 35 45 55 65 75 85 95 Frequency x mid-interval value 0 100 105 360 0 0 75 85 95 820 Mean = 45.56 Modal group = 40 50? Median is approximately 42? Range = 20 100? Conclusion Hypothesis 1 = I predict that if people are good at guessing the length of a line they will be good at guessing the degrees of an angle. Scatter graph from the scatter graph I found out that my hypothesis was nearly always correct I had 9 points of year 7 students that were good at estimating the line but not at estimating the angle (green area) so this proved my hypothesis wrong. 7 points on the graph were year 7 students that were good at estimating the angle but not the line (yellow area) this also proved my hypothesis wrong. There were 13 points in the pencil shaded area this meant that they were good at estimating the line and the angle. There were 5 points of year 7 students that were neither good at estimating the line or at estimating the angle this proved my hypothesis was right. 9 + 7 =16 this is how many points made my hypothesis wrong. 13 + 5 = 18 this is how many points of the year 7 estimate proved my hypothesis was correct. 52% of the year 7 points proved my hypothesis correct. Of the year 9 students there were no points on the graph that showed they were better at estimating the line than the angle. Although there were 4 points on the graph that showed year 9 students were better at estimating the angle than the line (yellow area). 16 points on the graph were that year 9 students estimated the line and the angle well (pencil shaded area). 6 points on the graph showed that they were neither good at estimating the line or the angle. 4 points proved hypothesis wrong. 16 + 6 = 22 this is how many points proved my hypothesis was correct. 81% of the points of year 9 students proved my hypothesis correct. Of the year 11 students there were 6 points on the graph that showed year 11 students were better at estimating the line than the angle (yellow shaded area). This proved my hypothesis wrong. There were no points in the yellow shaded area showing that they could estimate the angle better than the line. 2 points on the graph were neither good at estimating the line or the angle, although there were 17 points that were good at both hypothesis and line this proved my hypothesis correct. 6 points proved wrong, 2 + 17 = 19 proved hypothesis correct. 76% of the points on the graph proved my hypothesis correct Overall 76% + 81% + 52% = 209%/3 = 70% proved my hypothesis correct. I found out that year 9 students were better at estimating the angle that the line as there were no points that showed they were better at estimating the line. I found out that year 11 students were better at estimating the line as there were no points showing that they were better at estimating the angle. 5 points in year 7 were neither good at estimating the line or the angle, 6 points were good at neither in year 9 and 2 point6s were good at neither in year 11 this backs up my hypothesis that The higher the year the better the estimate. These results are not reliable because there were not even numbers of year 7,9 and 11 pupils and the points on the scatter graph may have been swayed if 2 or more members of the same year had guessed the same point because it was only marked once. Second hypothesis I predict that the higher the year the better the estimate. Cumulative frequency graphs Year 7 angle On the graph the median was 40? this was very close to the actual result although on the graph the inter-quartile range was 17.5? this shows the estimates were not very consistent you can see this better on the box and whisker chart underneath the boxes are fairly big. Year 7 line On the graph the median is 4.5 this is what the actual answer was although on the graph the inter-quartile range was 4.4cm this shows the estimates were not very constant. The boxes of the box and whisker chart are large. Year 9 line The median is 37.5 this is very close to the actual answer, the inter-quartile range is 15? this shows that the estimates are more consistent than the year 7 estimates this backs up my hypothesis the higher the year the better the estimate. Year 9 angle The median on this graph is 4.75cm this is very close to the actual but not as close as year 7 estimates as that was exactly on 4.5cm this proves my hypothesis wrong. The inter-quartile range was 3cm this is smaller that on the year 7 cumulative frequency graph, the boxes on the box and whisker chart are smaller than on the year 7 graph this shows that the estimates were more consistent which proves my hypothesis correct. Year 11 line The median is 40? this is the same as year 7 median but not as close as the year 9 median so this proves my hypothesis wrong. The inter-quartile range is 11.25? this is smaller than all the other inter-quartile ranges which proves my hypothesis is correct. Year 11 angle The median is 4.75cm this is the same as year 9 but not close as year 7 this proves my hypothesis wrong this may be because the estimates were very consistent but just scattered closely around the actual result. The inter-quartile range is 1cm this is very consistent and proves that my hypothesis was correct. The boxes on the box and whisker chart were very closer together by looking at this you can see how consistent the estimates were. I predict that the higher the year the better the estimate. I investigated the means of years 7,9 and 11s estimates of the line and angle Year of mean Mean of line (cm) Mean of angle (?) 7 5.70 42.61 9 5.50 44.25 11 4.94 38.53 The actual size of the line was 4.5cm so as the higher the year the better the estimate of the line this proves my hypothesis. The actual size of the angle was 38? so Year 11 students were better at estimating the angle although the year 7 mean was better than the year9 mean this proves my hypothesis wrong this may have been because we did not use a large enough sample, or because the mean was found from a frequency table which is only an estimate because we dont actually know the exact values of all the estimates from this. I also investigated the modal group to see if most the estimates were made in the correct group. Year Modal group (line) Modal group (angle) 7 2 4? 30 40? and 40 50? 9 4 6? 40 50? 11 4 6? 40 50? Year 7 was the only year that the modal group of the line that actually contained the correct answer. I found two modal groups for year 7 one of them contained the correct answer and years 9 and 11 modal groups both contained the correct answer this did not prove my hypothesis. I investigated the median to see if it got closer to the correct number the higher the year. Year Median (line) Median (angle) 7 5 38 9 5 43 11 4.5 40 Year 7 estimated the median exactly correct for the angle. The estimate of the line got better the higher the year although year 7 and 9 were the same. I investigated the range to see if the estimates became any more consistent as the year got higher. Year Range (line) Range (angle) 7 18 90 9 8 80 11 6 40 The consistency did become better as the year got higher This proves that my hypothesis was correct The higher the year the better the estimate. Not all these tables prove my hypothesis correct especially year 9 proved it wrong this may have been because we might of asked a lot of lower set year 9s due to systematic sampling so I will investigate the effect of the set on the estimate. I investigated the means of sets 1,3 and 5 estimates of the line and angle Set of mean Mean of line (cm) Mean of angle (?) 1 4.76 36.76 3 5.95 42.37 5 5.78 45.56 Set 1 is the best set and set 5 is the worst out of the three sets we have investigated. The actual size of the line was 4.5cm so as the better the set the better the estimate of the line apart from set 5 has a better mean than set 3 this proves my hypothesis wrong. The actual size of the angle was 38? so The higher the set the better the estimate this proves my hypothesis correct. I also investigated the modal group to see if most the estimates were made in the correct group. Set Modal group (line) Modal group (angle) 1 ;4 6? ;40 50? 3 ;2 4? ;40 50? 5 ;4 6? ;40 50? Set 1 and set 5 had the correct modal group but set 3 had the modal group too low. All the sets had the modal group for the angle too high as the correct answer would have been ;30 40? this has no effect on my hypothesis. I investigated the median to see if it got closer to the correct number the higher the year. Set Median (line) Median (angle) 1 4.5 40 3 5.5 43 5 5 42 Set one median of the line was exactly correct this helps prove my hypothesis correct. Set 5 median of the line was closer to the actual than set 3 I have found that set 5 are better at estimating the line than set 3. Again set 1 was closer to the actual but then set 5 was second best with set three being the worst. I investigated the range to see if the estimates became any more consistent as the year got higher. Set Range (line) Range (angle) 1 6 40 3 8 70 5 8 80 The range was smallest for set one this proves that my hypothesis was correct because the estimates were more consistent. The range of the angle proves my hypothesis was correct, as it is smaller for set 3 than it is for set 5. The range of the line for set 3 and 5 are the same this does not prove that my hypothesis was correct or wrong. I found out that set 5 students were better at estimating the line than set 3 students other than that my hypothesis was correct.