I have been given a set of a line and angle measuring and 50o. Using the data given to me for this investigation I am going to find the mode, mean and median from the inter-quartile range. I must do this for each specific group, both child and adult. I will do this because I will be able to compare all of my results. I will then see if those who are older have better results than children to check to see if my hypothesis is correct. I believe we were given the sizes of the angle and length for these reasons. Small lengths are within our grasp as estimations.
Smaller lines are simpler for us to see and predict more accurate measurements. As the angle is between 0o and 90o meaning we have estimation is our minds as we have to angles to base our prediction between. To test this hypothesis I am going to use a range of statistical measures in relation to the provided data. I will calculate the averages and the range to see if they support this claim or not. I will then display the data in different ways to see what other information I can gain from it. But this data is limited in its use. It tells us very little in regards to our hypothesis, as the results are very similar.
This makes it difficult to compare the difference between the children and the adults. They are very balanced results. The Children scored better median scores in both line and angle but the adults got better results Modally. In all other aspects the results were very similar. But overall the adults seemed to be slightly better as the percentage error of their estimation were slightly more accurate. What this information doesn’t tell us is where the estimations act actually lies. It only tells us the averages, the real results could be much more different. Other factors weren’t taken into the equation either.
More children were asked than adults, which could have lead to the huge difference in the range of answers in the comparison between children and adults. If there had been and equal sample this could be some evidence to support the hypothesis. Analysing the estimation for the length of the line it is difficult to clearly see who has greater estimation ability. The modal estimates are equal, however the adults have a lower percentage error, yet the children have a lower percentage error in the median. But the median isn’t affected by extreme values, as only the middle value of the data is taken.
This is why this type of statistical method is quite misleading. But overall, looking at the percentage errors for both children and adults I can see that they are quite small, suggesting that the estimation ability for both groups is quite equal. Even with this misleading statistical method, when I was analysing the estimation ability for the size of the angle and comparing the averages between children and adults I noticed that there was some evidence to support the hypothesis. There are great differences in the percentage errors, clearly showing that the adults had been closer at estimating the actual size of the angle than the children.
To get a better view of the pattern of estimation I am going to find the IQR of each set of data. The IQR gives us the middle 50% of the data. We calculate it so we are looking at the majority of the population, this is much more accurate reflection of estimation ability. This is because this method helps to exclude any outrageous results. The IQR is much more accurate than the previous method as it allows us to focus on the majority of the estimations and cuts out the bottom and top 25% of the estimations, where we could have extreme values.