Essay upon Channel of Distribution
Mathematics SL IB Collection Assignment two (Type II)
Gold Medal Heights
By: Petrel Liu
Olympic video game is a sport even that held internationally once every 4 years, different nation will have players gather about in one destination to compete one another in a particular sport. The purpose of this mathematics portfolio is to consider the winning height for the men's high jump in the Olympic Games. This kind of math collection will research the relationship among data details and features of the graph. The function will be designed multiple times to have accurate effect. This mathematics portfolio will probably be separated in 4 parts; each section has a further investigation in function. In the 1st section I will be graphing the data that is given and develop a function to support the graphed info. In the second section I am compare the developed function to the initial data, after which improve my own function based on the result. In the 3rd section an accurate function will be developed using technology, and I is going to compare the function of technology to my modeled function, also predicting and estimating the data that would not given using my modeled function. In the 4th section an investigation will be held to check if the capabilities that I allow us match the extra points, and a better function will be produced after the added data have already been added. The table listed below gives the level (in centimeters) achieved by the gold medalist at different Olympic games. Year| 1932| 1936| 1948| 1952| 1956| 1960| 1964| 1968| 1972| 1976| 1980| Level (cm)| 197| 203| 198| 204| 212| 216| 218| 224| 223| 225| 236
There were no Olympic games in 1940 and 1944 as a result of world war. Therefore the info point would not exist. During war time athletes are not able to meet to be competitive due to the war. In 1948 the jumper's height have got decreased compare to the year of 1936, I assume that the high jumpers got lost all their practicing period during the conflict. Therefore the info point will be lower than past year. Section I:
From this section all of us will check out the data that may be given, the most accurate way to investigate a set of data should be to graph the function and locate the appropriate equation to symbolize the graph. The formula will let you additional investigate by identifying the behaviour of the graph. This section will be separated in 2 steps the first is to graph the data and the next step is to find a model function to symbolizes the graph. Step 1 : Chart the data
If the number is too big, a computational error would be big too. In order to reduce the chances of error I scaled the figures down to help to make it perfectly ratio, so it will not impact the portion of the graph. | Equation| Variable| Example
12 months | Y= 1900 + 4(x)| Y= year X= Reduced number| 1932= early 1900s + 4(8) X=8| Elevation | Y= 100(x)| Y= Height X= Reduced number| 192=100(1. 97) X=1. 97
This is the info that has been scaled down and then the formula that I in the above list. Year| 8| 9| 12| 13| 14| 15| 16| 17| 18| 19| 20| Height (m)| 1 . 97| 2 . 03| 1 . 98| 2 . 04| 2 . 12| 2 . 16| 2 . 18| 2 . 24| 2 . 23| 2 . 25| 2 . thirty six
Step2: Find an equation
The graph display above reveals a framework that is generally increasing, even so some level of the chart shows within a decreasing structure for example when the data stage of x=9 to the data point of x=12 the graph is within a reducing structure. The point of the graph is generally within an increasing composition therefore I will probably be using a thready function to model the data by choosing the line of the very best fit.
I know that my function will probably be in linear form which is y=ax+b I am offering the y value and x value according to the info. I will get the value of " aвЂќ and " bвЂќ by fixing a system of equation that made up by 2 items that I pick from the data which can be (8, 1 . 97) and (19, 2 . 25), the points take the line of the finest fit and it will show the basic structure in the data. Arranged a system of equation:...