Visual Basic

SIriben Somboon

Olympic Games are held every 4 years. The heights for men’s high jump in the Olympic Games are collected from 1896 to 2008. The aim if this task is to consider the winning height for the men’s high jump in the Olympic Games.
Table 1: A data showing the heights achieved by for men’s high jumped by the gold medalists at Olympic Games from 1932 to 1980.
Year | 1932 | 1936 |1948 | 1952 | 1956 | 1960 | 1964 | 1968 | 1972 | 1976 | 1980 |
Number | 1 | 2 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 |
Height (cm) | 197 | 203 | 198 | 204 | 212 | 216 | 218 | 224 | 223 | 225 | 236 |

The heights are collected from year 1932 – 1980 for the first set of data. Since the Olympic Games are held every 4 years, so every 4 years, the number is increasing by 1. Let year 1932 benumber 1. Example is from year 1932 to year 1936, the number is 1 for year 1932 and 2 for year 1936. Olympic Games were not held in 1940 and 1944 because there were wars during that time (WW2). So the number skipped from 2 to 5 from year 1936 to 1948.

Figure 1 : A diagram showing the height for men’s high jump in Olympic Games from 1932 to 1980 (number from 1 to 13). X-axis is the number and y-axisis the height in cm that the gold medalists achieved in each Olympic Games.

According to the figure 1, I observe that the numbers are increasing between each Olympic Games (except from year 1936 to 1948). The amount that the heights for men’s high jump in the Olympic Games that are increasing each year is quite constant, so I use a linear line to find the equation of heights for men’s highjump for Olympic Games. With many points, I have to choose 2 points that can represent my graph if I want to find the linear equation for this data. I wouldn’t get an accurate result for this data, so I decided to use a median-median line.
I use a median-median line to find the equation of the line. The equation for median-median line is
y = ax + b. Where “a” = the slope of the median from thedata; “b” = y-intercept for the data; “x” = the number (the year); and “y” = height that the gold medalist achieved in that Olympic Game. The numbers are divided into 3 groups; in this case 4/3/4 because there are 11 numbers and 11 is not divisible by 3. The first and the last group must have the same size. Then I find the median for each group (both the number and the height).

Table 2: Findingmedian for first group.
Number | 1 | 2 | 5 | 6 |
Height (cm) | 197 | 203 | 198 | 204 |
Median for number = 2+5 2 = 3.5
Median for height = 198 + 203 2 = 200.5



Table 3: Finding median for middle group.
Number | 7 | 8 | 9 |
Height (cm) | 212 | 216 | 218 |

Median for middle group is (8,216).

Table 4: Finding median for last group.
Number | 10 | 11 | 12 | 13 |
Height (cm)| 224 | 223 | 225 | 236 |
Median for number = 11+122 = 11.5
Median for height = 224 + 225 2 = 224.5



The median for the first group is 3.5 for number and 200.5 for height (3.5, 200.5). The median for the middle group is (8, 216). The median for the last group is (11.5, 224.5). To find “a” for the median-median line equation, I find the slope of the median I got from last group and thefirst group. To get “b” for the median-median line equation, I need to find the y-intercept of the line.

To find “a”
Y3-Y1X3-X1 = 224.5-200.511.5-3.5 = 248 = 3
“a” = 3
To find “b”
Y1+Y2+Y3- a(X1+X2+X3)3 = 200.5+216+224.5- 3(3.5+8+11.5)3 = 641-3(23)3 = 190.67
“b” = 190.67

The median-median line equation is y = 3x + 190.67.Then I graph the line by using my equation that I found.Figure 2: A diagram showing the height for men’s high jump in Olympic Games from 1932 to 1980. The slope of the line Is 3 and the y-intercept is 190.7. This shows that every 4 year (every Olympic Games) the height for men’s high jump increases by 3 cm and at the year 1932, the height that should be achieved by the gold medalist is 190.7 cm.

Figure 3: A diagram showing the height for men’s high...