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John: “It’s still reasonable to see private cars in the first place.”
Sam: “Um, I think this may be because the drivers working in public transport are well trained enough and there are simply more private cars on the road!”
John: “Then judging by the graph, taking public transport is actually safer than driving my own private car!”
We hypothesize that one of the ways to minimize your risk of getting into a car accident is by taking public transport instead.
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“I think it is Sha Tin, ” Sam said.
Their opinions differed once more, so they started to search for data to analyse.
Out of the 18 districts in Hong Kong, Yau Tsim Mong district has the highest amount of car accidents happening there overall.
The number of car accidents happening in Yuen Long district and Sha Tin district are also noticeably higher. Yau Tsim Mong also has the highest amount of ‘light’ car accidents, followed by Yuen Long and Sha Tin once more. However, the district that has the highest amount of serious accidents, which is much higher than that of other districts, is Yuen Long.
Other districts have more or less the same amount (except for the Islands,
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which have much less). The amount of car accidents that involved deaths is constant across all districts.
“Hold on,” interrupted Sam, “Would some districts have a particularly higher amount of accidents because their area is bigger and the population density is higher?”
“Oh yeah… I didn’t think of that,” John admitted.
However, that may not always be the case. Here we have a star plot representing area, population density, and amount of road accidents each district has. The size of the sector is proportional to the respective value it represents. Large districts with low population density are expected to have fewer accidents, e.g. Islands, North and Sai Kung Districts. In contrast, Yau Tsim Mong and Kwun Tong districts have high accident rate while their size is small and the density is high. Yuen Long and Tai Po districts are an exception though. They are accident-prone despite its large area and low population density.
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“Hmm… That’s still too many exceptions to call it a clear trend,” Sam said,
“May be districts are too broad of an area to research on...”
“Let’s try looking at data on tunnels then!” suggested John.
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Note- Area of the tunnels are defined by the area dictated in the law, which include the interior and exterior of the tunnels.
The tunnel with the most accidents was the Cross Harbour Tunnel, not surprising at all, considering that it is the tunnel with the most traffic in Hong Kong. However, the amount of accidents in a tunnel doesn’t always have to do with its traffic conditions. Below is a scatter plot illustrating the relationship between the amount of accidents a tunnel has and the amount of cars that pass through it every day.
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Typically the higher the amount of average daily vehicles, the more accidents a tunnel has. But again, there are multiple exceptions. We can’t really reach a concrete conclusion since there isn’t much difference between the amounts of accidents each tunnel has.
In conclusion, Yau Tsim Mong and Kwun Tong are especially dangerous districts to drive in, and the Cross-Harbour Tunnel requires attention as well. The busiest areas always have the highest amount of traffic accidents, so we should be especially vigilant when driving through busy areas like those. But the population density and the average amount of vehicles daily don’t have a consistent relationship with the amount of car accidents an area has, so in other areas road conditions are probably a bigger factor.
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WHAT WEATHER CONDITIONS are Traffic Accidents more likely to occur in?
“I’m not sure how useful this information can be, but there is one thing I’m sure of. Traffic accidents are more likely to occur in the rain, right?” said Sam.
“But judging by what we learnt today, the answer to that might be surprising,” John challenged, “We should do some research before coming to conclusions.”
“No way, there’s no reason why wet roads wouldn’t be more dangerous than dry roads- It’s harder for cars to stop when the ground is slippery, that’s why accidents are more likely to occur in rainy days, everyone knows that!” Sam exclaimed.
“Then why don’t you see for yourself?” John said.
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“What?! The probability of getting into an accident on a wet road is much lower than the chance of getting into an accident on a dry road?” exclaimed Sam, “But how can that be?”
“I don’t really understand either,” confessed John, “Logically speaking, it would be more dangerous to drive on a slippery road, wouldn’t it? Maybe it is because people are especially alert when driving in dangerous conditions and end up performing better, or maybe more people take the MTR instead on those days.”
“That makes sense,” said Sam, “I guess there are things that we just can’t know for sure until we do more research.”
******
In the end, Sam and John forgot about the research they spent their precious time on. But then again, even if they followed the information they gained from these graphs and altered their lifestyle to be incredibly inconvenient, it still wouldn’t be a foolproof plan. After all as Murphy’s Law goes -
“Whatever can go wrong will go wrong”, so as long as cars exist, so will traffic accidents. The statistics shown today are a bit of extra knowledge, but please don’t follow them exactly. Ultimately, the best way to avoid traffic accidents is simply to be careful and stay alert at all times.
CONCLUSION
Collecting data and designing graphs were quite foreign tasks to us. After finishing the problem, we concluded that there isn’t a definite way to avoid
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car accidents since there is an infinite amount of factors that can affect our topic, such as the state of the driver, problems with cars, or even a planned murder etc. While there may be a trend, unpredictable exceptions can always occur, especially when there are so many factors that lead up to such events, so it is best that we stay vigilant at all times.
Yet, we still want to do the best we can do to avoid car accidents and help readers of this project to be a safe person by analysing data related to road accidents.
In conclusion, we found out that using public transport can lower our probability for getting involved in car accidents, that we should avoid busy areas and rush hours, and that the weather doesn’t necessarily indicate safer or more dangerous conditions.
Stay safe!
References:
[1] Data from the transport department:
https://www.td.gov.hk/tc/road_safety/road_traffic_accident_statistics/201 7/index.html
[2] The census and statistics department:
https://www.censtatd.gov.hk/hkstat/sub/sp150.jsp?productCode=FA1000 96
[3] Hong Kong Weather Observatory:
https://www.hko.gov.hk/cis/statistic/rf_1_e.htm
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優異作品:
運動成績與體格的關聯
學校名稱：梁文燕紀念中學（沙田）
學生姓名：方肇楠，方偉華，林均俊 指導教師：陳志文老師
摘要：
相信大家在中學生涯中都參加過陸運會，大家當時會否羨慕在頒獎 臺上的同學呢？而你們又有沒有想過他們是憑甚麽獲勝呢？是出色 的技術嗎；還是過人的體格？在本篇文章中我們會探討運動員的身 高體重對其表現的影響。
左方為謙謙，右方為林林
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在體育課上，體育老師問了我們一個問題：大家的身形究竟跟跑步 有什麽關係呢？林林認爲越高大的人就跑得越快。謙謙認爲體重 越重就跑得越慢。其實在醫學界有一個叫BMI 的指標，BMI 的設 計是一個用於公眾健康研究的統計工具。當需要知道肥胖是否為 某一疾病的致病原因時，可以把病人的身高及體重換算成 BMI， 再找出其數值及病發率是否有線性關連。BMI 指數可以通過以下 公式計算：
W 是重量（公斤），h 是高度（米）。
體重指標 類別
18.49 或以下 過輕 18.5 – 22.9 適中 23.0 – 24.9 過重 25.0 – 29.9 肥胖
30.0 或以上 極度肥胖
圖表(一)
於是，我們就連同體育科老師和數學科老師一起收集及分析了全校 學生的體適能數據，並集合了全港中學生的體適能數據，再加以分 析，我們得出了以下結果:
項目 林林 謙謙 本校同學平均水平 全港學生平均水平
一分鐘仰臥起坐(次) 30 10 20.3 33.07
坐地前伸(釐米) 40 9 23.8 34.26
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項目 林林 謙謙 本校同學平均水平 全港學生平均水平
掌上壓(次) 35 8 13.5 19.43
九分鐘跑(米) 1700 1350 1473.1 1538.77
身高(米) 1.73 1.6 1.692 1.6966
體重(千克) 75 63.7 59.8 59.26
圖表(二)
經過計算，林林的BMI 指數為 25.0，而謙謙的 BMI 指數為 24.8，
看上去林林的身形高大，但是BMI 指數卻和謙謙差不多。從圖表
(二)中可看到，他們在長跑項目中相差 350 米的距離，但短跑又如 何？
讓我們回顧2016 年裡約奧運會男子 100 米的首八名：
2016 年夏季奧林匹克運動會田徑 男子100 公尺比賽
身高（米） 體重（公斤） BMI 指數
尤塞恩·博爾特 1.95 86 22.6
賈斯汀·加特林 1.85 79 23
安德烈·德格拉塞 1.76 68 21.9
約安·布雷克 1.8 76 23.4
阿卡尼·西姆拜恩 1.74 67 22.1
本·約瑟夫·梅特 1.79 70 21.8
吉米·維科 1.86 83 23.9
特拉伊瑪·布魯梅爾 1.73 70 23.3
平均值 1.81 74.875 22.75
圖表(三)
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經過計算，他們BMI指數的總體標準差為0.7228，不高。而他們身高 和體重的總體標準差分別為6.892和6.7535。以上的數據顯示，雖然身 高和體重有不同的分別，但是只要你有一個適當的BMI指數，即是身 高和體重有一個一定的比例，你便能在短跑中取得佳績。我們在這裡 也可以作出一個大膽的假設：林林和謙謙的短跑時間不會相差太遠。
為了測試我們的假設是否正確，我們特別邀請了林林和謙謙進行一次 短跑100米競賽，林林的成績為13.75秒；而謙謙的成績是14.19秒，當 中只相差0.44秒，證明了林林和謙謙的BMI指數在短跑這項運動中表 現相仿。
除了短跑，其實其他運動都有一個特定的BMI指數範圍，該範圍內的 人取得勝利的機會很大。為了證明，我們也找到了馬拉松的世界紀錄 的前三名的BMI指數，分別為埃利烏德·基普喬蓋：20.0, 鄧尼斯·基普 魯托·基梅托：18.8，肯內尼薩‧貝克勒：21.0。可以看到馬拉松這類長 跑的選手BMI指數比較低，以上三位的BMI指數平均值為19.9。
謙謙和林林的 BMI 指數那麼高，有甚麼運動是適合他們的呢？2016
裡約奧運的鉛球冠軍里安·克勞澤身高 2.01 米，體重 132 公斤，BMI
指數32.1，但這對他們來說還算是太高了，而且我相信對香港的大部
分學童也不是十分適合的。此時我們的另一位朋友—小明走了過來參 與我們的討論，他是我們學校鉛球比賽的記錄保持者，他剛剛做完手 握力測試，於是他便問手握力的強度是否與推鉛球有關，爲了解答他 的疑問，我們再次收集了我校鉛球比賽八強的手握力數據作出比較：
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鉛球比賽八強的手握力 手握力數據 (千克) (左手+右手)
體重 (千克)
1. 79.5 85.0
2. 76.2 84.7
3. 75.6 76.8
4. 71.3 78.6
5. 71.0 65.9
6. 69.8 70.5
7. 68.7 69.0
8. 67.0 67.1
平均值 72.3875 74.7
圖表(四和五)
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從以上圖表可得知，發現手握力的強度與推鉛球的距離(成績)真的有 關聯。在圖表(四)中可看到第一名的手握力數據最高，有79.5千克，
然後手握力的強度隨著參加者的名次下降，到67千克: 有越高的手握 力能在推鉛球中取得更好的成績。
回到我們的主題，參加者的BMI 指數與手握力(及推鉛球成績)又是否
有關？我們根據推鉛球八強的體重及手握力數據繪畫了圖表(五)進 行比較。我們發現兩者成正比，參加者體重越高，手握力的指數便越 高。透過繪畫圖表後，我們便要尋找該條線性回歸的直線方程(最佳 配適線)，這次我們只需要進行簡單計算便能夠計算出圖中線性回歸 的直線方程。
A B C D E F
x 體重(kg) y 手握力數據(kg)
85 79.5 10.3 7.1125 73.25875 106.09
84.7 76.2 10 3.8125 38.125 100
76.8 75.6 2.1 3.2125 6.74625 4.41 78.6 71.3 3.9 -1.0875 -4.24125 15.21
65.9 71 8.8 -1.3875 12.21 77.44
70.5 69.8 -4.2 -2.5875 10.8675 17.64 69 68.7 -5.7 -3.6875 21.01875 32.49 67.1 67 -7.6 -5.3875 40.945 57.76 體重的
平均數
手握力的平均 數
總和 總和
74.7 72.3875 198.93 411.04
鈄率(m) 0.483967 y 軸截距(c) 36.23513
圖表(六)
在圖表(六)中，我們進行運算。該條直線方程的斜率只需將E欄總和除 以F欄總和，便能得出0.484(斜率, m) 。而y軸相交點(c)則為36.235。
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圖中線性回歸的直線方程是 y 0.484x36.235。十項全能的冠軍 羅曼·謝布爾勒的身高體重為1.86米，體重為88公斤，BMI指數為 25.8，對他們來說非常適合。
在最後，如果你希望在運動中取得佳績，根據上述的研究，我們可以
得出運動員的成績是與 BMI 指數直接掛鈎的。就如上述，謙謙和林
林的 BMI 指數與奧運選手大致相約，因此，推論他們能獲得獎項，
而事實證明他們在學校陸運會中取得獎項。而在鉛球比賽中，小明能 取得佳績亦是和體重與手握力息息相關。體重和手握力越高，在比賽 中取得的名次越高。因此，我們可以證明我們的推論是正確的。根據 以上對鉛球和短跑的分析。我們可以大膽地假設運動成績是和身體質 量指數成正比。我們根據這個猜想，搜集了上年度陸運會鉛球的冠軍 和他的各項身體數據，見以下圖表(七):
圖表(七)
在名次一欄中，第一名的推鉛球紀錄是8.84米，再參考圖表(八)看看 他的體重和身高，發現其BMI指數和手握力數據和紀錄保持者的相 似，因此他在比賽中取得佳績。由此我們發現身體質量指數能幫助
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我們在相應的運動項目中取得優勢，較易獲取好成績。
記錄保持者 上任鉛球冠軍
體重 90.5 千克 95.1 千克
身高 170 厘米 180.5 厘米
BMI 指數 31.3 29.1
手握力 79 公斤（左手加右手） 76.5 公斤（左手加右手）
圖表(八)
因此，各位在選擇運動時可以參考一些運動員的身體質量指數來選擇 一個適合自己的運動了。
67 參考資料：
[1] 維基百科: 2016年夏季奧林匹克運動會田徑男子100公尺比賽 [2] 梁文燕紀念中學（沙田）二零一八至二零一九陸運會數據 [3] 梁文燕紀念中學（沙田）體育科體適能數據
[4] 香港中學生體適能常模表：