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Graphs – Notes

Examples Based on Lecture Notes (GCNU308A)

Section 1. Quantitative Data and Qualitative Data (量性數據與質性數據)

  • Example 1.1
  • EN: The number of laptops owned by a household is discrete quantitative data, whereas their favorite computer brand is qualitative data.
  • TC: 一個家庭擁有的手提電腦數量屬於離散量性數據，而他們最喜歡的電腦品牌則屬於質性數據。
  • Example 1.2
  • EN: The exact time taken to run 100 meters is continuous quantitative data, while the blood type of an athlete is qualitative data.
  • TC: 跑完 100 米所需的實際時間屬於連續量性數據，而運動員的血型則屬於質性數據。

Section 2. Pictogram (象形圖)

  • Example 2.1
  • EN: A library uses a small book symbol to represent 50 borrowed books in order to show weekly borrowing records.
  • TC: 圖書館使用一個小書本圖案代表 50 本借出的書籍，以展示每週的借閱記錄。
  • Example 2.2
  • EN: A coffee shop uses a cup icon with a key indicating that each cup represents 20 cups of coffee sold per day.
  • TC: 一間咖啡店使用咖啡杯圖案並附上圖例，說明每個圖案代表每天售出 20 杯咖啡。

Section 3. Bar Chart (棒形圖)

  • Example 3.1
  • EN: A bakery draws a vertical bar chart to compare the total sales volume across four bread flavors.
  • TC: 一間麵包店繪製垂直棒形圖，用以比較四種麵包口味的總銷量。
  • Example 3.2
  • EN: A primary school uses a horizontal bar chart to display the frequency distribution of students commuting by bus, train, walking, or private car.
  • TC: 一所小學利用水平棒形圖來展示學生乘坐巴士、火車、步行或私家車上學的頻數分佈。

Section 3.1. Compound Bar Chart (複合棒形圖)

  • Example 3.1.1
  • EN: A smartphone company uses a clustered compound bar chart to compare male and female customer numbers across three different phone models.
  • TC: 一間智能手機公司使用並列式複合棒形圖，比較三種不同手機型號的男性與女性顧客人數。
  • Example 3.1.2
  • EN: A secondary school uses a segmented compound bar chart where each stacked column illustrates the proportion of lunch, transport, and stationery expenses for each grade.
  • TC: 一所中學採用接疊式複合棒形圖，每條堆疊柱形展示各個年級在午餐、交通及文具開支上的比例。

Section 4. Pie/Circle Chart (圓形圖/圓瓣圖)

  • Example 4.1
  • EN: A company uses a pie chart to display the percentage distribution of its annual marketing budget across social media, TV, and print advertisements.
  • TC: 一間公司使用圓形圖來展示其年度市場推廣預算在社交媒體、電視及印刷廣告上的百分比分佈。
  • Example 4.2
  • EN: A survey calculates the sector angles on a pie chart to show student preferences for four school club activities, where 25% corresponds to a 90° angle.
  • TC: 一項調查計算圓形圖上的扇形圓心角以展示學生對四種學會活動的偏好，其中 25% 對應 90 度的扇形角。

Section 5. Histogram (組織圖/直方圖/矩形圖)

  • Example 5.1
  • EN: A hospital plots a histogram with no gaps between columns to show the weight distribution of newborn babies grouped into 0.5 kg intervals.
  • TC: 醫院繪製柱形之間沒有空隙的直方圖，展示以 0.5 公斤為組距的新生嬰兒體重分佈。
  • Example 5.2
  • EN: An examination board constructs a histogram using class boundaries to display the final continuous exam scores of 200 candidates.
  • TC: 考試局利用組界繪製直方圖，以展示 200 名考生在期末考的連續考試成績分佈。

Section 6. Frequency Polygon (頻數多邊形)

  • Example 6.1
  • EN: A gym connects the class mid-points of members’ workout durations with straight lines and anchors both ends at zero frequency to observe the distribution shape.
  • TC: 健身室將會員運動時長的組中點用直線連接，並在兩端以零頻數定位，以觀察分佈的形狀。
  • Example 6.2
  • EN: A meteorologist constructs a frequency polygon to compare the daily average rainfall distribution between July and August.
  • TC: 氣象學家繪製頻數多邊形，用以比較七月與八月每日平均降雨量的分佈情況。

Section 6.1. Relative Frequency Polygon / Cumulative Frequency Polygon (相對頻數多邊形 / 累積頻數多邊形)

  • Example 6.1.1
  • EN: A supervisor draws a cumulative frequency polygon by plotting upper class boundaries against cumulative frequency to find how many employees arrive within 30 minutes.
  • TC: 主管將組上限與累積頻數繪製成累積頻數多邊形，以找出在 30 分鐘內到達公司的員工人數。
  • Example 6.1.2
  • EN: A teacher uses a cumulative frequency curve to determine the median test score and upper quartile of the entire class.
  • TC: 教師使用累積頻數曲線來找出全班測驗分數的中位數及上四分位數。

Section 7. (Broken) Line Graph (折線圖)

  • Example 7.1
  • EN: An investor tracks the daily closing price of a stock over thirty days using a broken line graph to identify price fluctuations and overall trends.
  • TC: 投資者使用折線圖追蹤某股票在連續三十天的收市價，以識別價格波動與整體趨勢。
  • Example 7.2
  • EN: An electronics store plots monthly smartphone sales over two years on a line graph to identify peak seasons and sales drops.
  • TC: 一間電器店將兩年內每月的智能手機銷量繪製在折線圖上，以找出銷售旺季及銷量下跌的時期。

Section 8. Scatter Plot/Diagram (散點圖)

  • Example 8.1
  • EN: A study places weekly study hours on the x-axis and final test scores on the y-axis to observe a strong positive linear relationship.
  • TC: 一項研究將每週溫習時數放在 x 軸並將期終考試分數放在 y 軸，以觀察兩者之間的強正線性關係。
  • Example 8.2
  • EN: A research lab constructs a scatter diagram between daily outdoor temperature and winter coat sales to demonstrate a clear negative correlation.
  • TC: 一間研究實驗室繪製每日室外氣溫與冬裝大褸銷量之間的散點圖，以展示明顯的負相關關係。

Section 9. Summary of Statistical Charts/Graphs (統計圖表摘要)

  • Example 9.1
  • EN: An analyst chooses a bar chart rather than a pie chart because the dataset contains twelve distinct product categories.
  • TC: 分析師選擇使用棒形圖而非圓形圖，因為該數據集包含十二個不同的產品類別。
  • Example 9.2
  • EN: A researcher selects a histogram instead of a broken line graph because the primary goal is to examine data skewness and outliers in grouped continuous data.
  • TC: 研究人員選擇直方圖而非折線圖，因為主要目的是檢視分組連續數據的偏度及離群值。

Section 10. Interpretation of Statistical Charts/Graphs (統計圖表的闡釋)

  • Example 10.1
  • EN: An executive uses interpolation to estimate company revenue at the midpoint of the second quarter based on confirmed April and June figures.
  • TC: 一名行政主管利用內插法，根據四月與六月的確認數據來估算第二季中段的公司收入。
  • Example 10.2
  • EN: A manager cautions that using extrapolation to forecast sales ten years into the future carries high uncertainty and risk.
  • TC: 經理提醒大家，使用外插法預測未來十年的銷售額具有高度不確定性與風險。

Section 11. Deception and Its Sources (騙局/做假及其根源)

  • Example 11.1
  • EN: An advertisement compresses the horizontal timeline axis inconsistently to make an irregular revenue increase appear steady and smooth.
  • TC: 一則廣告採用不一致的橫軸時間比例尺，使不規律的收入增長看似穩定且平滑。
  • Example 11.2
  • EN: A salesperson compares two competitors using graphs with different vertical axis scales to exaggerate minor performance gaps.
  • TC: 一名銷售員利用兩幅縱軸比例尺不同的圖表比較兩家競爭對手，藉此誇大微小的表現差距。

Section 12. Misinterpretation Due to Limited Data (因有限數據而導致的錯誤闡釋)

  • Example 12.1
  • EN: A restaurant assumes an overall surge in weekend customer traffic is driven by local families without collecting demographic data, only to discover later that tourists formed the majority.
  • TC: 一間餐廳在未收集人口特徵數據的情況下，假設週末顧客流量激增是由本地家庭帶動，後來才發現遊客佔了大多數。
  • Example 12.2
  • EN: A mobile app attributes higher downloads in July solely to a new interface update, overlooking the seasonal increase from students starting summer holidays.
  • TC: 一款手機應用程式將七月份下載量的上升完全歸功於介面更新，卻忽略了學生開始放暑假所帶來的季節性增長。

Section 13. Visual Deception (視覺錯覺)

  • Example 13.1
  • EN: A news report truncates the y-axis to start at 90 instead of 0, making a minor 2% price increase look like a dramatic surge.
  • TC: 一篇新聞報導將縱軸截斷並由 90 而非 0 開始，使微小的 2% 價格漲幅看起來像急劇暴升。
  • Example 13.2
  • EN: A company stretches the vertical axis of its competitor’s profit chart while shrinking its own to visually downplay the rival company’s growth.
  • TC: 一間公司拉長競爭對手盈利圖表的垂直軸並壓縮自己的圖表，在視覺上淡化對手公司的增長幅度。
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