Tutorial Exercise: Data Presentation and Interpretation (統計數據的組織與闡釋)
Questions (題目)
Question 1 The monthly revenue (in thousand dollars, $K) of a sports shop in 2024 is recorded as follows: 某體育用品店於 2024 年的每月營業額（單位為千元，$K）記錄如下：
| Month (月份) | Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Revenue ($K) (營業額) | 320 | 450 | 380 | 410 | 500 | 720 | 850 | 900 | 750 | 600 | 480 | 650 |
- (a) Classify the type of data for the monthly revenue. 請將每月營業額的數據類型進行分類。
- (b) What was the revenue in May? 五月份的營業額是多少？
- (c) Find the total revenue in the first quarter (Jan, Feb, and Mar). 計算第一季（一月、二月及三月）的總營業額。
- (d) Find the total revenue in the third quarter (Jul, Aug, and Sep). 計算第三季（七月、八月及九月）的總營業額。
- (e) Which month recorded the greatest rise in revenue compared to its previous month? 與前一個月相比，哪一個月份的營業額升幅最大？
- (f) Which month recorded the greatest drop in revenue compared to its previous month? 與前一個月相比，哪一個月份的營業額跌幅最大？
- (g) Can we use a line graph instead of a bar chart to represent this set of data, and what is one advantage of using a line graph? 我們能否使用折線圖代替棒形圖來展示這組數據？使用折線圖的一項優點是什麼？
Question 2 The pie chart distribution of the monthly operational expenses of a local café is investigated. 現對一間本地咖啡店的每月營運開支圓形圖分佈進行調查。
The percentages of expenses are: Rent (42%), Staff Salaries (30%), Ingredients (x%), Utilities (6%), Marketing (4%), and Miscellaneous (3%). 各項開支百分比如下：租金（42%）、員工薪金（30%）、食材（x%）、水電雜費（6%）、市場推廣（4%）及雜項（3%）。
- (a) Classify the type of data for the monthly operational expenses. 請將每月營運開支的數據類型進行分類。
- (b) If the café spent $84,000 on Rent, find the value of x and the actual amount spent on Ingredients. 若該咖啡店在租金上的開支為 $84,000，求 x 的值以及用於食材的實際開支金額。
Question 3 A training center recorded the weekly practice hours (x) and the final exam scores (y) of 8 students. 一間培訓中心記錄了 8 位學生的每週練習時數（x）以及期末考試成績（y）。
| Student (學生) | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| Weekly Practice (Hours) (每週練習時數) | 2 | 4 | 5 | 7 | 8 | 10 | 12 | 14 |
| Exam Score (Marks) (考試成績) | 45 | 55 | 50 | 68 | 70 | 82 | 88 | 95 |
- (a) Classify the data type of the examination marks. 請將考試成績的數據類型進行分類。
- (b) Which variable is the independent variable and which is the dependent variable? 哪一個變數是自變數？哪一個變數是倚變數？
- (c) Describe the relationship between weekly practice hours and examination scores. 描述每週練習時數與考試成績之間的關係。
Question 4 The daily study times (in minutes) of 20 college students are grouped into the following distribution table: 20 名大專學生的每日溫習時間（分鐘）被整理成以下分佈表：
| Study Time (min.) (溫習時間) | 30 – 39 | 40 – 49 | 50 – 59 | 60 – 69 | 70 – 79 | 80 – 89 |
|---|---|---|---|---|---|---|
| Number of Students (學生人數) | 2 | 4 | 7 | 4 | 2 | 1 |
- (a) Classify the type of data for study time. 請將溫習時間的數據類型進行分類。
- (b) Find the class boundaries and class marks (mid-points) for each class interval. 求各組別的組界及組中點。
- (c) Can we leave gaps between columns when drawing a histogram for this data set? Explain briefly. 在為這組數據繪製直方圖時，柱形之間可以留有空隙嗎？請簡略解釋。
Question 5 The table below shows the distribution of overtime working hours per month for 40 employees in an IT company: 下表顯示某資訊科技公司 40 名員工每月的超時工作時數分佈：
| Overtime Hours (超時時數) | 1 – 5 | 6 – 10 | 11 – 15 | 16 – 20 | 21 – 25 |
|---|---|---|---|---|---|
| Frequency (頻數) | 4 | 10 | 16 | 8 | 2 |
- (a) Classify the data type of overtime working hours. 請將超時工作時數的數據類型進行分類。
- (b) Complete the cumulative frequency table using upper class boundaries. 利用組上限完成累積頻數表。
- (c) Why do we need to anchor a frequency polygon at zero frequency at both ends? 為什麼繪製頻數多邊形時，兩端都需要以零頻數作定位？
Question 6 A survey recorded the daily commute expenses (in HK$) of 100 office workers: 一項調查記錄了 100 名上班族每日的交通開支（港元）：
| Expense ($) (開支) | 10 – 19 | 20 – 29 | 30 – 39 | 40 – 49 | 50 – 59 |
|---|---|---|---|---|---|
| Frequency (頻數) | 12 | 28 | 35 | 18 | 7 |
- (a) Classify the type of data for commute expenses. 請將交通開支的數據類型進行分類。
- (b) Construct the frequency distribution table including class boundaries and mid-points (anchored with zero frequency intervals at both ends). 建立包含組界及組中點的頻數分佈表（兩端需包含零頻數組別作定位）。
- (c) Construct the cumulative frequency distribution table. 建立累積頻數分佈表。
- (d) How many workers spend more than $39.5 daily on commute? 每日交通開支超過 $39.5 的上班族有多少人？
Question 7 An analyst presents the monthly profit growth of two rival tech brands using two separate charts with different vertical axis scales. 一位分析師利用兩幅縱軸比例尺截然不同的獨立圖表，展示兩家競爭科技品牌的每月利潤增長情況。
- (a) What kind of deception source does this practice belong to? 這種做法屬於哪一種圖表做假／誤導的根源？
- (b) State what common mistake might occur when managers make decisions based solely on these charts. 說明管理層若單憑此類圖表作決策時可能出現的常見錯誤。