Average、Median、Range:學英文嘅人成日睇錯嘅統計字眼
有個學英文嘅人喺寫作題目入面描述一個圖表:「The average salary in the company is forty thousand dollars, and the median is twenty-five thousand。」佢導師叫停咗佢。「如果 median 係兩萬五,噉即係一半員工嘅人工係噉或者更少。Average 係四萬,即係收入最高嗰班人將個數拉高咗。呢個係一個好值得講嘅故事 —— 但前提係你要用啱啲字。」呢個學生啲數字寫得啱晒;佢只係冇意識到 average 同 median 描述緊唔同嘅概念。呢兩個字喺英文入面只係差幾隻字母,但意思就差成個世界咁遠。
點解呢樣嘢重要
統計字眼會偷偷溜入新聞標題、體育轉播、商務會議、標準化考試嘅圖表描述,甚至日常傾人工或者樓價嘅對話。記者會講:「On average, families spend X。」朋友會講:「The median home price in that neighborhood is too high for us。」教練會講:「Her range is huge — she scored anywhere from 5 to 25 points per game。」如果你將呢啲字混為一談,你就會描述錯啲數據。喺寫作或者口語考試入面,噉會扣你分。喺會議入面,噉會令你失去公信力。
規律
四個核心統計字眼係 mean、median、mode 同 range。每一個都指向唔同嘅概念,而每一個都有個較平易近人嘅日常短語可以配埋一齊用。
Mean 係 average(平均)嘅技術字眼。要計 mean,你就要將所有數值 add up(加埋),然後 divide by(除以)數值嘅個數。以 2、4、6、8、10 呢組數嚟講,mean 係 (2 + 4 + 6 + 8 + 10) ÷ 5 = 6。喺英文入面,the mean 同 the average 通常可以互換:「The average score is six」同「The mean score is six」描述緊同一個數。Average 聽落較日常;mean 聽落較技術性。實用短語:on average、the average of、on a typical day。
Median 係將啲數由細排到大之後嘅 middle value(中間值)。以 2、4、6、8、10 嚟講,median 係 6。以 1、3、5、7 嚟講,median 係 (3 + 5) ÷ 2 = 4 —— 當組數有偶數個數值嗰陣,就取中間兩個嘅 mean。Median 出名抗拒極端值。如果一間細公司入面有一個人賺一千萬,average 人工就會跳得好高;median 人工就幾乎唔郁。
Mode 係 most frequent(出現最多次)嘅數值。以 2、2、3、5、5、5、7 嚟講,mode 係 5。一組數據可以 no mode(每個數值都只出現一次)、一個 mode,或者幾個 mode(叫做 bimodal 或者 multimodal)。Mode 喺講 最常見 嘅嘢嗰陣係日常嘅主角 —— 問卷答案、T 恤尺碼、眼睛顏色統計。
Range 係 spread(分佈幅度),計法係 maximum minus minimum(最大減最小)。以 2、4、6、8、10 嚟講,range 係 10 − 2 = 8。Range 答嘅問題係 分佈有幾闊? 佢唔係一個典型數值;佢係衡量變異程度。
仲有兩個值得識嘅短語:
Outlier 係一個離其他數值好遠嘅數值。「The team's outlier is the new hire, who finishes twice as many tickets as anyone else。」Outlier 會拉郁 mean,但唔會拉郁 median。
Standard deviation 係一個較技術性嘅分佈衡量方法。你通常唔需要喺一句普通句子入面定義佢,但你可能會喺一個科學演講入面聽到。
錯誤 / 自然 / 點解
| 錯誤 | 自然 | 點解 |
|---|---|---|
| The average is the middle value. | The median is the middle value. | Average(或 mean)係總和除以個數;median 係已排序清單嘅中間。 |
| The mean salary is forty thousand, which is the most common. | The mean salary is forty thousand; the most common (mode) is twenty-five thousand. | 最常見嘅數值係 mode,唔係 mean。 |
| The range is the average of the highest and lowest. | The range is the highest minus the lowest. | Range 係最大減最小;兩者嘅中點係另一個概念。 |
| In average, families spend X. | On average, families spend X. | 固定短語係 on average,唔係 in average。 |
| The mode is the second from the top. | The mode is the most frequent value. | Mode 係關於出現頻率,唔係喺排序清單入面嘅位置。 |
| The medium score is 75. | The median score is 75. | 統計字眼係 median,唔係 medium。(Medium 係解 中等尺寸或強度,唔係 中間值。) |
| The averages are 50, 60, and 70. | The means are 50, 60, and 70. (or: The averages of the three groups are 50, 60, and 70.) | Average 可以做名詞,但描述多組嗰陣兩種形式都得。留意介詞:係 average of,唔係 averages from。 |
| The range from 5 to 25 | The range is 5 to 25 (or: the values range from 5 to 25) | 動詞 range 用 from...to;名詞 range 用 is。 |
| Median score equals to 80. | Median score equals 80. (or: The median score is 80.) | Equals 唔接 to。 |
常見情境
喺寫作考試描述圖表。「The mean monthly rent in City A is $1,200, but the median is only $850. The gap suggests that a few very high rents are pulling the average up。」呢種句子可以攞分。兩個字一齊運作就講到一個故事:大部分租客住喺邊度(median),同埋啲數據幾偏斜(mean 高過 median)。
傾人工。「The average salary at this company is $80K, but I'd be more interested in the median if I were comparing offers。」每當有少數人賺得比其他人多好多或者少好多嗰陣,median 就係較誠實嘅典型數字。研究薪酬公平嘅人因為呢個原因而依賴 median。
講運動。「Her scoring range this season was 5 to 25 points. The average was 14, but she had three twenty-plus games。」留意三個統計數字 —— range、average 同個別高分 —— 點樣一齊砌出幅圖畫。
喺會議講問卷結果。「The mode for favorite color was blue, with 35 percent of responses。」當變數係一個類別(顏色、品牌、T 恤尺碼)而唔係一個數字嗰陣,mode 就係自然嘅選擇。
備試建議。「Don't worry about the highest mean score on the practice tests — focus on whether your median score is improving week to week。」當你有幾日異常好或者異常差嘅練習日子嗰陣,median 比 mean 較誠實噉顯示趨勢。
如果你想喺呢啲統計數字之上加埋變化嘅講法 —— 描述 median 或者 average 喺兩個時段之間點樣郁動 —— Percent、Percentage 同 Percentage Points:細細個字,大大個錯 就係下一步。佢同統計自然噉配埋一齊,因為圖表描述幾乎一定會將兩者結合。
常犯嘅錯誤
- 對調 average 同 median。佢哋唔係同一樣嘢。Average 係總和除以個數。Median 係排序後嘅中間值。
- 想講 median 嗰陣寫咗或者講咗 medium。Medium 描述尺寸、強度或者熟度嘅程度(「medium-rare steak」)。Median 係一個統計量。
- 用 the average of the highest and lowest 嚟做 range 嘅定義。Range 係 最高減最低。嗰兩個數值嘅平均有時叫做 midrange,係另一回事。
- 將 mode 當做 typical 嘅同義詞。Mode 係 最常見 嘅數值,就算佢只係比其他數值多出現少少。
- 講咗 in average,而唔係 on average。英文固定短語係 on average。
- 唔記得 median 可以等於 mean。喺一組對稱嘅數據入面,佢哋一致。差別喺數據偏斜嗰陣先重要。
- 喺 mean、median、mode 或者 range 後面講咗 equals to。動詞 equals 唔接 to:the mean equals 6。
- 用 range 做動詞而冇 from...to。名詞形式係 the range is 5 to 25;動詞形式係 the values range from 5 to 25。混埋一齊就會變成 the range from 5 to 25,呢個唔地道。
迷你練習
以數據組 4、6、6、8、10、20 為例,回答以下問題。
- What is the mean (the average)?
- What is the median?
- What is the mode?
- What is the range?
- Which value is the outlier, and what does it do to the mean compared with the median?
總結
統計英文歸納為四個字。Mean(或 average)係總和除以個數。Median 係排序清單嘅中間值。Mode 係出現最多次嘅數值。Range 係最高減最低。每一個都講一個唔同嘅故事,而將佢哋一齊用 —— the mean is X, the median is Y, the range is Z —— 就會畀到你一個聽落自信又準確嘅圖表描述。為啱嘅概念揀啱嘅字,啲數據就會幫你發聲。
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