【統計學：平均數、中位數、眾數、分佈域及四分位數】Statistics: Mean, Median, Mode, Range and Quartiles
SketchMath 數學團隊 SketchMath Maths Team ｜ 更新 Updated 2026-10-20
平均數 = 總和 ÷ 數據個數。中位數 = 排序後的中間值。眾數 = 出現最多次的值。分佈域 = 最大值 − 最小值。四分位數把排序後的數據分成四等份，四分位數間距 = Q₃ − Q₁。中位數及四分位數間距較不受極端值影響；平均數及分佈域則會。Mean = sum ÷ number of values. Median = middle value of the ordered data. Mode = most frequent value. Range = largest − smallest. Quartiles split the ordered data into quarters, and IQR = Q₃ − Q₁. The median and IQR are not pulled around by extreme values; the mean and range are.
把最後一個數 v 由 7 往右拖：紅色的平均數線向右移，藍色的中位數線卻留在 5。眾數是 5。 Drag the last value v from 7 upwards: the red mean line is pulled to the right, but the blue median stays at 5. Mode is 5. 自己試試 → Try it yourself →
統計學公式 Statistics Formulas
平均數Meanx̄ = Σx / n
頻數表的平均數Mean from a frequency tablex̄ = Σfx / Σf
中位數Median中間值；數據個數為偶數時，取中間兩個的平均數Middle value; for an even number of values, the mean of the middle two
分佈域Rangelargest − smallest
四分位數及四分位數間距Quartiles and IQRQ₁ = median of the lower half, Q₃ = median of the upper half, IQR = Q₃ − Q₁
⚠️ 先排序 Order the data first要先把數據由小至大排序，才能求中位數及四分位數。The median and quartiles only make sense after sorting the values from smallest to largest.
⚠️ 可以有兩個眾數，或沒有眾數 Two modes, or none若有兩個值並列最高頻數，便有兩個眾數；若每個值只出現一次，便沒有眾數。If two values tie for the highest frequency there are two modes; if every value occurs once, there is no mode.
平均數用上每個數值；中位數是中間值；眾數是最常出現的值。
The mean uses every value, the median is the middle value, and the mode is the most common value.
先排序，把數據分成下半部及上半部，各取中位數。數據個數為奇數時，常見的課本方法是不把中間值計入任何一半，請依你的老師或課本而定。
Sort the data, split it into a lower and an upper half, and take the median of each half. When there is an odd number of values, the usual textbook method leaves the middle value out of both halves; follow your teacher or textbook.
四分位數間距，因為它只用上中間一半的數據。
The interquartile range, because it only uses the middle half of the data.