{"{0} ÷ {1}":"{0} ÷ {1}","Average calculator":"平均數計算機","Average of the two middle values":"兩個中間值的平均數","Cochran's formula, n₀ = z² × p(1 − p) ÷ e², gives the responses needed for a survey proportion to be within the margin of error e at the chosen confidence; 50% is the safe guess for p because it needs the most. For a small population N, the finite population correction n = n₀ ÷ (1 + (n₀ − 1) ÷ N) reduces it. It assumes a random sample; low response rates and biased samples are not fixed by size.":"Cochran公式n₀ = z² × p(1 − p) ÷ e²，可計算在指定信賴水準下，讓調查比例落在誤差範圍e內所需的回覆數；p採用50%是安全的估計，因為這會需要最多樣本。對於較小的母體N，有限母體修正公式n = n₀ ÷ (1 + (n₀ − 1) ÷ N)會降低所需數量。此計算假設使用隨機樣本；回覆率偏低和樣本偏差不會因樣本數增加而獲得修正。","Combinations (nCr)":"組合（nCr）","Combinations with repetition":"可重複組合","Confidence level":"信賴水準","Each value counts in proportion to its weight: multiply each value by its weight, add the products, and divide by the total weight. Weights can be credits, hours, percentages that add to 100, or quantities; only their proportions matter.":"每個值會依其權重比例計算：將每個值乘以其權重，加總乘積，再除以權重總和。權重可以是學分、時數、總和為100的百分比或數量；重要的是彼此的比例。","Enter a margin of error between 0 and 50% and a proportion between 0 and 100%.":"請輸入介於0到50%的誤差範圍，以及介於0到100%的比例。","Enter at least one number.":"請至少輸入一個數字。","Enter the same number of values and weights ({0} values, {1} weights).":"請輸入相同數量的值和權重（{0}個值、{1}個權重）。","Enter whole numbers from 0 to 5,000.":"請輸入0到5,000之間的整數。","Expected proportion (%)":"預期比例（%）","Items can repeat":"項目可重複","Items chosen (r)":"選取項目數（r）","Margin of error (±%)":"誤差範圍（±%）","Mean (average)":"平均數（平均值）","Median":"中位數","Mode":"眾數","None (no value repeats)":"無（值不重複）","Numbers, separated by commas, spaces, or new lines":"數字，以逗號、空格或換行分隔","Order does not matter":"順序不重要","Order matters":"順序重要","Permutation and combination calculator":"排列組合計算機","Permutations (nPr)":"排列（nPr）","Permutations count ordered arrangements: nPr = n! ÷ (n − r)!, so choosing a gold, silver, and bronze winner from 10 runners gives 720. Combinations ignore order: nCr = n! ÷ (r! (n − r)!), so choosing any 3 of 10 gives 120. With repetition allowed, ordered choices number nʳ and unordered ones C(n + r − 1, r). Results are exact; very large ones are shown in scientific notation.":"排列計算有順序的排列方式：nPr = n! ÷ (n − r)!，因此從10位參賽者中選出金牌、銀牌和銅牌得主，結果為720。組合不考慮順序：nCr = n! ÷ (r! (n − r)!)，因此從10個項目中任選3個，結果為120。允許重複時，有順序的選法數量為nʳ，無順序的選法數量為C(n + r − 1, r)。結果皆為精確值；非常大的數字會以科學記號顯示。","Permutations with repetition (nʳ)":"可重複排列（nʳ）","Population size (optional)":"母體大小（選填）","Range":"全距","Responses needed":"所需回覆數","Sample size calculator":"樣本數計算機","sample; population {0}":"樣本；母體{0}","Share of the weight":"權重占比","Simple average, for comparison":"簡單平均數（供比較）","Sorted: {0}":"已排序：{0}","Standard deviation":"標準差","The mean adds the numbers and divides by how many there are; the median is the middle value when they are sorted, or the average of the two middle ones; the mode is the value that appears most often. A single very large or small value pulls the mean but not the median, which is why the median often describes incomes and house prices better.":"平均數是將數字相加後除以數字的個數；中位數是排序後位於中間的值，或兩個中間值的平均數；眾數是出現次數最多的值。單一個非常大或非常小的值會拉動平均數，卻不會影響中位數，因此中位數通常更能描述收入和房價。","The middle value":"中間值","Total items (n)":"項目總數（n）","Value":"值","Value × weight":"值×權重","Values (such as grades)":"值（例如成績）","Weight":"權重","Weighted average":"加權平均數","Weighted average calculator":"加權平均數計算機","Weights (such as credits or percentages)":"權重（例如學分或百分比）","Weights must be zero or more, and not all zero.":"權重必須大於或等於0，且不可全部為0。","Without a population limit":"不限母體大小","z for this confidence":"此信賴水準的z值"}