實驗 Data 的表示要有統計的基礎 : Examples: 高 = Z +/_  Z(where  Z = 幾次量測後 ,1 個標準差大小 )

實驗 Data 的表示要有統計的基礎: Examples: 高= Z+/_ Z(where  Z =幾次量測後,1 個標準差大小) 體積= V +/_V ,where V 由長寬高之誤差傳遞,請看 page 4 介紹, 而得: V= (AVE of長)X (AVE of寬) X (AVE of高) V= V x (( 1STD of 長)2 / (AVE of長)2 + (1STD of 寬)2 / (AVE of寬)2 + (1STD of 高)2 / (AVE of高)2 ) ) 1/2 ＮＴＨＵ 98上普物實驗　講師　侯宗昆　助教　陳慶鴻王宏哲

記數據的方法: (a.bcd ± e ) x 10 n (單位）誤差項 e: 取 1-2 位有效數字: 1 開頭者取 2 位有效數字, other than 1 開頭者, 誤差項取 1 位有效數字 Like ( 29.00 ± 0.12) x 10 1 CM ( 56.0 ± 0.3) x 10 1 CM 有效數字: 有效數字　＝　精確值　+ 　一位估計值 1.各別數字處理：Rounding answers properly (四捨五入法) 1.475 in 3 digits: 1.48 (逢單則入） 1.485 in 3 digits: 1.48 (逢雙則捨）ＮＴＨＵ 98上普物實驗　講師　侯宗昆　助教　陳慶鴻王宏哲

有效數字: 2.加、減、乘、除　時的　有效數字處理 09.9???? +00.3163? 10.2???? = 10.2 ? ? :估計不準位 3.413? x 2.3? can be written in long hand as 3.413? x 2.3? . ????? 10239? +6826? . 7.8????? = 7.8? Short Rule: ＮＴＨＵ 98上普物實驗　講師　侯宗昆　助教　陳慶鴻王宏哲

誤差傳遞: (a) Addition and Subtraction: z = x + y or z = x - y Average deviationsz = |x| + |y| in both cases. z = |x| + |y| Using simpler average errors Using standard deviations (b) Multiplication and Division: z = x y or z = x/y z +z = (x +x)(y +y) = xy + x y + y x + x y z = y x + x y ( ????) Using simpler average errors Using standard deviations ＮＴＨＵ 98上普物實驗　講師　侯宗昆　助教　陳慶鴻王宏哲

誤差傳遞: Example: w = (4.52 ± 0.02) cm, x = (2.0 ± 0.2) cm. Find z = w x and its uncertainty. z = w x = (4.52) (2.0) = 9.04 cm2 So z = 0.1044 (9.04 cm2) = 0.944 which we round to0.9 cm2, z = (9.0 ± 0.9) cm2. Using Eq. 2b we getz = 0.905 cm2 andz = (9.0 ± 0.9) cm2.The uncertainty is rounded to one significant figure and the result is rounded to match. We write 9.0 cm2 rather than 9 cm2 since the 0 is significant. ＮＴＨＵ 98上普物實驗　講師　侯宗昆　助教　陳慶鴻王宏哲

誤差傳遞: (c) Products of powers: z =xmyn Using simpler average errors Using standard deviations ＮＴＨＵ 98上普物實驗　講師　侯宗昆　助教　陳慶鴻王宏哲

誤差傳遞: (c) Products of powers: z =xmyn Example: w = (4.52 ± 0.02) cm, A = (2.0 ± 0.2) cm2, y = (3.0 ± 0.6) cm. Find . Z=wy2/A1/2 , Δ z/z=? … The second relative error, (y/y), is multiplied by 2 because the power of y is 2. The third relative error, (A/A), is multiplied by 0.5 since a square root is a power of one half. So z = 0.49 (28.638 cm2) = 14.03 cm2 which we round to 14 cm2， z = (29 ± 14) cm2 for using the average error. If consider the standard deviation using Eq. 3b, then, z=(29 ± 12) cm2. Because the uncertainty begins with a 1, we keep two significant figures and round the answer to match. ＮＴＨＵ 98上普物實驗　講師　侯宗昆　助教　陳慶鴻王宏哲

Example Ｓpherometer(球徑計)量測 圓面之曲率半徑= R +/-  R Where 圓面之曲率半徑　R = h/2 + S2 / 6h h : vertical 升降高度（由前面　Ｍicrometer 方法求得）　Ｓ：頂點間距離（較佳之Ｓ求法＝？）ＮＴＨＵ 98上普物實驗　講師　侯宗昆　助教　陳慶鴻王宏哲

Example Ｓpherometer(球徑計)量測 圓面之曲率半徑= R +/-  R Where 圓面之曲率半徑　R = h/2 + S2 / 6h h : vertical 升降高度（由Ｍicrometer 方法量得）　Ｓ：頂點間距離算 R: 先算 S2 之誤差傳遞 , h之誤差傳遞 (1STD) 再算 S2 / 6h 之誤差傳遞 (By 除法誤差傳遞_ S2 vs 6h) 最後算 h/2 + S2 / 6h 之誤差傳遞 (By 加法誤差傳遞_ h/2 vs S2 / 6h) ＮＴＨＵ 98上普物實驗　講師　侯宗昆　助教　陳慶鴻王宏哲

實驗 Data 的表示要有統計的基礎 : Examples: 高 = Z +/_  Z(where  Z = 幾次量測後 ,1 個標準差大小 )