111-1 NTU General Physics Laboratory
Data Analysis Assignment Answer Sheet
Student id:B11502158
Name：黃宥華
2022
1
Abbreviated Notation
[ 2 pts for each subheading ]
(i)18.8(1.5) × 10−6
(ii)
2.91
(iii)
10.72 (41 )
(iv)
220.10 (30)
(v)
4.60 (29 )
(vi)
337.7 (3.0)
2
(07 )
Estimating measure times
(i)
[6 pts]平均成不確定度
18.41(26)
(ii)
According to the appendix A in the textbook, What’s the name of the interval from (i) ?[3 pts] and what’s
it means? [5 pts]
The name for interval from (i)
是使用 A 類不確定度去取數據或測量的誤差，用來求取標準差
(iii)
[5 pts]
263
(iv) [6 pts]
0.049
3
Transforming Data for Least Squares
No. Constant(s) [pts]
ex
A,B
X
(i)
L
3
y=ax+b
Const.
lnR=-BT+lnA
𝐴 = 𝑒 𝑏 ; 𝐵 = −𝑎.
lnf = (-1/2 ln Vln(L)^(1/2))/2pi
1
L = ( 2 𝜋 ⁄ 𝑒 𝑏 )2
(ii)
k, n
3
lnN = lnk-(1/n)ln C
(iii)
f
3
1⁄𝜇=
−1⁄𝑣+ 1⁄ƒ
V = Acos(t)
(iv)
4
3
A
k = 𝑒𝑏
n=1⁄𝑎
ƒ=1/b
A=a
Least Squares Methods and Linear Correlation
(i)
[7 pts]
最小平方法是從很多測出的數據，找一個理論模型曲線，讓所有數據的應變數值和
理論預測之之差平方和最小。
(ii)
[7 pts]
最小平方法要成立的條件是，假設測量值得不確性的機率分佈為常態分佈。因為常
態分佈是鐘型曲線，所以當樣本很多時，樣本的平均會是常態分佈中心的好
的估計值。
(iii)
[2 pts]
-0.86
(iv)
Plot a graph of temperature versus volume and indicate the linear line of best fit (plot T on the y axis and
V on the x axis). The x title, the y title, the legend, the equation and the R2 need to show properly on the
graph.[7 pts]
Variation of temperature of the cold surface of
TEC with the volume of heat sink
40
35
30
25
溫 20
度
(體積,溫度)
15
Линейная ((體積,溫
度))
10
y = -0,5854x + 31,794
R² = 0,7458
5
0
0
20
40
60
體積
(v) Do you think that the assumption of linearity between T and V is valid? Why or Why not?[7 pts]
這假設是有效的，因為那些數據點都跟迴歸直線很近且有分布在線的兩端。
2
5
Probability Density Function and Type B Uncertainty
(i)
Calculate A…
1
∫ 𝑓(𝑥)𝑑𝑥 = 1
0
A = 3/2
f(x) = 3/2 - x
(ii)
Plot the graph of f(x) versus x.
3
(iii)
𝑏
∫𝑎 𝑓(𝑥)𝑑𝑥=(1/2)(a+b)
(iv)
(上邊+下邊)/2=0
(v)
∫−𝑎 𝑥 + 𝑎⁄𝑎2 d(x) + ∫0 𝑎 − 𝑥⁄𝑎2 d(x) + 0 = 𝑎⁄√6
0
𝑎
[ 5 pts for each subheading above ]
(vi)
Vernier caliper Delta函數
Regular ruler 常態分布
[3 points for one, up to 6 points]
4