LAB #1: Uncertainties
Theory:
Explain different types of error that may occur during the experiment. Give an example
for each. Is there a way random errors can be statistically described? How? Draw
Gaussian distribution and write down an equation. How data are “spread” around the
mean for Gaussian distribution? Define mean and standard deviation and write down the
equations. What is statistical error?
Experiment:
In today’s lab you will investigate random errors. This will be done by measuring the
distance meter stick falls before you catch it and calculating the reaction time using the
equation:
1
Y = ⋅ 9 .8 ⋅ t 2
……. (1)
2
1. Measure the distance meter stick falls (Y) before being caught.
2. Repeat 30 times.
3. From the 30 values of Y calculate 30 t’s using equation (1).
Trial
1
2
3
Y (m)
t (s)
29
30
4. Calculate taver, σ t and δ t
50
∑t
t=
i
i =1
30
1
σ=
N
 N 
N ∑ ti −  ∑ ti 
i =1
 i =1 
N
2
2
δt =
σ
30
5. Histogram your data.
• Calculate bin width
b.w. = σ t /2
•
Set up axes of histogram
•
•
Put each data point in the appropriate bin.
How many of your data (in %) falls within 3σ? Does you distribution
follow the Gaussian?