General Physics

1. z
ESTIMATION FROM
MULTIPLE
MEASUREMENT OF
PHYSICAL
QUANTITIES

2. z
Important Question:
 How errors are being
estimated from
multiple measurement
of physical quantities?

3. z
What is a Variance?
- Is a statistical measure
that tells us how
measured data vary from
the average value of the
set of data.
- It is express using the
lower-case sigma (𝝈)
𝝈2 =Ʃ(𝓍-𝒙)2
N
Variance Formula:
Where:
𝝈2 =variance
X= individual
measurement
𝒙= Mean of all the
measurements
N= Population
size

4. z
Note: if we’re looking for the
ff.
Sample variance
For population variance
𝝈2 =Ʃ(𝓍-𝒙)2
N
𝝈2 =Ʃ(𝓍-𝒙)2
N-1

5. z
Lets Study:
-Measurements
of the height of a
table in terms of
meter.
Data: 1.10, 1.0,
0.97, 1.02, 1.15,
1.20, 1.10, 1.15
X 𝑥 X-𝑥 ( X-𝑥)2
1.10 1.09 0.01 0.0001
1.0 1.09 -0.09 0.0081
0.97 1.09 -0.12 0.0144
1.02 1.09 -0.07 0.0049
1.15 1.09 0.06 0.0036
1.20 1.09 0.11 0.0121
1.10 1.09 0.01 0.0001
1.15 1.09 0.06 0.0036

6. z
Lets Study:
𝝈2 =Ʃ(𝓍-𝒙)2
N
Note: A variance is a single value that is the best
estimate of the true unknown parameter.
 Confidence interval
- Is a range of values and indicates the uncertainty of the
estimate.
 Finding out the variance between the errors is a vital part of the
learning to design it with better experiments and to minimize any
sort of errors.

7. z
Activity 1: Compute for the
variance.
1. The Grade 12 Stem learners
were given an activity of
measuring the length of their
building and they obtained the
following measurements after.
( 45, 45.7, 45.8, 45.9, 46, 46.6, 47,
47.5, 48 and 48.9) in ft.
Compute for the variance.
𝝈2 =Ʃ(𝓍-𝒙)2
N
Variance Formula:
Where:
𝝈2 =variance
X= individual
measurement
𝒙= Mean of all the
measurements
N= Population
size