Summary
Summary Notes for STEM12
- Course
- Institution
lecture notes for grade 12 STEM
[Show more]
Seller
Follow
kenalejo
Content preview
ESTIMATING UNCERTAINTY IN REPEATED MEASUREMENTSUsing a digital instrument, you time the period of oscillation of a pendulum and find T = 0.44 seconds.
This single measurement of the period suggests a precision of ± 0.005 s, but the precision may not give a
complete sense of the uncertainty. If you repeat the measurement several times and examine the
variations among the measured values, you can get a better idea of the uncertainty in the period. For
example, here are the results of 5 measurements, in seconds: 0.46, 0.44, 0.45, 0.44, 0.41.
Another way to express the variations among the measurements is to use the average deviation. This
statistic tells us on average (with 50% confidence) how much the individual measurements vary from the
mean. However, the standard deviation is the most common way to characterize the spread of a data
set. The standard deviation is always slightly greater than the average deviation, and is used because of
its association with the normal distribution that is frequently encountered in statistical analyses.
STANDARD DEVIATION
To calculate the standard deviation for a sample N measurement: 1. Sum all the measurements and
divide by N to get the average, or mean. 2. Now, subtract this average from each of the N
measurements to obtain N “deviations”. 3. Square each of these deviations and add them all up. 4.
Divide this results by (N -1) and take the square root. The significance of the standard deviation is this: if
you now make one more measurement using the same meter stick, you can reasonably expect that the
new measurement will be within 0.12 cm of the estimated average of 31.19 cm.
What are physical quantities and standards?
In physics and in other branches of science, the quantities used to describe nature are defined so that
they have the same meaning for any person using them. Quantities such as time, length, speed, and
pressure can be measured and given specific values. Each quantity, when measured, has magnitude (a
number) and a unit of measure. We can see that it is important to have standards that are precisely
defined and are used in common by people involved in trade, science and industry. The unit of length
presently in science is called meter. It was originally defined as a distance between two lines inscribed
on a bar of metal stored in a special vault in a small town near Paris, France. Replicas made from
standard were distributed around the world. A meter in France had the same length as a meter in
Canada, as used in any other country.
SCALAR AND VECTOR QUANTITIES
Scalar is a quantity with magnitude and usually a unit of measure. Scalars are given algebraic symbols
such as E, t and v. The familiar rules of algebraic addition, subtraction, multiplication, and division are
used to mathematically manipulative scalars. Often, we need to indicate the direction as well as the
magnitude of a quantity. Perhaps you have been told that a hidden treasure has a “displacement” from
you of 100 miles in a direction 50º north of west. Displacement is a vector quantity indicating (1) the
distance from one point to another and (2) the direction of an arrow pointing from the first to the
second point. Distance is the corresponding scalar quantity; it indicates only the separation of the
points, not the direction from one to the other. A vector is a quantity with magnitude, direction, and
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller kenalejo. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $8.39. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
66579 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now