levo

Fundamental Data Analysis

Calculating and combining uncertainties

  • 3 things to know
  • Components 01, 02 and 03

Overview

Recall questions on absolute against percentage uncertainty, combining them through sums, products and powers, why subtracting similar values is costly, uncertainty in a gradient or intercept, and quoting an uncertainty.

What you need to know

Answer each one before you reveal it.

Your recallNot started
Key term

How does uncertainty combine for a power, for a density from 250 ± 2 g and 100 ± 1 cm³, and for a gradient?

Key term

What is the difference between absolute uncertainty and percentage uncertainty?

Numbers

Five readings give 12.1, 12.5, 12.3, 12.4 and 12.2 s. Calculate the mean and its absolute uncertainty.

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    What is the difference between absolute uncertainty and percentage uncertainty?

    Model answer

    Absolute uncertainty is stated in the unit of the measurement, while percentage uncertainty expresses that absolute value as a percentage of the measurement itself.

  2. 2

    How is the uncertainty in a mean estimated from a set of repeated readings?

    Model answer

    It is taken as half the range of the readings, that is half the difference between the largest and the smallest.

  3. 3

    Five readings give 12.1, 12.5, 12.3, 12.4 and 12.2 s. Calculate the mean and its absolute uncertainty.

    Model answer

    The mean is 12.3 s and half the range is ±0.2 s.

  4. 4

    Calculate the percentage uncertainty in a value of 12.3 ± 0.2 s.

    Model answer

    It is (0.2 ÷ 12.3) × 100 = 1.6%.

  5. 5

    How are uncertainties combined when two quantities are added or subtracted?

    Model answer

    Their absolute uncertainties are added.

  6. 6

    A length of 15.0 ± 0.1 cm has 12.0 ± 0.1 cm subtracted from it. State the result with its absolute and percentage uncertainty.

    Model answer

    The result is 3.0 ± 0.2 cm, which is a percentage uncertainty of 6.7%.

Other ways to work this

The same content, four other ways.

What is inside Levo

Six ways to work the same material.

1Closed book
2Open book
3Closed book

The 3-step method, run for you

Answer cold, learn it, then prove it stuck. Levo tracks the jump between your first attempt and your last.

Planning
Implementing
Analysis
Evaluation

Cram a whole paper in one sitting

Sort every topic into what you know and what you do not, then drill only the weak ones.

The two charges .
attractrepelcombine

Blank Blitz makes facts automatic

Rapid timed gap-fills on the terms and numbers you need to recall without thinking.

AThe neutron has lepton number 0.
BOn the other side the proton has 0.
CThe electron has +1 and the antineutrino has −1.

Build It gets the exam shape right

Assemble a full-mark answer from its marking points, in the order an examiner wants them.

There are 2π rad in a full circle.
TrueFalse

Test It catches misconceptions

Spot the fault in a statement. The traps are the mistakes students actually make.

721941163128510

Brain Breaks between sessions

Short focus games to reset attention, so the next set lands better than the last.

Every question in Fundamental Data Analysis, on a schedule.

Attempt a question from memory, write the correct version, then attempt it again. Levo records the jump between your first attempt and your last, and brings each question back on the day you are due to forget it.

Or £46 a year, about £3.83 a month. Cancel anytime.