levo

Mathematical Requirements for Research Methods

Order of magnitude estimates and statistical symbols

  • 3 things to know
  • Component 01

Overview

Recall questions on order of magnitude calculations, estimating and calculating means, comparing sample sizes by orders of magnitude, spotting impossible results, and the symbols <, >, ~, ∝ and those for significance levels.

What you need to know

Answer each one before you reveal it.

Your recallNot started
Study

One study uses a sample of 20 and another uses 2000. By how many orders of magnitude do the samples differ?

Key term

What is an order of magnitude calculation?

Key term

A total of 12,000 points was scored by 240 participants. What is the mean score?

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    What is an order of magnitude calculation?

    Model answer

    A rough calculation using rounded values that establishes the approximate size of an answer rather than an exact figure.

  2. 2

    Sixty-one participants produced a total score of 5,842. Estimate the mean by rounding.

    Model answer

    Rounding the total to 6,000 and the sample to 60 gives an estimated mean of about 100.

  3. 3

    One study uses a sample of 20 and another uses 2000. By how many orders of magnitude do the samples differ?

    Model answer

    By two orders of magnitude, since the larger sample is 10² times the smaller.

  4. 4

    A total of 12,000 points was scored by 240 participants. What is the mean score?

    Model answer

    The mean is 50 points.

  5. 5

    Why is an order of magnitude estimate useful before a full calculation?

    Model answer

    It gives an expected size for the answer, so a result that is out by a factor of ten reveals a misplaced decimal point or a keying error.

  6. 6

    A student calculates a mean of 4.7 from scores that all lie between 40 and 60. What has gone wrong?

    Model answer

    The mean must fall within the range of the scores, so a value of 4.7 shows the total has been divided incorrectly or a decimal point has been misplaced.

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.

Research Methods and Techniques
Planning and Conducting Research
Data Recording, Analysis and Presentation
Report Writing and Scientific Communication

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 tests are a old.
centurydecadeyear

Blank Blitz makes facts automatic

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

APunishment requires deprivation, loss of autonomy and stigma.
BReform requires trust, responsibility and self-respect.
CThe regime that achieves one tends to undermine the other.

Build It gets the exam shape right

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

Range means the highest score minus the lowest score.
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 Mathematical Requirements for Research Methods, 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.