Lecture 3_Statistics of Repeated Measurements Flashcards
What is mean? Why is it calculated?
The mean is the average or the most common value in a collection of numbers. It is a measure of central tendency of a probability distribution along median and mode. It is also referred to as an expected value.
What is standard deviation?
It measures the spread or dispersion of a dataset around its mean, with a higher SD indicating a wider spread and a lower SD indicating data points clustered closer to the mean.
What is variance?
The square of standard deviation. Variance is a measurement of how far each number in a data set is from the mean (average)
Examples of relative errors in statistics?
Coefficient of Variation
Relative Standard Variation
What is the purpose of these relative errors? Why are they being calculated?
Relative errors are often used to compare the precision of results which have different units or magnitudes.
What does standard deviation do?
The sd gives a measure of the spread of a set of results, it does not indicate the shape of the distribution.
It shows that the distribution of the measurements is roughly symmetrical about the mean, with the measurements clustered towards the centre
Histogram
Define what is a sample.
Sample a set of measurements from the theoretically infinite number
The actual material being studied.
Define what is a population.
Population the set of all possible measurements.
F(z) is called the _______.
standard normal cumulative distribution function
What is a specimen in chemistry?
A test portion from a population which varies with time.
In the absence of systematic errors, x̄ provides us with ____________, 𝝁, we are trying to measure.
an estimate of the true value
Why do we repeat measurements?
Repeating measurements implies that we have more confidence in the mean of several values than in a single value.
The more measurements we make, the more reliable our estimate of 𝝁, the true value, will be.
The distribution of all possible sample means (in this case, an infinite number) is called the ________.
sampling distribution of the mean
Define what is a confidence interval.
A range which we may reasonably assume includes the true value.
Define what is confidence limits.
are extreme values of the interval.
