Data and Measurement

Qualitative (aka nominal) data is not numerical. This includes eye color, voting preference or if a vaccinated patient still gets infected. In fact, counting is the only way that qualitative data can be represented numerically (ie, 60 aye votes and 40 nay votes), but this has no physical meaning. Quantitative data is numerical, such as [...]

Sampling

Sampling can be grouped as probability sampling or non-probability sampling. In probability sampling, every person in a population has an equal chance of being chosen; for instance, randomly querying people to gauge public opinion or collecting random patients from hospitals across the country to participate in a cancer study. In non-probability sampling, not everybody in [...]

Numerical Methods: Dispersion

Range This can either be presented by giving the minimum and maximum (ie, 100 to 150) or just the amount between (ie, 50). Population Varianceσ2 σ2 = (Σ(x-µ)2)/N Population StandardDeviation (σ) σ = √σ2 Sample Variance Sample StandardDeviation Empirical Rule Interquartile Range Interquatile Division

Numerical Methods: Location

Minimum (Min) The smallest value. Maximum (Max) The largest value. Population Mean (μ) Equivalent to (ΣX)/N. Sample Mean (X) The sample means will perhaps be greater or less than µ, but the average of all possible X will be µ — X is an unbiased estimation of µ. Median Order the data from smallest to [...]

Statistics

In statistics, we try to draw inferences about a population based on a sample, a technique called statistical inference. The inference is valid if the sample is random, and the bigger the sample the more reliable the inference. Any measure computes on a population is called a population parameter or simply a parameter, such as [...]

Mean Absolute Deviations from the Mean

Measures dispersion but Not often used. Mathematically better is the sample standard deviation, which is the square root of the sample variance. MAD = [ Σ | X - X | ] / n

Sample Variance

Computational formula for sample variance σ2 = [ Σ ( X2 ) - ( Σ X )2 ] / [ n - 1 ] Definitional formula for sample variance σ2 = [ Σ ( X - X2 ) ] / [ n - 1 ]