Sampling

• Population: complete collection of all measurements or data that are being considered.

• Sample: sub-collecion of members selected from a population

• Simple Random Sample: each member of the population has the same change of being included, and samples are chosen independently

• Cluster Sampling: dividing the population into groups by a category. All of the individuals within the single group are the sample.

• Stratified Random Sampling: divide the population into groups (strata) based on one+ classification criteria. Then perform a simple random sample within each strata

• Sampling Bias: some members of the population have a higher chance to be selected than others.

Variables

• Categorical Variables: two+ categories, but no intrinsic ordering (ex: blood type)

• Ordinal Variable: categorical variables but with a clear ordering (small/medium/large)

• Numeric Variables

  • Discrete Variables: a numeric variable for which we can list the possible values (think: integers)

  • Continuous Variable: a numeric variable that is measured on a continuous scale (temperature, height)

• Bar Charts: frequency distribution for categorical variables

• Histograms: frequency distribution but no spaces

Frequency Variables

• Mean, denoted by ȳ

  • Mean: The average of the observations

  • Only for discrete or continuous data

  • ȳ = (Σ yi)/(n)

  • Sensitive to outliers

• Median, denoted by ỹ

  • N is odd: (n + 1)th largest value

  • N is even: average of (n/2)th largest value and (n/(2) + 1)th

• Symmetric and Unimodal Curve

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• Symmetric and Multimodal Curve

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Box Plots

• Quartiles

  • Q1 = 25th Percentile

  • Q2 = 50th Percentile (Median)

  • Q3 = 75th Percentile

• Fences

  • LF = Q1 - h

  • UF = Q3 + h

  • h = 1.5(Q3 - Q1)

  • Outliers are any points that lie outside of the LF and UF

• Drawing a Box Plot

  • Central box from Q1 to Q3

  • Line in the middle is Q2

  • Whiskers extend to the point CLOSEST to the LF & UF (not the actual values of the fences)

  • Outliers are marked by small circles

Label y axis

Variance

• Sample variance

  • s^2 = Σ(yi - ȳ)^2 / n - 1

  • Remember to subtract one from n

• Simple Standard deviation

  • Sqrt(s^2)

  • Same unit as the original data value