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Descriptive Statistics
Collecting, organising, summarising and presenting numerical data, to enable meaningful interpretation and to support decision making.
 Graphs
 Tables
 Summary Measures

Inferential Statistics
Drawing conclusions about a population based on the sample information.

Statistical Inference
Using the sample statistic to estimate the parameter of interest.

Population
Is the entire collection of items about which in which information is required.

Sample
A subset of the population that we collect data from.

Variable
A characteristic of a population or sample that is of interest to us.

Data
The actual (or observed) values of variables.
 Quantitative data  numerical observations.
 Qualitative data  categorical.

Levels of Measurement (LOM)
Data can also be described in terms of the level of measurement attained.
 Nominal
 Ordinal
 Interval
 Ratio

Qualitative Data (LOM)
Nominal scale  classifies data into distinct categories in which no ordering is implied
Ordinal  classifies data into distinct categories in which ordering is implied

Quantitative Data (LOM)
Interval Scale  an ordered scale in which the difference between measurements is a meaningful quantity that does not include a true zero point.
Ratio Scale  an ordered scale in which the difference between two points includes a true zero point.

Parameter
Is a number that describes a population.
 Population mean  μ
 Population standard deviation  σ
 Population proportion  ρ
A parameter is a fixed number.

Statistic
Is a number that describes a sample.
 Sample mean  x ( over)
 Sample standard deviation  s
 Sample proportion  p (^ over)
A statistic is a variable whose value varies from sample to sample.

Histogram
A graphical summary of a set of data showing the number (frequency) of observations in each of several nonoverlapping classes.
  Select the number of classes.
  Select an appropriate width for each class.
  Make sure that classes are nonoverlapping and contain all observations.

Relative Frequency Histogram
Replace the class frequency on the y axis by the class relative frequency.
Class relative frequency = class frequency / total number of observations

Relative Frequency
Useful when comparing two or more populations (samples) especially when the number of observations in the samples are different (males to female).
The vertical scale of the relative frequency is common allowing easy comparisons across different populations.

Symmetry Histogram
Said to be symmetric if, when we draw a vertical line down the centre, the two sides are identical in shape and size.

Skewed Histogram
Positively skewed  A long tail extending to the right, indicates few larger values and more smaller values.
Negatively skewed  A long tail extending to the left, indicates few smaller values and more larger values.

Number of Modes (Modal classes) Histogram
Unimodal  Histogram with one peak.
Bimodal  Histogram with two peaks, not necessarily the same height.
Multimodal  Histogram has several peaks.

Bell Shape Histogram
Special type of symmetric unimodal histogram.

Cumulative Frequency Distribution
The number or proportion of observations less than or equal to some value.

Ogive
A graph of the cumulative relative frequency.
The ogive is closed at the lower end by extending a straight line to the lower limit of the first class.

