Basic statistics

Sample

A portion of a population

Parameter

A quantitative attribute of a population

Statistic

A quantitative attribute of a sample

Gaussian Distribution

Also called normal curve In replicate measurements, a pattern of clustering about the mean with symmetric distribution of outlying values

Measures of Central Tendency

Arithmetic average or mean ( x ) Sum number of individual values and divide by n Median The middle value or 50th percentile value when values are rank ordered Mode The most frequently occurring value

Main Components of Statistics

Descriptive statistics Inferential statistics

Z-score

Determines how many sigmas or standard deviations the value in question is away from the mean Calculation Population Sample

Bias

Difference between 2 means Presence of nonrandom events which make the sample nonrepresentative of the target population Lack of accuracy

Descriptive statistics

Graphs, tables, frequencies, averages, medians, percentages, and ranges Mean, range, variability, distribution of a data set

Symmetric Distribution

Mean = Mode = Median

Range

Measure of how data are distributed around the mean Highest value minus lowest value Often includes values that are not entirely representative Limited in describing relationship between data and the mean Provides no prediction of what the dispersion will be in the future

Inferential statistics

Method of making conclusions based on numerical data derived from a sample of the population Relationships among different sets or samples of data

Degrees of freedom (df)

Number of data points that have impact on the system Small samples Use n - 1 Population calculations Use n

Statistics

Organization and interpretation of numerical information or data

Standard Deviation (s)

Principle estimator of dispersion Predictable Always expressed in the units being measured Calculation

Measures of Dispersion

Range Standard deviation Variance Degrees of freedom Confidence interval Coefficient of variation *all indicate degree of precision

Confidence Interval

Sometimes called control range Calculation When Gaussian distribution exists

Variance

Standard deviation squared

Population

The universe of values or attributes

Mode

Unimodal Bimodal Polymodal No distinct mode

Random

Unpredictable No algorithm or formula can predict next event All events appear equally probable

Probability

p = 1 means 100% probability p= 0.5 means 50% probability