WPC_300 Descriptive_Statistics_Notes.docx.pdf

Descriptive Statistics Notes

Statistics

oScience concerned with developing and studying methods for collecting, analyzing,

interpreting, and presenting empirical data to assist in making effective decision

Descriptive Statistics

oStudy data with entirety

3 Principles of Describing Data:

Center

Spread

Shape

Inferential Statistics

oStudy sample data

oEstimate uncertainty (using probability) some member of the data to infer about

population data

Population vs. Sample

oPopulation: Whole collection of persons, objects, or items under study

oCensus: Gathering data from the entire population

oSample: portion of the whole/population

Subset of the population must be large enough to represent the whole

Measuring Data Centrality

oMeasures of Central Tendency:

Yield information about the center, or middle part, of a group of numbers

Mean

Median

Mode

Percentiles

Quartiles

Sample vs. Population Mean

oMean

Average of a group of numbers

Not applicable for categorical (nominal / ordinal) data

Affected by each value in the data set, including extreme values

Computed by summing all values in the data set and dividing the sum by the

number of values in the data set

oMedian

Middle value in an ordered array of numbers

Applicable for quantitative (ordinal / interval ratio) data

Ex: Median Housing price in a State

Not applicable for nominal data

Unaffected by extremely large and extremely small values

oMode

Most frequently occurring value in a data set

Applicable to all levels of data measurement (nominal, ordinal, interval, and

ratio)

Measuring Data Variability

oMeasures of variability describe the spread or the dispersion of a set of data

oCommon Measures of Variability:

Range

Interquartile Range

Mean Absolute Deviation

Variance

Standard Deviation

Measuring Data Spread

oRange

Difference between the largest and the smallest values in a set of data

Simple to compute

Ignores all data points except the two extremes

oMean Absolute Deviation

Average of the absolute deviations from the mean

Equation:



M . A . D.=∑

x−μ

Variance and Standard Deviation

oVariance

Average of the squared deviations from the arithmetic mean

oStandard Deviation

Square root of the variance

Data Shape

oMeasures of Shape

Describe the skewness of a set of data

oCommon measure of skewness is called Kurtosis

Measure of whether the data are peaked or flat relative to a normal distribution

Data sets with high kurtosis tend to have a distinct peak near the mean,

decline rather rapidly, and have heavy tails

Data sets with low kurtosis tend to have a flat top near the mean rather

than a sharp peak

Data Association

oTwo variables have a strong statistical relationship with one another if they appear to

move together

oWhen two variables appear to be related, you might suspect a cause and-effect

relationship

oStatistical relationships exist even though a change in one variable is not caused by a

change in the other

Measure of Data Association – Covariance

oCovariance

Measure of the linear association between two variables, X and Y

Covariance between X and Y is the average of the product of the deviations of

each pair of observations from their respective means

Correlation coefficient is scaled between -1 and 1

Measure of Data Association – Correlation

oCorrelation

Measure of the linear relationship between two variables, X and Y, which does

not depend on the units of measurement

Measured by the correlation coefficient, also known as the Pearson product

moment correlation coefficient

Correlation coefficient is scaled between -1 and 1

Students also viewed