# Week 3 Study Notes

GGR 270 ā Lecture 3 ā September 29, 2010

Statistics vs. Parameters

īGraphs are limited in what they can tell us

īDifficulty making inferences about a population when looking at a subset or sample

īTherefore, we need to use numerical measures

īMeasures associated with the population are called parameters

īMeasures associated with a sample are called statistics

Measures of the centre

Mean:

īMost commonly used measure of central tendency

īSum of all values or observations divided by the number of observations

Sample Population

Median:

īValue occupying the āmiddle positionā in an ordered set of observations

īOrder the observations, lowest to highest, and find the middle position

www.notesolution.com

īExpressed as: .5(n+1)

Mode:

īValue that occurs with the highest frequency

īAllows you to locate the peak of relative frequency histogram

Choosing appropriate measure

Mean is usually the best measure as it is sensitive to change in a single observation

Not a good measure when:

īDistribution is bimodal

īSkewed distribution

īOutliers (extreme values) are present in the data set

Normal

ī

Mean, Median, Mode

Bimodal

ī

Mode, Mean, Median, Mode

Positive skew

ī

mode, med, mean ā mean>median

Negative skew

ī

mean, median, mode ā mean<median

*Mean always dragged in direction of skew

Measures of dispersion

www.notesolution.com

## Document Summary

Ggr 270 lecture 3 september 29, 2010. graphs are limited in what they can tell us. difficulty making inferences about a population when looking at a subset or sample. measures associated with the population are called parameters. measures associated with a sample are called statistics. most commonly used measure of central tendency. sum of all values or observations divided by the number of observations. value occupying the middle position" in an ordered set of observations. order the observations, lowest to highest, and find the middle position www. notesolution. com. value that occurs with the highest frequency. allows you to locate the peak of relative frequency histogram. Mean is usually the best measure as it is sensitive to change in a single observation. outliers (extreme values) are present in the data set. Positive skew mode, med, mean mean>median. Negative skew mean, median, mode mean