Unit 3: Getting Started with Variability

Review – Data and AveragesData may be drawn from a sample, or from each member of the population.Averages use a single number to summarize the values of a set of data pointsThree averages are commonly usedThe Mode for qualitative dataThe Mean and the Median for quantitative data

Review – Mean and MedianStrengths of the MeanMost common form of averageInfluenced by the value of each data pointWidely used in more advanced statistical techniquesStrengths of the MedianNot influenced by extremely high or low scoresCan be computed in some circumstances in which it is not possible to compute the Mean

Review – Symbolsn is the number of scores or data pointsX represents a single score and M represent the mean of a set of scoresΣ indicates that the items that follow shouldbe added together(….)² indicates that the items inside the parentheses should be squared indicates that the square root of the items inside is required.

What IS Variability? Variability is a measure of how different scores are from one another within a set of data points.Synonyms: spread,dispersion.Novels are 100,000 words long, on averageMoby Dick is 213,724 wordsA Christmas Carol is 29,100How could we measure the variability of book length?.Bookhaven by waffler at http://www.flickr.com/photos/adrian_s/23441729/

An ExampleJulian comes to the Tutor Center with an average quiz score of 15 out of 25.Delia also comes to the Tutor Centerwith a 15 out of 25 average score.Both want to improve their scoresDo we know enough to begin to help them? Let’s look at their scores…

Here are their scores for the first 20 daily quizzes:Let’s analyze the pattern of each student’s scores.

Describing Julian’s scoresBest score = 18Worst score = 13Most scores are 14, 15, or 16Consistent, stableLow variability

Describing Delia’s scoresBest score = 22Worst score = 8Few scores repeatErratic, up-and-downHigh variability

Variability guides your advice!Both students want a higher mean score.With low variability, Julian might focus on new study methods to master more material.With high variability, Delia might focus on consistent study habits to repeat her high scores.How can we measureanddescribe variability?

Chapter 3 and the lecture for this module describe several measures of variabilityThe Range and Interquartile Range (IQR) describe the distance from high to low scoresThe Standard Deviation describes the “average” distance from a score to the mean.The Variance measures the total amount of variability in the data set.Variability can be measured!

Preview Variability is a key concept for the rest of the courseLectures in this unit are a bit longerStatistical Analysis Toolpak computes these measures for youAn Excel Video demonstrates these methods fully

Unit 3: Getting Started with Variability