Stats in a Hurry Mean Median Standard Deviation

Stats in a Hurry Mean, Median, Standard Deviation, and more A WUTUG presentation by Cindy Traub and Maggie Konich

What does “Statistics” mean to you?

Image source: http: //weknowmemes. com/2013/02/stats-show-teenage-pregnancy-drops-dramatically/

Image source: https: //lovestats. wordpress. com/dman/survey-research-statistics-meme/

Source: http: //www. nytimes. com/interactive/2015/05/21/us/your-contribution-to-the-california-drought. html

Source: http: //www. nytimes. com/interactive/2015/05/21/us/your-contribution-to-the-california-drought. html

Source: https: //mathwithbaddrawings. com/2014/02/26/scary-statistics/

Source: https: //mathwithbaddrawings. com/2014/02/26/scary-statistics/

So what is statistics? a branch of mathematics dealing with the collection, analysis, interpretation, and presentation of masses of numerical data ("Statistics. " Merriam-Webster. com. Accessed July 12, 2017. https: //www. merriam-webster. com/dictionary/statistics. ) the study of how best to collect, analyze, and draw conclusions from data. (Diez, David M. , Christopher D. Barr, and Mine C etinkaya-Rundel. 2016. Open. Intro statistics. [S. l. ]: Open. Intro. )

Many ways to tell a story The fact is that, despite its mathematical base, statistics is as much an art as it is a science. A great many manipulations and even distortions are possible within the bounds of propriety. (How to lie with statistics, Darrell Huff)

3 questions to keep in mind: 1. Compared to what? 2. Since when? 3. Says who?

Common measures of central tendency & spread • • Mean Median Range Standard deviation

Mean (aka Average) • Add the values, divide by number of values • Sensitive to outliers (values much bigger/smaller than others) • Mean of 9, 3, 2, 5, 1, 10: ( 9 + 3 + 2 + 5 + 10) / 6 = 30/6 = 5

Median • The “middle” number when put in order. • If no true middle, average the two closest. • Not as sensitive to outliers • Median of 9, 3, 2, 5, 1, 10: reordered: 1, 2, 3, 5, 9, 10 average 3 rd and 4 th value: (3 + 5)/2 = 8/2 = 4

Range • Largest number minus smallest number • Gives some indication of spread of values • Range of of 9, 3, 2, 5, 1, 10: 10 -1 = 9

Anscombe's quartet Four different data sets, with… Same mean Same variance Same correlation Same regression line By Anscombe. svg: Schutz Derivative works of this file: (label using subscripts): Avenue - Anscombe. svg, CC BY-SA 3. 0, https: //commons. wikimedia. org/w/index. php? curid=9838454

Takeaway 1 • Always look at your data!

Takeaway 2: just because it’s a number… …doesn’t mean you should average it! Consider your data: - Does adding, subtracting, etc. make sense? - Are values naturally ordered? - Does the average have meaning?

What boxplots tell us • • • First quartile separates bottom 25% from top 75% Third quartile separates bottom 75% from top 25% IQR (Interquartile range) = (Third quartile – First quartile) “middle 50%” of data Upper, lower whiskers reach out to actual observations up to 1. 5 times IQR away from 1 st and 3 rd quartiles Values beyond whiskers (outliers) shown as dots Image source: (Diez, David M. , Christopher D. Barr, and Mine C etinkaya-Rundel. 2016. Open. Intro statistics. [S. l. ]: Open. Intro. )

Standard deviation in five easy steps… Observations: 1, 3, 4, 4, 18 • Mean = sum/(# obs) = 30/5 = 6. • Deviation = Observation – mean -5, -3, -2, 12 • Squared Deviation (multiply each by itself) 25, 9, 4, 4, 144 • Sample Variance = sum of squared deviations/(# obs - 1) = 186/4 = 46. 5 • Standard Deviation = square root of variance, here approx. 6. 82

Standard deviation video • Source: Cone head height and standard deviation

Rule of thumb Image source: (Diez, David M. , Christopher D. Barr, and Mine C etinkaya-Rundel. 2016. Open. Intro statistics. [S. l. ]: Open. Intro. )

Can’t I just look at mean and standard deviation? Image source: (Diez, David M. , Christopher D. Barr, and Mine C etinkaya-Rundel. 2016. Open. Intro statistics. [S. l. ]: Open. Intro. )

How do we compute/display in Tableau? • • • Mean Median Standard deviation Boxplot Histogram

Some things are naturally normal; some are not • Normal illustration: https: //youtu. be/lb 2 Snixmu. Rg • Skewed distributions: https: //www. ma. utexas. edu/users/mks/statmistakes/skeweddistrib utions. html • Lognormal distributions: https: //stat. ethz. ch/~stahel/lognormal/lnboard/brochure. html