Introduction to Data Visualization
- 1. TODAY! Review of Descriptive Statistics • Mean, Median, Mode, Standard Deviation • Frequency tables and histograms • The Normal Distribution (AKA: Gaussian, Bell-curve) BREAK Descriptive Statistics with Excel • Find Mean, Median, Mode, and Standard Deviation for two different example distributions • Create histograms for the two different distributions • Compare them with the normal distribution Descriptive Statistics with Tableau • Create histogram for an example distribution • Compare it to the normal distribution BREAK Introduction to Processing • Create histogram for an example distribution • Compare it to the normal distribution.
- 2. But First: - For those of you interested in tracking search trends, check out Google Trends https://www.google.ca/trends/ - For those of you interested in tracking your site traffic, look at Google Analytics http://www.google.com/analytics/ - Unfinished from last class: Geographical Representations using Tableau
- 3. Descriptive Statistics Explained Using Cows Farmer Number of Cows John 1 Bob 2 Sue 2 Mary 3 Jim 4 Sally 5 Fran 5 Pat 6 Bill 18 Tom 20 mean = total _cows number _of _ farmers 1) Find the average number of cows per farmer. mean = 1+2+2+3+4+5+5+6+18+20 10 = 6.6 Average (mean) is 6.6 cows per farmer
- 4. Descriptive Statistics Explained Using Cows Farmer Number of Cows John 1 Bob 2 Sue 2 Mary 3 Jim 4 Sally 5 Fran 5 Pat 6 Bill 18 Tom 20 2) Find the median number of cows per farmer. The median is the value that separates the lower half of the distribution from the higher half of the distribution. Half of all farmers have more cows than the median, and half of the farmers have fewer cows than the median. The median of this distribution is about 4.5
- 5. Descriptive Statistics Explained Using Cows Farmer Number of Cows John 1 Bob 2 Sue 2 Mary 3 Jim 4 Sally 5 Fran 5 Pat 6 Bill 18 Tom 20 3) Find the mode number of cows per farmer. The mode is the value that appears most often in a set of data. In a probability distribution, it is the most probably value in the distribution. A distribution that has two modes is said to be bimodal. The modes of this distribution are 2 and 5
- 6. Descriptive Statistics Explained Using Cows Farmer Number of Cows John 1 Bob 2 Sue 2 Mary 3 Jim 4 Sally 5 Fran 5 Pat 6 Bill 18 Tom 20 std = Σ(cows − mean)2 number _of _ farmers 4) Find the standard deviation in the number of cows per farmer. std = (1−6.7)2 +(2−6.7)2 +(2−6.7)2 +(3−6.7)2 +(4−6.7)2 +(5−6.7)2 +(5−6.7)2 +(6−6.7)2 +(18−6.7)2 +(20−6.7)2 10 The standard deviation of this distribution is 6.7 The Standard Deviation is a measure of how spread out numbers are.
- 7. Frequency Table Farmer Number of Cows John 1 Bob 2 Sue 2 Mary 3 Jim 4 Sally 5 Fran 5 Pat 6 Bill 18 Tom 20 Number of Cows Number of Farmers 1 1 2 2 3 1 4 1 5 2 6 1 7 0 8 0 9 0 10 0 11 0 12 0 13 0 14 0 15 0 16 0 17 0 18 1 19 0 20 1
- 8. Histograms Number of Cows Number of Farmers 1 1 2 2 3 1 4 1 5 2 6 1 7 0 8 0 9 0 10 0 11 0 12 0 13 0 14 0 15 0 16 0 17 0 18 1 19 0 20 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 3 2 1 Number of Cows
- 9. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 3 2 1 Histogram of our cow distribution Number of Cows NumberofFarmers Mean (average) Standard deviationStandard deviation Median Note: the number of farmers having a given number of cows is proportional to the probability of a farmer having a given number of cows.
- 10. The Normal Distribution Also known as the Gaussian function, and as the Bell Curve. This is the most commonly occurring distribution. It the the special case in which mean, median, mode are the same It describes random variations around an average measure (random fluctuations about the mean) Examples: heights of men, heights of women, motion of particles in the air, grade distributions for a course, … P σ = standard deviation µ = mean x = number of cows
- 11. The Normal Distribution σ = standard deviation µ = mean (the average) x = number of cows P(x) x Here x=µ This is the average (the mean) This is also the median. This is also the mode. P
- 12. The Normal Distribution σ = standard deviation µ = mean (the average) x = number of cows P
- 13. Back to cows 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 3 2 1 Number of Cows NumberofFarmers Mean (average) Standard deviationStandard deviation Median Normal distribution for: Mean = 6.6 cows Standard Deviation = 6.7 cows Probability of having this many cows
- 14. Now – Let’s remove the outliers to see what happens 1 2 3 4 5 6 7 3 2 1 Number of Cows NumberofFarmers Farmer Number of Cows John 1 Bob 2 Sue 2 Mary 3 Jim 4 Sally 5 Fran 5 Pat 6 Bill 18 Tom 20 Number of Cows Number of Farmers 1 1 2 2 3 1 4 1 5 2 6 1 Mean = 3.5 Median = 3.5 Standard Deviation = 1.8
- 15. 1 2 3 4 5 6 7 3 2 1 Number of Cows NumberofFarmers Now – Let’s remove the outliers to see what happens Mean (average), also the Median σσ Mean = 3.5 Median = 3.5 Standard Deviation σ = 1.8 Probability of having this many cows The normal distribution for these numbers:
- 16. Next, we will look at larger distributions and use Excel and Tableau to manipulate the data, draw a histogram, and compare our data to the normal distribution. For our next example, we will look at distribution of class grades. Please download the example data from Canvas If you are running Excel from windows, the histogram feature is already built in: http://www.excel-easy.com/examples/histogram.html But if you are running Excel from a Mac, then you will need this add-on: http://www.analystsoft.com/en/products/statplusmacle/ Here are additional instructions: http://www.gilsmethod.com/how-to-enable-statsplus-in-excel-2011-for-mac During the break, please: - download the data - download and install the Excel add-on (if needed) - download and install Tableau Public (if you haven’t already) During the second break: - download Processing, and download my example code.