STA3032 Module 1
STA3032 Module 1 STA3032
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This 3 page Class Notes was uploaded by Tia Belvin on Tuesday January 19, 2016. The Class Notes belongs to STA3032 at University of Florida taught by Demetris Athienitis in Spring 2016. Since its upload, it has received 32 views. For similar materials see Engineering Statistics in Engineering and Tech at University of Florida.
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Date Created: 01/19/16
STA3032 MODULE 1 ARTICLE I. 1.1-1.3.5 1) 1.1 Descriptive Statistics a) Population parameters- “a numerical summary concerning the complete collection of subjects” i) Notated by Greek characters b) Sample statistics- “a numerical summary concerning a subset of the population, from which we try to draw inference about the population parameter” i) Notated by the hat symbol over a population parameter c) i.e. σσstandard deviation 2) 1.2 Summary Statistics 3) 1.2.1 Location a) Mode: most frequent number b) Mean: average of the observations c) p percentile: p% of data are less than that specific value and 100%-p% are greater i) position of p percentile value: (p/100)(n+1) (1) i.e. value x was in the 90 percentile which means that 90% of all valuethwere less than value x d) Median: 50 percentile e) Trimmed Mean: a% trimmed mean means that a% multiplied by your total numerical values= some value that is equal to how many values you “trim” from the lower and upper side of your data (assuming your data is ordered smallest to largest). With the remaining values you recalculate the new average. i) i.e. if you have 10 values, ordered, and you want to calculate the 10% trimmed mean. 10%=0.1 so 0.1 x 10 (your total number of values) =1. Therefore, you would trim off one value from the lower side and one value from the upper side. With these 8 remaining values you would recalculate the mean and that is your “trimmed mean”. NOTE: The mean is more sensitive to outliers than the median. 4) 1.2.2 Spread a) Variance: a measure of spread of observations from their center (mean). n 2 1 2 2 i) σ σ ([ ] )−nx n−1 i=1 b) Standard Deviation: the square root of the varianceσ=σ c) Range: maximum observation- minimum observation d) Interquartile Range (IQR): 75 percentile-25 percentile (Q3-Q1) 5) 1.3 Graphical Summaries 6) 1.3.1 Dot Plot a) Stack each observation on a horizontal line. This gives an idea of the shape of the data. 7) 1.3.2 Histogram a) Step 1: Create class intervals (you choose boundary points) b) Step 2: Construct a frequency table c) Step 3: Draw a rectangle for each class 8) 1.3.3 Box-Plot a) A box plot only uses quartiles. b) You need to find Q , 1 , 2 an3,the IQR given your data. c) Constructing the graph i) Left vertical line: Your lowest value within 1.5IQR of Q ( if 1t is not within 1.5IQR of Q i1 is considered an outlier) ii) Make a box connecting your: (1) Lower whisker: your Q value 1 (2) Upper whisker: your Q val3e iii) The median is your Q an2 should be the vertical line within the box iv) Right vertical line: Your highest value within 1.5IQR of Q (if i3 is not within 1.5IQR of Q i3 is considered an outlier) NOTE: outliers are marked with a dot and your min value should have a horizontal line connecting it to the first quartile as should your maximum value have a horizontal line connecting it to the third quartile 9) 1.3.4 Pie Chart a) Size of slice is determined by fraction of the 360˚ that corresponds to that category. b) Each slice is labeled and color coordinated to your choosing. 10) 1.3.5 Scatter Plot a) Used to plot points of two variables in order to display a relationship between the two
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