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lecture notes covering 2.5 and 2.6

by: Andrej Sodoma

lecture notes covering 2.5 and 2.6 STP 231

Marketplace > Arizona State University > Statistics > STP 231 > lecture notes covering 2 5 and 2 6
Andrej Sodoma
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These notes cover the lectures that went over sections 2.5 and 2.6.
Statistics for Biosciences
Dr. Ye Zhang
Class Notes
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This 2 page Class Notes was uploaded by Andrej Sodoma on Friday September 16, 2016. The Class Notes belongs to STP 231 at Arizona State University taught by Dr. Ye Zhang in Fall 2016. Since its upload, it has received 14 views. For similar materials see Statistics for Biosciences in Statistics at Arizona State University.


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Date Created: 09/16/16
Week 4 lecture content, 2.5 and 2.6  I. 2.5 A. Univariate summary and Bivariate summary  i. Univariate summary uses graphical or numerical summaries for one variable data sets.  ii. Bivariate is the same thing as univariate summary but for two variables.  B. Relationship between two variables  i. Use a bivariate frequency table or a contingency table they mean the same thing.  Teams Low GPA Medium GPA High GPA total Red 20 5 1 26 Blue 30 10 2 42 green 40 15 3 58 total 90 40 6 136 ii. Total low GPA is 90. Total participants 136.  C. Relationship between two numeric variables i. The data set is first made into a scatter plot. A relationship is then derived from the plot whether it can be linear or quadratic.  ii. The dependent variable is placed on the y­axis. The dependent variable is influenced by the independent variable. It is also the variable that is measured.  iii. The independent variable is placed on the x­axis. The independent variable is the variable that is manipulated.  D. Relationship between a numeric variable and a categorical variable  i. Use a boxplot to describe the data. ii. An example is the number of squats (numeric) a man vs. woman (categorical) can do.  iii. Two categorical variables use stacked bar chart (profession and ethnicity)  iv. Two numeric variables use a scatterplot (gas mileage and model year) II. 2.6 A. Range and standard Deviation  i. Range is the maximum value minus the minimum value. IT is NOT robust ii. Deviation is the difference between a variable and the mean. ­ X­iean iii. X is the i­th observation meaning any observation with which you start your standard deviation with. iv. Sample standard deviation: it is always greater than zero and means how much a value differs from the mean. Not Robust ­  v. E means the summation.  vi. n is the number of observations vii. n­1 is needed in order to get a more exact difference prevents low balling the amount.  viii. First (Xi­X). Second (Xi­X)^2. Third, add up all of these values. Divide by (n­1). Fourth, get the square root of all of that.  ix. Sample variance simply means your sample standard deviation times two.  x. When given the variable and its frequency and you need to find the standard deviation: 1. Find the mean (X1times frequency)+(Xn times frequency) / n  2. Get the difference (Xi­mean)  3. Square it 4. Multiply by the frequency of that variable  5. Add all of them up 6. Divide by n­1 7. Square it B. Empirical rule i. Can only be applied when the sample is symmetric meaning the mean is equal to the median, it is a unimodel distribution, and it follows the rules below: 1. 68% values are with one standard deviation of the mean (x plus or minus s) 2. 95% of values are within two standard deviation of the mean (x plus or minus 2s) 3. 99.7% of values are within three standard deviations of the mean (x plus or minus 3 s)  ii. Review: 1. Robust measurements: median, mode, quartiles, IQR 2. Not Robust measurements: mean, range, standard deviation


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