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# Stats Chapter 1 Notes (Definitions, Equations) Stat 1000

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This 3 page Class Notes was uploaded by Leela Morris on Sunday September 27, 2015. The Class Notes belongs to Stat 1000 at University of Pittsburgh taught by Dr. Kehui Chen in Fall 2015. Since its upload, it has received 56 views. For similar materials see Applied Statistical Methods in Statistics at University of Pittsburgh.

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Date Created: 09/27/15

Applied Statistical Methods Chapter 1 NotesDefinitionsEquations Definitions Notes Population any complete collection of people animals or other objects that a scientistresearcher is interested in Parameter a value that describes some characteristic of a population Sample a set of units selected from a population that the statistician analyzes in order to better understand that population Statistic a quantity calculated from a sample that serves as an estimate of the parameter Variable a characteristic of a population that differs from a person to person or object to object within a population closely related to the parameter of interest Data the observed values of variables in our sample Two Types of Data Categorical variables takes categories as variables Quantitative variables take numbers as variables numerical Discrete take only finite numbers of distinct values ex of siblings of movies you saw last month Continuous take an infinite number of distinct values ex Total points weight height temperature Graphical Summaries of one variable Bar plots pie charts categorical variables Bar Plots each category is represented by a bar bar s height shows the count or percentage for the particular category Pie charts each category is represented by a pie the pie s area shows the percentage for particular category Histogram quantitative variables range of values that a variable can take is divided into equal size intervals shows the number of individual data points that fall in each interval Density Curves tells the shape of distribution roughly has the same shape as the histogram Symmetric right and left sides of the histogram approximately mirror each other Leftskewed the left side extends much farther than the right Rightskewed the right side extends much farther than the left Outliers observations that lie outside the overall pattern of a distribution Numerical summaries for one quantitative variable 0 Location mean median quartiles 0 Spread standard deviation range IQR interquartile range SD 5 used to describe how data are spread out around the mean Range Max Min IQR Q3 Q1 0 Five Number summary Min Q1 Median Q3 Max Box Plot drawing out the five number summary 0 To calculate mean add all values then divide by total number of values 0 Median midpoint of distribution if n is odd the median position is n 12 if n is even is the mean of the two middle observations n2 and n2 1 o Quartiles Q1 25 of the data at or below it median of the lower half of the sorted data Q3 75 of the data at or above it the median of the upper half of the sorted data 0 Outlier equation 15 IQR 0 Density curves the total area under the curve by definition is equal to 1 or 100 Normal distribution 0 Exactly an area of 1 underneath it density curve 0 Continuous over all possible real values has values near the mean occurring more often than values away from the mean bellshaped 0 Has the same mean and median symmetric o The mean controls the center of the distribution 0 The standard deviation controls the variability of the distribution 0 Notation Mp C 0 The 6895997 Rule 68 of all observations are within 1 standard deviation 0 of the mean u 95 of all obs are within 2 o of the mean 1 almost a 997 obs are within 3 o of the mean Standard Normal distribution 0 When u 0 and o 1 a normal distribution is called a standard normal distribution 0 Notation is N 0 1 o Standardization any normal distribution can be converted into the standard normal distribution Z SCORE 0 Z variable mean std dev 0 Table A gives area to the left of z score Eguations Standard deviation 1 N 3 f Ii ij Variance 52 standard deviation squared Linear Transformation y a bx

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