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1 Chapter 2: Organizing and Presenting Data (Page 31) Why do we use graphs? Organize Summarize Analyze Data In a nutshell, Graphs make it easier to: understand describe what is going on with the data Definition 2.1 Raw data- data before it has been arranged in a useful manner or analyzed using statistical techniques. Example: Actual Major League Baseball Salaries ( ) 1
2 Definition 2.2 (page 33) Variable- type of information that is measured or observed. (Also known as a data element. ) Definition 2.3 (page 34) Dataset- collection of several data (rows or observations) pertaining to one or more variables (columns). 2
3 Variables: Definition 2.4 (page 34) 1. Categorical represents categories (categorical data). Non-numerical in nature. Definition 2.5 (page 34) 2. Numerical results from a measurement process (numerical data) Definition 2.6 (page 35) a. Continuous- Can assume any value between 2 numbers. A measurement that has been rounded off. Definition 2.7 (page 35) b. Discrete- Only a limited # of values. Have a break between successive discrete values. Usually count data which are expressed as whole numbers. 3
4 Exploratory data analysis- (page 36) We want to learn as much about the data as possible before conducting any statistical analysis. 1. Looking for: useful aspects, information, unanticipated patterns that may exist. 2. We use visual displays, e.g. tables and/or graphs to reveal vital information. Definition 2.8 (page 36) Distribution- (of a numerical variable) represents the data values of the numerical variable from the lowest to the highest value, along with the # of times each data value occurs (frequency). Also called a frequency distribution. 4
5 Definition 2.9 (page 37) Outlier- a data value which lies far above or below from most or all of the other data values. Why? (page 36-37) 1. Recording error (typo) 2. Due to chance 3. Due to an unusual occurrence- may help to provide valuable info about the dataset. 5
6 Another Example of Raw Data: Artist Song Genre Year Length # of times played A1 AAA Rock :55 3 B2 BBB Jazz :23 4 C3 CCC Country :24 24 D4 DDD Classical : And the Frequency Distribution: # of times played Frequency
7 Shapes of Distributions: (page 66) (Negatively Skewed) (Bell Shaped) (Positively Skewed) Definition 2.25 (page 66) 1. Symmetric (bell-shaped) distribution- peak at the center (highest frequency), with the frequency steadily decreasing but identically distributed on both sides of the center. Definition 2.26 (page 67) 2. Skewed distribution- non-symmetric distribution that has most of the data values falling into one side of the distribution with very few but extreme data values falling in the other side. 7
8 Definition 2.27 (page 67) a. Positively Skewed (skewed right) distributionhas a greater number of relatively low scores and a few extremely high scores. The shape has a longer tail on the right side which represents the few extremely high scores. Definition 2.28 (page 67) b. Negatively Skewed (skewed left) distributionhas a greater number of relatively high scores and a few extremely low scores. The shape has a longer tail on the left side which represents the few extremely low scores. Definition 2.29 (page 68) Uniform (Rectangular) Distribution- all of the classes contain the same number of data values or frequencies. 8
9 Definition 2.30 (page 68) U-shaped Distribution- two greatest frequencies occurring at each extreme end of the distribution with the lowest frequencies occurring in the center. Definition 2.31 (page 68) Reverse J-shaped Distribution- the greatest frequency of data values occurring at one end of the distribution and then tails off gradually in the opposite direction. 9
10 Definition 2.32 (page 68) Bimodal Distribution- a distribution that has two separate, distinct and relatively high peaks with the greatest frequencies. It usually indicates that the distribution represents two different populations. Bimodal Distribution 10
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