Organizing Data. Variables. Days to maturity for 40 shortterm investments. Data


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1 Variables Organizing Data Variable: A characteristic that varies from one entity (e.g., person or thing) to another. Qualitative variable: A nonnumerically valued variable. Quantitative variable: A numerically valued variable. Discrete Variable: A quantitative variable whose possible values form a finite (or countably infinite) set of numbers. 1 Continuous variable: A quantitative variable whose possible values form some interval of numbers. 2 Data Days to maturity for 40 shortterm investments Data: Information obtained by observing values of a variable. Qualitative data: Data obtained by observing values of a qualitative variable. Quantitative data: Data obtained by observing values of a quantitative variable. Discrete data: Data obtained by observing values of a discrete variable. Continuous data: Data obtained by observing values of a continuous variable. 3 4
2 Classes and counts for the daystomaturity data Relativefrequency distribution for the daystomaturity data 5 6 Groupeddata table for the daystomaturity data Weights of 37 males, age years 7 8
3 Groupeddata table for the weights of 37 males, age Number of schoolage children in each of 30 families 9 10 Groupeddata for number of schoolage children Political party affiliations of the students in introductory statistics 11 12
4 Frequency and relativefrequency distributions for political party affiliations Terms Used in Grouping Classes: Categories for grouping data. Frequency: The number of observations that fall in a class. Frequency distribution: A listing of all classes along with their frequencies. Relative frequency: The ratio of the frequency of a class to the total number of observations. 13 Relativefrequency distribution: A listing of all classes along with their relative frequencies. 14 Terms Used in Grouping Frequency and RelativeFrequency Histograms Lower cutpoint: The smallest value that can go in a class. Upper cutpoint: The smallest value that can go in the next higher class. The upper cutpoint of a class is the same as the lower cutpoint of the next higher class. Midpoint: The middle of a class, obtained by taking the average of its lower and upper cutpoints. Width: The difference between the upper and lower cutpoints of a class. Frequency histogram: A graph that displays the classes on the horizontal axis and the frequencies of the classes on the vertical axis. The frequency of each class is represented by a vertical bar whose height is equal to the frequency of the class. Relativefrequency histogram: A graph that displays the classes on the horizontal axis and the relative frequencies of the classes on the vertical axis. The relative frequency of each class is represented by a vertical bar whose height is equal to the relative frequency of the class
5 Daystomaturity: (a) frequency histogram (b) relativefrequency histogram To Constrict an Histogram 17 S1: calculate the range = max min value S2: divide the range into (min 5 max 20) classes; rule of thumb observations classes Less than 25 5 or More than Define the aprox_class_with = range/classes The lowest (first class boundary) should be below the smallest measurement S3: for each class calculate the number of observation falling inside S4: calculate the relative class frequency 18 Schoolage children: (a) frequency histogram (b) relativefrequency. histogram Oats yields 19 20
6 Dotplot for oats yields Political party affiliations: (a) pie chart (b) bar graph Histogram for the daystomaturity data Relativefrequency histogram and approximating smooth curve for the. distribution of heights 23 24
7 Common distribution shapes Relativefrequency histogram for household size Population and Sample Distributions; Distribution of a Variable Population and Sample Distributions The distribution of population data is called the population distribution or the distribution of the variable. The distribution of sample data is called a sample distribution. The distribution of a random sample from a population approximates the population distribution. In other words, if a random sample is taken from a population, then the distribution of the observed values of the variable under consideration will approximate the distribution of the variable. The larger the sample, the better the approximation tends to be
8 Relativefrequency histograms for household size for six random samples of size 100 from the population of U.S. households Relativefrequency histograms for household size for six random samples Relativefrequency histograms for household size for six random samples Project effort Histogram of d$effort.month Effort_month Duration_month Size_LOC 16, ,6 15, , ,9 9, ,3 13, ,7 24, ,1 15, ,3 14, ,6 7, , Frequency d$effort.month 32
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