Organizing Data. Variables. Days to maturity for 40 short-term 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 non-numerically 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 short-term 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 days-to-maturity data Relative-frequency distribution for the days-to-maturity data 5 6 Grouped-data table for the days-to-maturity data Weights of 37 males, age years 7 8

3 Grouped-data table for the weights of 37 males, age Number of school-age children in each of 30 families 9 10 Grouped-data for number of school-age children Political party affiliations of the students in introductory statistics 11 12

4 Frequency and relative-frequency 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 Relative-frequency distribution: A listing of all classes along with their relative frequencies. 14 Terms Used in Grouping Frequency and Relative-Frequency 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 aver-age 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. Relative-frequency 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 Days-to-maturity: (a) frequency histogram (b) relative-frequency 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 School-age children: (a) frequency histogram (b) relative-frequency. histogram Oats yields 19 20

6 Dotplot for oats yields Political party affiliations: (a) pie chart (b) bar graph Histogram for the days-to-maturity data Relative-frequency histogram and approximating smooth curve for the. distribution of heights 23 24

7 Common distribution shapes Relative-frequency 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 Relative-frequency histograms for household size for six random samples of size 100 from the population of U.S. households Relative-frequency histograms for household size for six random samples Relative-frequency 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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