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# Intro Prob & Stat for Business STT 315

MSU

GPA 3.72

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This 2 page Class Notes was uploaded by Aryanna Jerde on Saturday September 19, 2015. The Class Notes belongs to STT 315 at Michigan State University taught by Lyudmila Sakhanenko in Fall. Since its upload, it has received 28 views. For similar materials see /class/207815/stt-315-michigan-state-university in Statistics and Probability at Michigan State University.

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Date Created: 09/19/15

21 Describing Qualitative Data A class is one of the categories into which qualitative data can be classified The classfrequency is the number of observations in the data set falling into a particular class The classrelativefrequency is the class frequency divided by the total number of observations in the data set The classpercentage is the class relative frequency multiplied by 100 Summary of Graphical Descriptive Methods for Qualitative Data Bar Graph The categories classes of the qualitative variable are represented by bars where the height of each bar is either the class frequency class relative frequency or class percentage Pie Chart The categories classes of the qualitative variable are represented by slices of a pie circle The size of each slice is proportional to the class relative frequency Pareto Diagram A bar graph with the categories classes of the qualitative variable ie the bars arranged by height in descending order from left to right 22 Graphical Methods for Describing Quantitative Data Dot Plot The numerical value of each quantitative measurement in the data set is represented by a dot on a horizontal scale When data values repeat the dots are placed above one another vertically StemandLeaf Display The numerical value of the quantitative variable is partitioned into a quotstemquot and a quotleafquot The possible stems are listed in order in a column The lead for each quantitative measurement in the data set is placed in the corresponding stem row Leaves for observations with the same stem value are listed in increasing order horizontally Histogram The possible numerical values of the quantitative variable are partitioned into class intervals where each interval has the same width These intervals form the scale of the horizontal axis The frequency or relative frequency of observations in each class interval is determined A vertical bar is placed over each class interval with height equal either to class frequency or class relative frequency 23 Summation Notation Tl 2 rm 1 1 Sum the measurements on the variable that appears to the right of the summation symbol begxinning with the 1st measurement and ending with the n h measurement 24 Numerical Measures of Central Tendency n X 1 n The mean of a set of quantitative data is the sum of the measurements divided by the number of measurements contained in the data set x bar sample mean u sample population The median of a quantitative data set is the middle number when the measurements are arranged in ascending or descending order The data is said to be skewed if one tail of the distribution has more extreme observations than the other tail If the median is less than the mean the data set is skewed right If the median is greater than the mean the data set is skewed left If the median equals the mean the data set is symmetrical 25 Numerical Measures of Variability The range of a quantitative data set is equal to the largest measurement minus the smallest measurement The sample variance for a sample of n measurements is equal to the sum of the squared deviations from the mean divided by nl ln symbols using s2 to represent the sample variance The sample standard deviation s is defined as the positive square root of the sample variance s2 sample variance s sample standard deviation 62 population variance 6 population standard deviation

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