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STAT 2060 (6)
Peter Kim (6)
Chapter 2

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STAT 2060
Peter Kim

Chapter 2- Methods for Describing Sets of Data Qualitative Data Class- one of the categories into which qualitative data can be classified Class frequency- number of observations in the data set falling into a particular category Class relative frequency- class frequency/total number of observations in data set Class percentage- class relative frequency * 100 Graphical Descriptive Methods for Qualitative Data: Bar graph- categories (classes) of qualitative variables are represented by bars, where the height of each bar is either: the class frequency, class relative frequency, or class percentage Pie chart- categories (classes) of qualitative variables are represented by slices of pie (circle). The size of each slice is proportional to class relative frequency Pareto Diagram- bar graph where categories (classes) of qualitative variables are arranged by height in descending order from left to right Quantitative Data Graphical Methods for Describing: Dot plot- numerical value of each quantitative measurement in the data set is represented by a dot on the horizontal scale. When data values repeat, the dots are placed above one another vertically Stem-and-Leaf plot- numerical value of the quantitative variable is partitioned into a ‘stem’ and ‘leaf’ The possible stems are listed in order in a column. The leaf 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- possible numerical values of 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 to either the class frequency or class relative frequency Summation Notation ∑ n – number of measurements in data set ∑ = “The summation of x from i=1 to n” i- starting number i Numerical Measures of Central Tendency Measures of Central tendency- data clusters, or centres, about a certain numerical value 1. Mean–sum of measurements divided by the number of measurements contained in the data set ∑ =Sample mean μ = Population mean 2. Median, m- middle observation when measurements are arranged in ascending/descending order (note, if n is an even number, average the two middle values) 3. Mode- measurement that occurs most frequent in data set Numerical Measures of Variability Measures of Variability: -spread of data 1. Range-quantitative data set is equal to the largest measurement minus the smallest measurement 2. Variance- for a sample of n measurement is equal to the sum of the squared deviations from the mean divided by (n-1(measures spread) ∑ ∑ Variance= ∑ ( ) Variance= Standard Deviation, s – positive square root of the sample variance, s=√s 2 Sample standard deviation Standard Deviation= √ ∑ s Sample variance σ(sigmPopulation standard deviation σ2 Population variance Empirical Rule #1: Relationship2between and s -for any number k>1, at least (1-1/k ) of the
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