Chapter 2 Continued Notation 2.3 Measures of Center Finding the - PowerPoint PPT Presentation

Chapter 2 Tim Busken Table of Contents Data Characteristics The Different Parameters and Statistics Chapter 2 Continued Notation 2.3 Measures of Center Finding the mean from a Distribution Professor Tim Busken Weighted Mean Measures of Center: Advantages and Disadvantages Mathematics Department Skewness 2.4 Measures of Variation February 7, 2016 Standard Deviation Empirical Rule Chebyshev’s Theorem Range Rule of Thumb 2.5 Measures of Relative Standing z scores Percentiles Quartiles Box and Whisker Plot Works Cited

Table of Contents 1 Table of Contents Data Characteristics The Different Parameters and Statistics 2 Notation 3 2.3 Measures of Center Finding the mean from a Distribution Weighted Mean Measures of Center: Advantages and Disadvantages Skewness 4 2.4 Measures of Variation Standard Deviation Empirical Rule Chebyshev’s Theorem Range Rule of Thumb 5 2.5 Measures of Relative Standing z scores Percentiles Quartiles Box and Whisker Plot 6 Works Cited

Chapter 2 Tim Busken Table of Characteristics Contents of Data Data Characteristics The Different Parameters and Statistics Notation 2.3 Measures of Center Finding the mean from a Distribution Weighted Mean Center Time Measures of Center: Advantages and Disadvantages Skewness Variation Outliers 2.4 Measures of Variation Distribution Standard Deviation Empirical Rule Chebyshev’s Theorem Range Rule of Thumb 2.5 Measures of Relative Standing z scores Percentiles Quartiles Box and Whisker Plot Works Cited

Chapter 2 Characteristics of Tim Busken Data [ ? ] Table of Contents Data Characteristics The Different 1 Center: A representative or average value that indicates Parameters and Statistics where the middle of the data set is located. Notation 2 Variation: A measure of the amount that the data values vary. 2.3 Measures of Center 3 Distribution: The nature or shape of the spread of data over Finding the mean from a Distribution the range of values (such as bell-shaped, uniform, or skewed). Weighted Mean 4 Outliers: Sample values that lie very far away from the vast Measures of Center: Advantages and Disadvantages majority of other sample values. Skewness 5 Time: Changing characteristics of the data over time. 2.4 Measures of Variation Standard Deviation Empirical Rule Chebyshev’s Theorem Range Rule of Thumb 2.5 Measures of Relative Standing z scores Percentiles Quartiles Box and Whisker Plot Works Cited

Chapter 2 Mean Tim Busken z scores Table of Median Contents Data Characteristics Measures The Different Measures Parameters and of Central Statistics of Relative Percentiles Tendency Standing Notation The different types Mode 2.3 Measures of Parameters of Center & Statistics Finding the mean from Quartiles a Distribution Midrange Weighted Mean Measures of Center: Advantages and Disadvantages Skewness 2.4 Measures of Variation Standard Deviation Empirical Rule Measures Chebyshev’s Theorem of Variation Range Rule of Thumb 2.5 Measures Range of Relative Variance Standing z scores Standard Percentiles Deviation Quartiles Box and Whisker Plot Works Cited

Chapter 2 Notation Tim Busken Table of � Contents denotes the sum of a set of values. Data Characteristics The Different Parameters and Statistics x is the variable usually used to represent the individual data values. Notation 2.3 Measures n represents the number of data values in a sample. of Center Finding the mean from a Distribution N represents the number of data values in a population. Weighted Mean Measures of Center: Advantages and Disadvantages ¯ x the symbol that represents the sample mean. Skewness 2.4 Measures of Variation µ the symbol that represents the population mean Standard Deviation Empirical Rule Chebyshev’s Theorem Range Rule of Thumb 2.5 Measures of Relative Standing z scores Percentiles Quartiles Box and Whisker Plot Works Cited

Chapter 2 Tim Busken mean Table of Contents Data Characteristics The Different Parameters and Statistics Notation median 2.3 Measures of Center Finding the mean from Measures of Center a Distribution Weighted Mean Measures of Center: Advantages and Disadvantages mode Skewness 2.4 Measures of Variation Standard Deviation Empirical Rule Chebyshev’s Theorem Range Rule of Thumb midrange 2.5 Measures of Relative Standing z scores Percentiles Quartiles These are Statistics and Parameters! Box and Whisker Plot Works Cited

Chapter 2 Tim Busken Definition A Measure of Center is a value at the center or middle of a Table of Contents data set.[ ? ] Data Characteristics The Different Parameters and Statistics Notation 2.3 Measures of Center Finding the mean from 0.4 a Distribution Weighted Mean Measures of Center: 0.35 Advantages and Disadvantages 0.3 Skewness 2.4 Measures 0.25 of Variation Standard Deviation 0.2 Empirical Rule Chebyshev’s Theorem 0.15 Range Rule of Thumb 2.5 Measures 0.1 of Relative Standing 0.05 z scores Percentiles 0 Quartiles −4 −3 −2 −1 0 1 2 3 4 Box and Whisker Plot Works Cited

Chapter 2 Definition Tim Busken The mean (average) is the value obtained by adding all of the Table of data values and dividing the total by the number of values. Contents Data Characteristics The Different Parameters and Statistics Definition Notation The median is the middle value when the original data values 2.3 Measures are arranged in order of increasing (or decreasing) magnitude of Center Finding the mean from a Distribution Weighted Mean Definition Measures of Center: Advantages and Disadvantages The mode is the value that occurs with the greatest frequency. Skewness 2.4 Measures of Variation Standard Deviation Definition Empirical Rule Chebyshev’s Theorem The midrange is the value midway between the maximum and Range Rule of Thumb minimum values in the original data set. [ ? ] 2.5 Measures midrange = max. value + min. value of Relative Standing 2 z scores Percentiles classroom worksheet Quartiles Box and Whisker Plot KEY. Works Cited

Chapter 2 Mode Tim Busken Table of Contents Data Characteristics A data set can have one mode, more than one mode, or no The Different Parameters and mode. Statistics Notation Definition 2.3 Measures Whenever two data values occur with the same greatest of Center frequency, we say the data is bimodal . Finding the mean from a Distribution Weighted Mean Definition Measures of Center: Advantages and Disadvantages Whenever more than two data values occur with the same Skewness greatest frequency, we say the data is multimodal . 2.4 Measures of Variation Standard Deviation Definition Empirical Rule Whenever no data value is repeated, there is no mode . Chebyshev’s Theorem Range Rule of Thumb 2.5 Measures of Relative Standing z scores Percentiles Quartiles Box and Whisker Plot Works Cited

Chapter 2 Median Tim Busken Table of Example : What is the median of the following data set? Contents Data Characteristics The Different 21 85 15 43 75 12 Parameters and Statistics Notation 2.3 Measures of Center Finding the mean from a Distribution Weighted Mean Measures of Center: Advantages and Disadvantages Skewness 2.4 Measures of Variation Standard Deviation Empirical Rule Chebyshev’s Theorem Range Rule of Thumb 2.5 Measures of Relative Standing z scores Percentiles Quartiles Box and Whisker Plot Works Cited

Chapter 2 Median Tim Busken Table of Example : What is the median of the following data set? Contents Data Characteristics The Different 21 85 15 43 75 12 Parameters and Statistics Notation 2.3 Measures We begin answering the question by sorting the data in a ascending of Center fashion: Finding the mean from a Distribution 12 15 21 43 75 85 Weighted Mean Measures of Center: Since the number of data entries is even, there is no single data entry Advantages and Disadvantages representing the median. Instead, we take the median to be the Skewness midpoint between the two middle numbers then divide by 2. 2.4 Measures of Variation median = 21 + 43 Standard Deviation = 32 Empirical Rule 2 Chebyshev’s Theorem Range Rule of Thumb 2.5 Measures of Relative Standing z scores Percentiles Quartiles Box and Whisker Plot Works Cited

Chapter 2 Finding the mean from a Distribution Tim Busken Table of Contents Suppose you are presented with a frequency distribution table Data Characteristics related to a particular data set, but not with the actual data set. It The Different Parameters and is possible to compute a good approximation of the average, ¯ Statistics x , Notation with the following formula: 2.3 Measures of Center � ( f · x ) Finding the mean from ¯ x = � f a Distribution Weighted Mean Measures of Center: Advantages and Disadvantages Skewness 2.4 Measures of Variation Standard Deviation 0.4 Empirical Rule 0.35 Chebyshev’s Theorem Range Rule of Thumb 0.3 2.5 Measures 0.25 of Relative 0.2 Standing 0.15 z scores Percentiles 0.1 Quartiles 0.05 Box and Whisker Plot 0 Works Cited −4 −3 −2 −1 0 1 2 3 4