ChaPTER 3 Statistical Description of data to accompany Introduction to business statistics fourth edition by ronald m. Weiers Presentation by Priscilla Chaffe-Stengel Donald N. stengel o The Wadsworth Group
CHAPTER 3: Statistical Description of Data to accompany Introduction to Business Statistics fourth edition, by Ronald M. Weiers Presentation by Priscilla Chaffe-Stengel Donald N. Stengel © 2002 The Wadsworth Group
l Chapter 3- Learning objectives Describe data using measures of central tendency and dispersion for a set of individual data values, and for a set of grouped data Convert data to standardized values Use the computer to visually represent data Use the coefficient of correlation to measure association between two quantitative variables C 2002 The Wadsworth Group
Chapter 3 - Learning Objectives • Describe data using measures of central tendency and dispersion: – for a set of individual data values, and – for a set of grouped data. • Convert data to standardized values. • Use the computer to visually represent data. • Use the coefficient of correlation to measure association between two quantitative variables. © 2002 The Wadsworth Group
ll Chapter 3-Key terms Measures of·Mean Centra u, population; x, sample Tendency, Weighted mean The center Median Mode Note comparison of mean median, an d mode) @2002 The Wadsworth Group
Chapter 3 - Key Terms • Measures of Central Tendency, The Center • Mean – µ, population; , sample • Weighted Mean • Median • Mode (Note comparison of mean, median, and mode) x © 2002 The Wadsworth Group
ll Chapter 3-Key terms · Measures of· Range Dispersion Mean absolute deviation The spread Variance (Note the computational difference between o and s2 ● Standard deviation Interquartile range Interquartile deviation Coefficient of variation o 2002 The Wadsworth Group
Chapter 3 - Key Terms • Measures of Dispersion, The Spread • Range • Mean absolute deviation • Variance (Note the computational difference between s 2 and s 2 .) • Standard deviation • Interquartile range • Interquartile deviation • Coefficient of variation © 2002 The Wadsworth Group
ll Chapter 3-Key terms Measures of Q uantiles Relative Quartiles Position Deciles Percentiles Residuals Standardized values @2002 The Wadsworth Group
Chapter 3 - Key Terms • Measures of Relative Position • Quantiles – Quartiles – Deciles – Percentiles • Residuals • Standardized values © 2002 The Wadsworth Group
l Chapter 3-Key terms Measures of Coefficient of correlation, r Association Direction of the relationship direct(r>0 or inverse(r<O Strength of the relationship When r is close to 1 or-1, the linear relationship between x and y is strong. When r is close to 0, the e linear relationship between x and y is weak When r=0, there is no linear relationship between x and y Coefficient of determination r2 The percent of total variation in y that is explained by variation in x @2002 The Wadsworth Group
Chapter 3 - Key Terms • Measures of Association • Coefficient of correlation, r – Direction of the relationship: direct (r > 0) or inverse (r < 0) – Strength of the relationship: When r is close to 1 or –1, the linear relationship between x and y is strong. When r is close to 0, the linear relationship between x and y is weak. When r = 0, there is no linear relationship between x and y. • Coefficient of determination, r 2 – The percent of total variation in y that is explained by variation in x. © 2002 The Wadsworth Group
l The Center. Mean Mean Arithmetic average=(sum all values)/# of values Population:=(Σx)/N >>Sample X =(Σx)/n Be sure you know how to get the value easily from your calculator and computer softwares Problem: Calculate the average number of truck shipments from the united States to five Canadian cities for the following data given in thousands of bags Montreal, 64.0: Ottawa, 15.0: Toronto, 285.0 Vancouver, 228.0; Winnipeg, 45.0 (Ans:1274 o 2002 The Wadsworth Group
The Center: Mean • Mean – Arithmetic average = (sum all values)/# of values »Population: µ= (Sxi )/N »Sample: = (Sxi )/n Be sure you know how to get the value easily from your calculator and computer softwares. Problem: Calculate the average number of truck shipments from the United States to five Canadian cities for the following data given in thousands of bags: Montreal, 64.0; Ottawa, 15.0; Toronto, 285.0; Vancouver, 228.0; Winnipeg, 45.0 (Ans: 127.4) x © 2002 The Wadsworth Group
l The Center: Weighted Mean When what you have is grouped data compute the mean using u= 2w;xi/Ew Problem: Calculate the average profit from truck shipments, United States to Canada, for the following data given in thousands of bags and profits per thousand bags Montreal 64.0 Ottawa 15.0 Toronto 285.0 $15,00$13,50 $15.50 Vancouver 228.0 Winnipeg 45.0 1200 100 (Ans: $14.04 per thous. bags o 2002 The Wadsworth Group
The Center: Weighted Mean • When what you have is grouped data, compute the mean using µ= (Swixi )/Swi Problem: Calculate the average profit from truck shipments, United States to Canada, for the following data given in thousands of bags and profits per thousand bags: Montreal 64.0 Ottawa 15.0 Toronto 285.0 $15.00 $13.50 $15.50 Vancouver 228.0 Winnipeg 45.0 $12.00 $14.00 (Ans: $14.04 per thous. bags) © 2002 The Wadsworth Group
l The Center: median To find the median: 1. Put the data in an array 2A. If the data set has an Odd number of numbers the median is the middle value median is the average of the middle two values o 2B. If the data set has an even number of numbers the (Note that the median of an even set of data values is not necessarily a member of the set of values.) The median is particularly useful if there are outliers in the data set which otherwise tend to sway the value of an arithmetic mean. o 2002 The Wadsworth Group
The Center: Median • To find the median: 1. Put the data in an array. 2A. If the data set has an ODD number of numbers, the median is the middle value. 2B. If the data set has an EVEN number of numbers, the median is the AVERAGE of the middle two values. (Note that the median of an even set of data values is not necessarily a member of the set of values.) • The median is particularly useful if there are outliers in the data set, which otherwise tend to sway the value of an arithmetic mean. © 2002 The Wadsworth Group
lI The Center: Mode The mode is the most frequent value While there is just one value for the mean and one value for the median there may be more than one value for the mode of a data set The mode tends to be less frequentl used than the mean or the median o 2002 The Wadsworth Group
The Center: Mode • The mode is the most frequent value. • While there is just one value for the mean and one value for the median, there may be more than one value for the mode of a data set. • The mode tends to be less frequently used than the mean or the median. © 2002 The Wadsworth Group