应用统计学英文课件 Business Statistics Ch03 Numerical Descriptive Measures.ppt
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1、Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,Chap 3-1,Chapter 3 Numerical Descriptive Measures,Business Statistics: A First Course Fifth Edition,Choice is yours, part 2,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,Chap 3-3,In this chapter, you learn: To descri
2、be the properties of central tendency, variation, and shape in numerical data To calculate descriptive summary measures for a population To construct and interpret a boxplot To calculate the covariance and the coefficient of correlation,Learning Objectives,Business Statistics: A First Course, 5e 200
3、9 Prentice-Hall, Inc.,Chap 3-4,Summary Definitions,The central tendency is the extent to which all the data values group around a typical or central value. The variation is the amount of dispersion, or scattering, of values The shape is the pattern of the distribution of values from the lowest value
4、 to the highest value.,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,Chap 3-5,Measures of Central Tendency: The Mean,The arithmetic mean (often just called “mean”) is the most common measure of central tendency For a sample of size n:,Sample size,Observed values,The ith value,Pron
5、ounced x-bar,Measures of Central Tendency: The Mean,Example volume of Coke Listed below are the volumes (in ounces) of the Coke in five different cans. Find the mean for this sample. 12.3 12.1 12.2 12.3 12.2,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,Chap 3-7,Measures of Centra
6、l Tendency: The Mean,The most common measure of central tendency Mean = sum of values divided by the number of values Affected by extreme values (outliers),(continued),0 1 2 3 4 5 6 7 8 9 10,Mean = 3,0 1 2 3 4 5 6 7 8 9 10,Mean = 4,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,Cha
7、p 3-8,Measures of Central Tendency: Locating the Median,The location of the median when the values are in numerical order (smallest to largest): If the number of values is odd, the median is the middle number,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,Chap 3-9,Measures of Centr
8、al Tendency: Locating the Median,If the number of values is even, the median is the average of the two middle numbers Note that is not the value of the median, only the position of the median in the ranked data,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,Chap 3-10,Measures of Ce
9、ntral Tendency: The Median,In an ordered array, the median is the “middle” number (50% above, 50% below) Not affected by extreme values,0 1 2 3 4 5 6 7 8 9 10,Median = 3,0 1 2 3 4 5 6 7 8 9 10,Median = 3,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,Chap 3-11,Measures of Central T
10、endency: The Mode,Value that occurs most often Not affected by extreme values Used for either numerical or categorical data There may be no mode There may be several modes,0 1 2 3 4 5 6 7 8 9 10 11 12 13 14,Mode = 9,0 1 2 3 4 5 6,No Mode,Measures of Central Tendency: The Mode,Mean Mode Mode,Business
11、 Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,Chap 3-13,Measures of Central Tendency: Review Example,House Prices: $2,000,000 $500,000 $300,000 $100,000 $100,000 Sum $3,000,000,Mean: ($3,000,000/5) = $600,000 Median: middle value of ranked data = $300,000 Mode: most frequent value = $100,
12、000,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,Chap 3-14,Measures of Central Tendency: Which Measure to Choose?,The mean is generally used, unless extreme values (outliers) exist. The median is often used, since the median is not sensitive to extreme values. For example, median
13、 home prices may be reported for a region; it is less sensitive to outliers. In some situations it makes sense to report both the mean and the median.,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,Chap 3-15,Measures of Central Tendency: Summary,Central Tendency,Arithmetic Mean,Med
14、ian,Mode,Middle value in the ordered array,Most frequently observed value,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,Chap 3-16,Same center, different variation,Measures of Variation,Measures of variation give information on the spread or variability or dispersion of the data va
15、lues.,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,Chap 3-17,Measures of Variation: The Range,Simplest measure of variation Difference between the largest and the smallest values:,Range = Xlargest Xsmallest,0 1 2 3 4 5 6 7 8 9 10 11 12 13 14,Range = 13 - 1 = 12,Example:,Business
16、Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,Chap 3-18,Measures of Variation: Why The Range Can Be Misleading,Ignores the way in which data are distributed Sensitive to outliers,7 8 9 10 11 12,Range = 12 - 7 = 5,7 8 9 10 11 12,Range = 12 - 7 = 5,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,3,3
17、,3,4,5,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,4,120,Range = 5 - 1 = 4,Range = 120 - 1 = 119,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,Chap 3-19,Average (approximately) of squared deviations of values from the mean Sample variance:,Measures of Variation: The Variance,Whe
18、re,= arithmetic mean n = sample size Xi = ith value of the variable X,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,Chap 3-20,Measures of Variation: The Standard Deviation,Most commonly used measure of variation Shows variation about the mean Is the square root of the variance Has
19、 the same units as the original data Sample standard deviation:,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,Chap 3-21,Measures of Variation: The Standard Deviation,Steps for Computing Standard Deviation 1. Compute the difference between each value and the mean. 2. Square each di
20、fference. 3. Add the squared differences. 4. Divide this total by n-1 to get the sample variance. 5. Take the square root of the sample variance to get the sample standard deviation.,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,Chap 3-22,Measures of Variation: Sample Standard Dev
21、iation,Sample Data (Xi) : 10 12 14 15 17 18 18 24,n = 8 Mean = X = 16,A measure of the “average” scatter around the mean,Variance of the Getting-Ready Time,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,Chap 3-24,Measures of Variation: Comparing Standard Deviations,Mean = 15.5 S =
22、3.338,11 12 13 14 15 16 17 18 19 20 21,11 12 13 14 15 16 17 18 19 20 21,Data B,Data A,Mean = 15.5 S = 0.926,11 12 13 14 15 16 17 18 19 20 21,Mean = 15.5 S = 4.570,Data C,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,Chap 3-25,Measures of Variation: Comparing Standard Deviations,Sm
23、aller standard deviation Larger standard deviation,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,Chap 3-26,Measures of Variation: Summary Characteristics,The more the data are spread out, the greater the range, variance, and standard deviation. The more the data are concentrated,
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