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Practical Statistics Descriptive Statistics There are six statistics that will answer 90% of all questions! There six are: 1. Descriptive There six are: 1. Descriptive 2. Chi-square There six are: 1. Descriptive 2. Chi-square 3. Z-tests There six are: 1. 2. 3. 4. Descriptive Chi-square Z-tests t-tests There six are: 5. Correlation (association) There six are: 5. Correlation 6. Regression Descriptive Statistics These are utilized to describe the characteristic of a population (parameter), or the characteristics of a sample (a statistic) Many business problems can be solved by knowing only descriptive statistics. Geodemography http://www.youtube.com/watch?v=7UCxzYpXhpI Geodemography Geodemography 2012 Map http://www.geocurrents.info/2012/11#!gallery/6/ Descriptive Statistics Simple counts: frequency Descriptive Statistics Simple counts: frequency The amount of time (in seconds) needed for assembly-line workers to complete a weld was recorded for 40 workers. 69 60 75 74 68 66 73 76 63 67 69 73 65 61 73 72 72 65 69 70 64 61 74 76 72 74 65 63 69 73 75 70 60 62 68 74 71 73 68 67 a. What is the frequency for each amount of time? Descriptive Statistics Simple counts: histograms 5 Frequency 4 3 2 1 Mean =68.975 Std. Dev. =4.76896 N =40 0 60.00 65.00 70.00 VAR00001 75.00 On SPSS: Open the file called WeldDat.sav Do the following: Graphs Graphboard Template… Select WeldTime Select histogram with Normal… OK Descriptive Statistics Simple counts: histograms 5 Frequency 4 3 2 1 Mean =68.975 Std. Dev. =4.76896 N =40 0 60.00 65.00 70.00 VAR00001 75.00 Descriptive Statistics Simple counts: ogive 100.0% Cumulative Percent 80.0% 60.0% 40.0% 20.0% 0.0% 60.00 65.00 70.00 VAR00001 75.00 80.00 Descriptive Statistics Simple counts: ogive http://mathworld.wolfram.com/Ogive.html Symmetry Right Left Descriptive Statistics Back to the workers making welds….. The amount of time (in seconds) needed for assembly-line workers to complete a weld was recorded for 40 workers. 69 60 75 74 68 66 73 76 63 67 69 73 65 61 73 72 72 65 69 70 64 61 74 76 72 74 65 63 69 73 75 70 60 62 68 74 71 73 68 67 Descriptive Statistics Central tendency: A single number to represent a group. Statistics Time N Mean Std. Error of Mean Median Mode Std. Deviation Skewness Std. Error of Skewness Kurtos is Std. Error of Kurtosis Sum Valid Missing 40 0 68.9750 .75404 69.0000 73.00 4.76896 -.379 .374 -.985 .733 2759.00 Descriptive Statistics The average is 68.98. The standard deviation is 4.77. The amount of time (in seconds) needed for assembly-line workers to complete a weld was recorded for 40 workers. 69 60 75 74 68 66 73 76 63 67 69 73 65 61 73 72 72 65 69 70 64 61 74 76 72 74 65 63 69 73 75 70 60 62 68 74 71 73 68 67 Descriptive Statistics Central tendency: 1. Mode The most frequent score. Descriptive Statistics Central tendency: 1. Mode 2. Median Half the numbers are larger, half are smaller. Descriptive Statistics Central tendency: 1. Mode 2. Median 3. Mean The center of gravity of a distribution Descriptive Statistics Central tendency: 1. Mode 2. Median 3. Mean Arithmetic Harmonic Geometric Descriptive Statistics Central tendency: 1. Mode 2. Median 3. Mean Arithmetic n x x i 1 n i Descriptive Statistics Central tendency: 3. Mean Harmonic Clayson Power Data 180 160 140 120 100 80 60 40 20 0 1/6/00 1/2/02 1/10/03 1/6/05 1/2/07 1/10/08 1/6/10 1/2/12 1/10/13 1/6/15 Legend Temp KWH Cost Descriptive Statistics Central tendency: 3. Mean Harmonic Clayson Power Data 80 70 60 50 40 30 20 10 0 1/6/00 1/2/02 1/10/03 1/6/05 1/2/07 1/10/08 1/6/10 1/2/12 1/10/13 1/6/15 Legend Temp Descriptive Statistics Central tendency: 3. Mean Harmonic Clayson Power Data 80 70 60 Legend Temp Linear Trend 50 40 30 20 10 0 1/5/00 1/1/02 1/9/03 1/5/05 1/1/07 1/9/08 1/5/10 1/1/12 1/9/13 1/5/15 Descriptive Statistics Central tendency: 1. Mode 2. Median 3. Mean Harmonic n 1 1 1 H n i 1 xi Descriptive Statistics Central tendency: 1. Mode 2. Median 3. Mean Geometrical (For pure ratio numbers) G x n i 1 i 1 n Geometric Mean: Does pricing following perception or volume? If a package holds twice as much should it be priced as twice that of a package that holds half as much? Problem: Customers do not perceive volume correctly. Geometric Mean: Does pricing following perception or volume? The perception of volume follows: Seven’s Law: kS How should this be done? p Descriptive Statistics Measure of Variation: Again a single number to represent a group. Statistics Time N Std. Error of Mean Std. Deviation Variance Skewness Std. Error of Skewness Kurtos is Std. Error of Kurtosis Range Minimum Maximum Valid Missing 40 0 .75404 4.76896 22.743 -.379 .374 -.985 .733 16.00 60.00 76.00 Descriptive Statistics Measure of Variation: 1. Range a. (Highest – Lowest) + 1 b. Subject to deviancy Descriptive Statistics Measure of Variation: 1. Range 2. Mean Deviation a. Problem: Variation logically would be the average deviation around a measure of central tendency. x x / n i Descriptive Statistics Measure of Variation: 1. Range 2. Mean Deviation a. Problem: But… x x 0 i Always!! Descriptive Statistics Measure of Variation: 1. Range 2. Mean Deviation a. Problem: So negative can be removed by looking at the absolute value. Abs( xi x ) / n Descriptive Statistics Measure of Variation: 1. Range 2. Mean Deviation a. Problem: Negative can be removed by squaring the value. x i x / n 2 Descriptive Statistics Measure of Variation: 1. Range 2. Mean Deviation a. Problem: This is the definition of: 3. Variance x i x / (n 1) 2 Descriptive Statistics Measure of Variation: 1. Range 2. Mean Deviation 3. Variance a. Problem: This is difficult to work with descriptively, so the square root can be taken. x x n Sx i 1 i n 1 2 Descriptive Statistics Measure of Variation: 1. Range 2. Mean Deviation 3. Variance a. This is called the: 4. Standard Deviation x x n Sx i 1 i n 1 2 The standard deviation is: Roughly the average difference scores are from the average. Or: It is roughly the average difference between two measures taken from the same population. It is an intuitive measure. The amount of time (in seconds) needed for assembly-line workers to complete a weld was recorded for 40 workers. 69 60 75 74 68 66 73 76 63 67 69 73 65 61 73 72 72 65 69 70 64 61 74 76 72 74 65 63 69 73 75 70 60 62 68 74 71 73 68 67 a. Give the central tendency measures of this sample. b. What is the range, variance and standard deviation? c. Explain what you now know about the time it takes to make welds. d. When should a worker be reprimanded or fired for working too slow? a. Give the central tendency measures of this sample. Statistics Time N Mean Std. Error of Mean Median Mode Std. Deviation Variance Skewness Std. Error of Skewness Kurtos is Std. Error of Kurtosis Range Minimum Maximum Valid Missing 40 0 68.9750 .75404 69.0000 73.00 4.76896 22.743 -.379 .374 -.985 .733 16.00 60.00 76.00 a. Give the central tendency measures of this sample. b. What is the range, variance and standard deviation? Statistics Time N Mean Std. Error of Mean Median Mode Std. Deviation Variance Skewness Std. Error of Skewness Kurtos is Std. Error of Kurtosis Range Minimum Maximum Valid Missing 40 0 68.9750 .75404 69.0000 73.00 4.76896 22.743 -.379 .374 -.985 .733 16.00 60.00 76.00 a. Give the central tendency measures of this sample. b. What is the range, variance and standard deviation? c. Explain what you now know about the time it takes to make welds. Statistics Time N Mean Std. Error of Mean Median Mode Std. Deviation Variance Skewness Std. Error of Skewness Kurtos is Std. Error of Kurtosis Range Minimum Maximum Valid Missing 40 0 68.9750 .75404 69.0000 73.00 4.76896 22.743 -.379 .374 -.985 .733 16.00 60.00 76.00 a. b. c. d. Give the central tendency measures of this sample. What is the range, variance and standard deviation? Explain what you now know about the time it takes to make welds. When should a worker be reprimanded or fired for working too slow? Statistics Time N Mean Std. Error of Mean Median Mode Std. Deviation Variance Skewness Std. Error of Skewness Kurtos is Std. Error of Kurtosis Range Minimum Maximum Valid Missing 40 0 68.9750 .75404 69.0000 73.00 4.76896 22.743 -.379 .374 -.985 .733 16.00 60.00 76.00