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...data Chapter 3: Histograms – Looking at the Distribution of Data • Histogram: a picture that gives you a visual impression of many of the basic properties of the data set as a whole o Answers – what values are typical in this data set, how different are the numbers from one another, are the data values strongly concentrated near some typical value, what is the pattern of the concentration (do data values trail off at the same rate at lower values as they do at higher values), are there any special data values that might require special treatment, and do you have single/ homogeneous collection or are there distinct groupings within the data that might require separate analysis o Many standard methods of statistical analysis require that the data be approximately normally distributed 3.1 – A List of Data • List of Numbers: the simplest kind of data set, representing some kind of information (a single statistical variable) measured on each item of interest (each elementary unit) • Number Line: a straight line with the scale indicated by numbers o In order to visualize the relative magnitudes of a list of numbers o The numbers need to be regularly spaced on a number line so that there is no distortion 3.2 – Using a Histogram to Display the Frequencies • Histogram: displays the frequencies as a bar chart rising above the number line, indicated how......

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...Measurement, Instrumentation, Statistics and Error Group 1A Lab Performed: 9-5-2012 Report Submitted: 10-11-2012 Table of Contents: I. Motive…………………………………………………………….…………….iii II. Experimental…………………………………………………………………..iv III. Results/Discussion ………………….………………….…………..…….v-viii Part 1 Data…………………………………………..………………………….......v Part 1 Histogram……………………………………...……………………………vi Part 1 Calculations…………………………………...………………………….v-vi Part 2 Data summary……………………………………..…………………….…vii Part 2 Calculations……………………………………….………………………viii IV. Conclusion…………………………………………………………………….ix V. Appendix…………………….……………………………………………...x-xii I. Motive: The purpose of this lab is to analyze the error and deviation of manmade and manufactured objects. Measuring the marbles 100 times gives a population. The block’s dimensions (length, width, height) were measured 20 times each. This gives a sample for each dimension. From the population and samples, a histogram can be made of the data. Additionally, from these mean, mode, median, and standard deviation can be calculated. Lastly, the error and error propagation must be included because there is human and instrumental error. II. Experimental: This lab had two parts. For the first part, 100 glass spheres were measured. The A spheres were used. In the second part, the dimensions of block #15......

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...Provide all histograms you are asked to print, but DO NOT print data you are asked to generate. 1. Continuous distributions: Generate and store in column c1 10,000 values from the uniform distribution on the interval [3,7] as follows: random 10000 c1; uniform 3 7. [3] a. Use mean command to ﬁnd the sample mean x of these data———————– ¯ [2] b. What is the mean µ of the uniform distribution on the interval [3,7]?————[1] c. Compare µ to the value x you found in part a). ———————– ¯ Generate and store in column c2 1,000 values from exponential distribution with parameter λ = .125 as follows: random 1000 c2; exponential 8. Note: The mean µ and the standard deviation σ of such distribution are both equal to 1/λ = 8 and this is the value you are asked to enter in the command above. [3] d. Use desc command to ﬁnd the sample mean x and sample standard deviation s for ¯ these 1,000 data —————– and —————— Are x and s close to the value 1/λ = 8?———————– Why?——————————¯ [3] e. Print (and include in your assignment) the histogram of the 1,000 values you generated from this exponential distribution. What is the shape of this distribution?———————– 2. Normal distribution: Generate and store in column c3 10,000 values from the standard normal distribution as follows: random 10000 c3; normal. [3] a. Print (and include in your assignment) the histogram for these data. What is the shape of this histogram?———————————– [3] b. What is the value on the horizontal axis around which the histogram seems......

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...LAB 1 –Mohammed Abdo 1.Analyze and discuss the results shown in the Statistics table (including definitions of the following statistical measures: Mean, Std. Error of Mean, Median, Mode, Std. Deviation, Variance, Skewness, Std. Error of Skewness, Kurtosis, Std. Error of Kurtosis, Range, Percentiles) (15%) Statistics | | Variable 1Life expectancy at birth (years), 2006 | Variable 2 Adult literacy rate (% aged 15 and above), 2006 | Variable 2 Combined gross enrolment ratio in education (%), 2006 | Variable 4GDP per capita (PPP US$), 2006 | N | Valid | 179 | 172 | 179 | 179 | | Missing | 1 | 8 | 1 | 1 | Mean | 67.7291 | 83.8767 | 71.5654 | 12258.81 | Std. Error of Mean | .80424 | 1.44937 | 1.33369 | 1066.857 | Median | 71.3000 | 91.2000 | 73.5000 | 6679.00 | Mode | 71.30a | 99.90 | 59.60a | 630a | Std. Deviation | 10.76001 | 19.00828 | 17.84362 | 14273.577 | Variance | 115.778 | 361.315 | 318.395 | 203735005.245 | Skewness | -.901 | -1.378 | -.470 | 1.811 | Std. Error of Skewness | .182 | .185 | .182 | .182 | Kurtosis | -.168 | 1.156 | -.040 | 3.633 | Std. Error of Kurtosis | .361 | .368 | .361 | .361 | Range | 42.20 | 77.10 | 88.70 | 76808 | Minimum | 40.20 | 22.90 | 25.50 | 281 | Maximum | 82.40 | 100.00 | 114.20 | 77089 | Percentiles | 10 | 50.1000 | 54.3300 | 45.1000 | 888.00 | | 20 | 57.8000 | 69.6200 | 57.3000 | 1592.00 | | 25 | 62.0000 | 73.7500 | 60.8000 | 1965.00 | | 30 | 64.5000 | 80.0500 | 63.2000 | 2489.00 | | 40 |......

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...Discuss your 1st variable, using graphical, numerical summary and interpretation Numerical Summary of Credit Balance are as follows: Mean: 3970.5 Minimum: 1864 Standard Deviation: 931.9 Q1: 3109.3 Variance: 868429.8 Median: 4090 Skew: -0.15043 Q3: 4747.5 N: 50 Max: 5678 The histogram above shows the Credit Balance variable of the 50 customers surveyed. The histogram is almost symmetrical with one outlier which is the credit balance of $2,000. While it being symmetrical you can almost fold the y-axis in half to have it look the same. While observing the histogram, its skewed to the left because of the outlier, and the skew is -.015043. Using the Anderson-Darling Normality Test, the P-value for Credit Balance is 0.400, and A^2 is 0.38. Throughout the mean, median, and Standard Deviation there is a 95% confidence interval as well. Discuss your 2nd variable, using graphical, numerical summary and interpretation Numerical Summary of Size are as follows: Mean: 3.4200 Minimum: 1.000 Standard Deviation: 1.7390 Q1: 2.0000 Variance: 3.0241 Median: 3.0000 Skew: 0.527896 Q3: 5.0000 N: 50 Max: 7.0000 The histogram above shows the Size variable of the 50 customers surveyed. The graph is not symmetrical compared to the Credit Balance (shown above), this graph is also skewed to the right. This graph also shows that 15 people......

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...in-depth statistical analysis. The objective of performing data analysis on a population of professor salaries at one college will be to learn any salary discrepancies between the males and females. The following statistical analyses will be performed: * Compare the proportion of males to females in the population * Compare the mean and median salaries for males and females * Compare the distribution of salaries for males and females * Determine if equitable salaries between males and females, and * Determine if there is an association between years of service and salary level for the population, males, and females. We will use basic statistical methods to perform the above analyses, which include frequency tables, histograms, boxplots, and scatterplots. We first calculated the proportion of males to females in the population and created a frequency table to display the results. For this calculation we are only using one categorical variable: gender. The proportion of males in the population can be found using the equation: p̂ = number of malestotal number = 237255 = 0.93, and the proportion of females in the population can be found using the same equation: p̂ = number of femalestotal number = 18255 = 0.07. The proportions can then be input into a frequency table: Gender - Frequency Table | Response | Relative Frequency | Male | 0.93 | Female | 0.07 | Total | 1.00 | The proportion of males in the population is a substantial......

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...problems of annual returns on investment of three stocks. Characterize the key features of the returns on investment on each stock. After use the data analysis tool of excel, we can get the following solutions. We can see that stock2 has a largest mean, standard deviation and sample variance. It means that stock has a much more higher expected value than the other two stocks. However, the standard deviation and sample variance reveal the risk level of losing money in stock market. Stock2 has a higher expected value with a higher level of risk. Then, in order to visually understand the feature of return on investment for each stock, we will build some histograms relatively. Then we can use Excel to construct the histograms as follow: Excel automatically generates 10 bins for the histograms which is calculate by the range of each stocks /10. This histogram has two peaks – -0.27607 and 0.100033 whose relative frequency are both 15. That means if we invest in stock 1, the most possible outcome of expected return would be -0.27607 or 0.100033. This histogram which has only one peak 0.40169 whose relative frequency is 23. It seems that the most possible expected return from investing in stock 2 would be 0.401089. This histogram has only one peak –0.01111 whose relative frequency is 23. It seems that the most possible expected return from investing in stock 3 would be -0.01111. As in a whole, stock 2 has a higher frequency and positive expected value in investing, it may be......

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...If the data are continuous, then a grouped frequency distribution is used. • Typically, a distribution is portrayed using a frequency polygon or a histogram. Mathematical distributions are often used to define distributions. The normal distribution is, perhaps, the best known example. Many empirical distributions are approximated well by mathematical distributions such as the normal distribution. Graphical presentation of Frequency distribution • Histogram: A histogram is a graphical display of tabulated frequencies. A histogram is the graphical version of a table that shows what proportion of cases fall into each of several or many specified categories. Advantages • Visually strong • Can compare to normal curve • Usually vertical axis is a frequency count of items falling into each category Disadvantages • Cannot read exact values because data is grouped into categories • More difficult to compare two data sets • Use only with continuous data Frequency Polygons Frequency Polygons: • Frequency polygons are a graphical device for understanding the shapes of distributions. They serve the same purpose as histograms, but are especially helpful in comparing sets of data. Frequency polygons are also a good choice for displaying cumulative frequency distributions. • To create a frequency polygon, start just as for histograms, by choosing a class interval. Then draw an X-axis representing the values of the scores in your data. Mark the middle of each class interval with......

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...investment of three stocks. Characterize the key features of the returns on investment on each stock. After use the data analysis tool of excel, we can get the following solutions. We can see that stock2 has a largest mean, standard deviation and sample variance. It means that stock has a much more higher expected value than the other two stocks. However, the standard deviation and sample variance reveal the risk level of losing money in stock market. Stock2 has a higher expected value with a higher level of risk. Then, in order to visually understand the feature of return on investment for each stock, we will build some histograms relatively. Then we can use Excel to construct the histograms as follow: Excel automatically generates 10 bins for the histograms which is calculate by the range of each stocks /10. This histogram has two peaks – -0.27607 and 0.100033 whose relative frequency are both 15. That means if we invest in stock 1, the most possible outcome of expected return would be -0.27607 or 0.100033. This histogram which has only one peak 0.40169 whose relative frequency is 23. It seems that the most possible expected return from investing in stock 2 would be 0.401089. This histogram has only one peak –0.01111 whose relative frequency is 23. It seems that the most possible expected return from investing in stock 3 would be -0.01111. As in a whole, stock 2 has a higher frequency and positive expected value in investing,......

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...Group Project: Coca Cola CocaProProposal Group Project: Coca Cola CocaProProposal Megan Bond (Team Lead) Taryn Keenan Allysa Kiedpool Krista Samples Nicole Smith July 12, 2014 BA 615 Dr. Mohammad Oskoorouchi Megan Bond (Team Lead) Taryn Keenan Allysa Kiedpool Krista Samples Nicole Smith July 12, 2014 BA 615 Dr. Mohammad Oskoorouchi Contents Executive Summary………………………………………………………………………………………………3 Analysis & Approach…………………………………………………………………………………………….4 Pie Charts……………………………………………………………………………………………………4 Line Charts……………………………………………………....……………………………………..…5 Descriptive Statistics and Variation…………………………………….………………………8 Histograms…………………………………..…………………………………….……………….……10 Confidence Intervals…………………………………..……………………………………….……13 Hypotheses and Hypothesis Test…………….……………………..………………………..15 Scatter Plots and Correlation……………….……………………………………………….....18 Conclusion……………………………………………………………………………………………….…………22 Recommendations…………….…………………………………………………………………….…………22 Executive Summary As a company, Coca Cola always strives to keep their customers happy. The corporate goal is to deliver all customer orders with 100% accuracy and within the customer’s time window. A metric the company has developed to measure this is On Time and In Full (OTIF), which illustrates the percentage of the orders sent out on a particular day that were within the customer’s time window and with 100% of the cases the......

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...Variability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.4 Linear Transformations . . . . . . . . . . . . . . . . . . . . . . . 5 1.5 Position . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.6 Dispersion Percentages . . . . . . . . . . . . . . . . . . . . . . . . 7 2 Graphs and Displays 2.1 9 Histograms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.1.2 Medians, Modes, and Means Revisited . . . . . . . . . . . 10 2.1.3 z-Scores and Percentile Ranks Revisited . . . . . . . . . . 11 2.2 Stem and Leaf Displays . . . . . . . . . . . . . . . . . . . . . . . 11 2.3 Five Number Summaries and Box and Whisker Displays . . . . . 12 3 Probability 13 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3.2 Random Variables . . . . . . . . . . . . . . . . . . . . . . . . . . 16 3.2.1 Deﬁnition . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 3.2.2 Expected Value . . . . . . . . . . . . . . . . . . . . . . . . 17 3.2.3 Variance and Standard Deviation . . . . . . . . . . . . . . 17 3.2.4 “Shortcuts” for Binomial Random Variables . . . . . . . . 18 1 4 Probability Distributions 19 4.1 Binomial Distributions . . . . . . . . . . . . . . . . . . . . . . . . 19 4.2 Poisson Distributions . . . . . . . . . . . . . . . . . . . . . . . . . 21 4.2.1 Deﬁnition . . . . . . . . . .......

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...numbers large (shown above). B. 1,2,3 Using excel and the methods STDEV(), AVERAGE(), MODE(), and MEDIAN() so that the standard deviation, mean/average, mode and median are calculated. Examples of these are shown below for unsuccessful applicants the process is the same for successful applicant using the other data set. To find the mean using the AVERAGE method, Excel finds the sum of all the numbers selected and divides them by the number of data points, in this case 50. Example Mean: n=1n=50Xn=2184 Where Xn=Unsuccessful applicant Mean=218450=43.68 For the MODE() method, Excel looks over all the data that is selected and finds the value that occurs the most often. In the case of unsuccessful applicants, the age of 44 occurred 6 times, which was more times than any other number. To find the median using the MEDIAN() method, Excel arranges all the ages into numerical order and finds the age that is in the center of the data. In the case of unsuccessful applicants, the median was the age of 44. Example of Standard deviation: To calculate the standard deviation, the method STDEV() method was used. This method uses a formula (shown below) and plugs in every age to calculate the standard deviation. s= 1N-1n=1n=50(xn-x)2 Where N=size of sample=50 xn=Unsucessful appicant x=mean unsucessful applicant=43.68 The standard deviation for unsuccessful applicants is 7.7 To calculate range, the difference between the maximum and the minimum is found. Example......

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...table creat pivot table colum 1-3 session 2 bar chart=column chart histogram :can be symmetrical normal distribution positively right skewed page 46, table 3.1 determining the class width largest observation-smallest observation number of rows ---classes bins are the upper class limits xo2-o4 long distance .. DATA –DALA ANALYSIS—HISTOGRAM OGIVE CUMULATIVE FREQUENCY CATEGORIZE DATA stem&leaf display chapter 4 measure of central location mean arithmetic mean symbol for the mean---MU mean for ungrouped data median: the value of the middle term in a data set that has been ranked in increasing order mode: most frequently occurring value in your data relationship between mean, median, mode histogram is symmetric when mean=median=mode histogram is skewed to right when mean is to the right of median histogram is skewed to left when mean is to the left of median chapter4 section 2 measures of dispersion dispersion ,spread variation or variability all mean the same thing there are no measures of variability in normal data simplest measure of dispersion range=largest value-smallest value the range ,like the mean, can be influenced by outliers average difference from the mean squared units variance=20 feet2 sumbpl used for the variance population: variance SIGMA squared sample: variance s 2 measures of dispersion: standard deviation how closely the values of a data set are clustered around the......

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...data and charts. Descriptive Statistics The research topic for this paper is “McDonald’s is Closing Hundreds of Stores.” As part of the research a sample size of 400 was selected to ensure accuracy of results based on the population size of 410. The given sample size was randomly surveyed to test the variables – Independent Variable - Change in consumer food preference and competitive market place and Dependent Variable – Reduced sales hence reduced profit. Age Three Hundred and Eighty-Five McDonald’s consumers were randomly selected and their ages measured. The age ranges were 15 and 65 years. Average consumer is aged 31 with a standard deviation of 14 years. Approximately half or more of their ages are above 31. Income The income of the randomly surveyed consumers is averaged at $30.82 and with a standard deviation of $14.04. Income range is $15 to $65 and there is enough evidence that half or more of these consumers averages $30.82 per year. Strengths and Weaknesses of Team Members’ Individual Assignments Efforts were made by each team member to better understand the use of the statistical tool made available to us (MegaStat). More knowledge was gained and applied in the interpretation of data and findings on this paper. Additionally, each team member pulled their weight in the interpretation and findings in the completion of their individual assignments. The team however had some differences with the interpretation and findings. This was brought......

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...Estimating the standard deviation of grouped data The Internal Revenue Service (IRS) determines which income tax returns to audit by looking at, among other things, whether there are any unusual deductions claimed on the return. Last year, charitable deductions for a family of four earning between and averaged , with a standard deviation of . The IRS wishes to know whether the standard deviation this year is still around . To determine this, income tax returns for families of four earning between and were randomly selected from this year's tax filings. The charitable deductions claimed on the returns are summarized in the following histogram: 20 15 10 5 0 Frequency 4 16 12 4 4 900 1000 1100 1200 1300 1400 Charitable deduction (in dollars) Based on this histogram, estimate the standard deviation of the sample of deduction amounts. Carry your intermediate computations to at least four decimal places, and round your answer to at least one decimal place. (If necessary, consult a list of formulas.) The process for solving these problems is fairly long. Aleks recommends: . Then . I watched a video that condenses the process a bit. Its easier to group the sections included in this process into 4 rows and 4 columns. The first column should list the frequencies in the histogram. Next list the midpoints in the 2nd column. Then multiply the two columns by one another which produces column 3. Next......

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