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 TOPICS This page:   statistics    Search   Dr. Math See also the Internet Library:   statistics COLLEGE Algorithms Analysis Algebra    linear algebra    modern algebra Calculus Definitions Discrete Math Exponents Geometry    Euclidean/plane      conic sections/        circles      constructions      coordinate plane      triangles/polygons    higher-dimensional      polyhedra    non-Euclidean Imaginary/Complex   Numbers Logic/Set Theory Number Theory Physics Probability Statistics Trigonometry Browse College Statistics Stars indicate particularly interesting answers or good places to begin browsing. Line of Best Fit For Points in Three Dimensional Space [11/22/2005] How can I find the line that most closely fits a set of points in 3D space, like the least squares line does in two dimensions? Maximum Value of Binomial Random Variables [09/12/2001] For a binomial random variable X with parameters (n,p), show that P{X= i} first increases and then decreases, reaching its maximum value when i is the largest integer less than or equal to (n+1)p. Mean and Standard Deviation [03/01/1999] Prove that the mean (u) and standard deviation (s) for a binomial distribution are np and the square root of (npq). Mean and Variance of Distributions [12/07/2000] How can I derive the expected value (mean) and variance for an exponential with parameter 1/k, and a hypergeometic distribution? Mean and Variance of the T & F Distributions [02/16/2007] In my statistics class we learned formulas for the means and variances of the T and F distributions. I've been trying to derive the formulas but have not been able to do so. Can you help me get started? Mean-Variance Ratio of the Poisson Distribution [03/27/2001] How can I show that V(X)/E(X) = 1 for the Poisson distribution? Measures of Dispersion [6/30/1996] What are the different characteristics of: Range, Mean Absolute Deviation, Standard Deviation, Variance, Quantiles (percentile, decile, quartiles), covariance? Minimum Sample Size for Confidence Interval [09/21/2000] Given a population of 400 people, what is the minimum sample size necessary for a 90% level of confidence with a maximum of 10% margin of error? Modal Class of a Histogram with Unequal Class Widths [07/12/2007] Why is the modal class of a histogram with unequal class widths the bar with the highest frequency density? I have always been taught that the modal class is the one with the highest frequency from a histogram or frequency table. What role does the density play? Moment-generating Function of Poisson Distribution [10/25/1999] What statistical information (mean, variance, etc.) can I get from the moment-generating function of Poisson distribution? How can I derive the expectation? Noisy Data Known to Estimate a Function [05/15/2003] How do we find the maximum value of a function with a high level of noise? Normal Distribution and the Lottery [6/20/1995] I wrote a Visual Basic program to generate "Pick 6" lottery numbers, producing six random numbers from 1 to 46... the result being a somewhat normal distribution, but I can't understand why. Ogive, More or Less [09/05/2014] A student stumbles over the boundaries of the cumulative distribution function. Doctor Peterson clarifies ogive, starting with its definition. Origin of Ogive [08/26/2002] What is the origin of the term 'ogive'? Orthogonal Distance Regression Line [07/05/2005] How can I calculate the standard deviation of the error in the independent and dependent variables when I want to fit a straight line with both variables subject to error? Orthogonal Distance Regression Planes [07/30/2003] I have a set of data points that I have collected from an experiment. I want to fit a 3D plane (best-fit) into these points (the points are in the form (x1,y1,z1), (x2,y2,z2),...) in order to evaluate my results. Outliers in a Box-And-Whisker Plot [12/07/2000] Would a point that is exactly 1.5 times the IQR away from the inner or outer quartiles be considered an outlier? Poisson as a Limit to a Binomial Distribution [05/29/2000] How do I prove that the limit of a binomial distribution with large n and small p is a Poisson distribution? Potential Limitations of ANOVA Testing [11/13/2005] Are there any drawbacks or problems with the information reported by use of the ANOVA test in statistics? Probability Density Functions [07/23/2003] My boss has given me the responsibility of taking a set of data, finding the correct distribution that goes with it, and then drawing the PDF onto the histogram chart. Probability for a Given Distribution of Objects [7/23/1996] 80 percent of light bulbs last 2400 hours, 20 percent last 2400 hours... Given a collection of screws with a Gaussian distribution of size.... The frequency of a mistake for wires is once in 25 meters... Proof of Bernoulli's Law [6/22/1996] I would like to know how one can prove Bernoulli's law of large numbers Quadratic Interpolation [03/27/2003] How do I come up with this polynomial? y = [(x - x2)(x - x3)]/[(x1 - x2)(x1 - x3)]*y1 + [(x - x1)(x - x3)]/[(x2 - x1)(x2 - x3)]*y2 + [(x - x1)(x - x2)]/ [(x3 - x1)(x3 - x2)]*y3. Range - Difference or Difference + 1? [08/05/2003] Is range the same as 'difference' or not? RMS and RSS in Error Analysis [10/28/2005] In error analsysis, sometimes an RMS equation is used and sometimes an RSS equation is used to calculate overall error given a list of contributing variables. Can you explain both concepts and the stipulation of the dependencies between the contributing variables? Standard Deviation for Variance? [01/25/2001] I would like to calculate a measure of the reliability of my data. The best would be the standard deviation of variance. Does such measure exist? Standard Deviation of Cauchy Distribution [06/12/2005] If the variance of a probability distribution for a continuous random variable with a mean of zero can be found by integrating (x-squared times f(x)) between the end bounds of distribution, and the indefinite integral is easily obtained, but leads to an infinite value when the definite integral is calculated, how do you work out the standard deviation of the Cauchy distribution? Standard Deviation of Grouped Data [10/16/2000] How do I find the standard deviation of grouped data in a frequency table? Also, how many significant digits should the mean of a data set have? Statistical Analysis - z and t Statistics [07/06/2004] Could you tell me the differences between z-statistics and t-statistics? Statistics - t-test [01/15/2002] I am comparing scores of basketball games to see if playing at home is an advantage over playing away. Testing a Set of Data for Normal Distribution [08/02/2008] I have a set of data which I have obtained through experiments, and I need a way to determine if the data is or is not normally distributed. T-Tests, P-Values, and Statistical Significance [03/18/2004] I am doing a lab report comparing two different samples of fish. For the results the teacher wants a t test. What does the t value and two-tailed p value tell me and how do they compare to each other? Is this information 'significant' enough to say that variable 2 came from the same family as variable 1? Two Random Variables, Each Correlated to a Third [04/29/2003] If X, Y, and Z are 3 random variables such that X and Y are 90% correlated, and Y and Z are 80% correlated, what is the minimum correlation that X and Z can have? Using Matrix Equations to Find Regression Polynomials [06/27/2006] Is there a formula for determining the coefficients of a cubic regression given a set of data points to fit? Using Z-Scores to Calculate Probability [05/25/2008] Train cars are loaded with ore. The distribution of ore into the cars is normally distributed with a mean of 70 tons per car and a standard deviation of 0.9 tons. What is the probability that the weight of ore in a randomly selected car will be 70.7 tons or more? Variance and Expected Value [09/12/2004] How can you prove that the variance is equal to the expected value of the square of the random variable minus the mean squared? Variance of T-Student Distribution with Density Function [02/18/2005] I need help in deriving the variance (n/(n-2)) (n: degrees of freedom) of the T-Student Distribution. The most difficult thing is how to apply the VAR to a ratio of a normally distributed variable divided by a Chi-Square. Why Do We Calculate Standard Deviation the Way We Do? [02/05/2004] Why do we square the deviations and then take the square root when calculating standard deviation? Why can't we just take the absolute value of the deviations? Why Is the Least Squares Line the Best Choice? [11/03/2005] When looking for a prediction line for the relationship between two variables, one method is to find the least-squares line. What about the least squares line makes it the best fit for the data? Witch of Agnesi Curve [09/25/2003] Do you know of any everyday uses for the witch of Agnesi curve? Page: []

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