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Calculating Breast Cancer Survival Rates [06/30/2003]
Survival of a group of breast cancer patients is 100 at year 0, 100*X at year 1, 100*X*X at year 2, 100*X*X*X at year three and so on to year 10. How do I find the nth year survival?

Analyzing Survey Results [05/04/2000]
How can I determine a ranking of priority (1st, 2nd, 3rd, etc.) for the results of a satisfaction survey that asked people to rank, in order of importance, seven factors?

Applications of Arithmetic, Geometric, Harmonic, and Quadratic Means [11/22/2006]
How do I choose what sort of mean to calculate for a given set of data?

Are Two Formulas for Finding Standard Deviation the Same? [10/29/2007]
My statistics text gives a shortcut formula for calculating sample SD as the square root of [(the sum of x^2) minus (the sum of x)^2/n all divided by n-1]. Is this really just another form of the full formula?

Bayesians and Frequentists [08/21/2001]
What is the difference between Bayesian and "regular" statistics?

Bell Numbers Formula [02/13/2001]
How is the formula for Bell numbers derived from the Stirling numbers formula?

Best Curve Fit [01/30/2003]
I have a series of points on a graph that form a piecewise equation that 'steps' down as x increases. I need to create an equation from these points that approximates values through the step, i.e. a natural log graph.

Best Fit for Linear Data [8/7/1995]
If you have a set of data, x1,y1....xn,yn with a known linear relationship between x & y (y = mx + c), I was taught at university that the best straight line fit MUST go through xbar,ybar (xbar average of all x values, ybar is average of all y values).

Best-fitting Line to a Number of Points [04/25/2001]
I have a number of points on a plane and want to find a line that best- fits through the points, minimizing the sum of squares of the distances of each point from the line.

Bivariate Distribution [6/7/1995]
I am looking for methods for generating bivariate distributions. Are there techniques for generating random bivariate distribution that are not normal?

Box and Whisker Plots [02/13/2000]
Can you explain how to make and use box and whisker plots?

Calculating and Interpreting Z-Scores [12/13/2005]
Please help me by providing a step-by-step process for calculating the z-score, or standard score.

Chi Squared Distribution with Over 100 Degrees of Freedom [03/21/2005]
I want to find the critical value for the chi squared distribution with 198 degrees of freedom. I can only find tables on the internet up to 100 degrees of freedom. Can you help?

Chi-Squared Test for Independence [05/24/2000]
A hospital commissioned a study to see if there was a difference between the quality of care provided by hospital-trained and tertiary- trained nurses. How can I tell if the two events are independent?

Class Intervals in Statistics [02/23/2009]
How can a class boundary be negative when all the data points are positive? Shouldn't the first interval start at 0 rather than -0.5?

Confidence Intervals [06/09/1999]
How can we find confidence limits and the number of trout in a lake for a fish tagging experiment?

Confidence Intervals [07/24/2006]
A definition of confidence intervals and discussion of how they are sometimes incorrectly interpreted.

Correlation Coefficients of Random Numbers [12/18/2000]
I have to generate random numbers that have a certain correlation coefficient.

Cosine of a Uniform Random Variable [05/31/2005]
Given a uniformly distributed random variable between [0,pi/2], I want to know the cosine of this variable. I already know the answer, and it is 2/pi. The problem is, I don't know WHY this is true.

Covariance [02/05/1997]
What does covariance represent?

Defining Quartiles [07/20/2002]
I collected some data, and used several different programs to find the quartiles, but they gave different results! What's going on?

Definition of a Rolling or Moving Average [03/05/2004]
When someone says they have calculated a "rolling average," what exactly does that mean? I cannot find the definition in any math books.

Derivation of Linear Interpolation Median Formula [09/23/2007]
Can you explain why the median formula m = L + [(N/2 F)/f]*C works? This formula is used to find the median in a group of data with class intervals.

Difference in Standard Deviation Formulas [01/31/2006]
When calculating a population standard deviation, why is (n-1) used in the denominator rather than n?

Difference of Two Proportions in Statistics [08/15/2005]
In stats class we are studying the binomial distribution and we tackled the difference of two proportions. Why is it that we assume np > 5 and n(1-p) > 5? Where does the 5 come from?

Different Formulas for Calculating Mode [09/11/2008]
My teacher gave us the mode formula Z = L1 + [(F1-F0)/(2F1-F0-F2)]*i involving modal class frequencies, but most research I've done reveals a much simpler formula. Why do we need the more complicated one? What does it tell us that the other does not?

Discrete and Normal Distribution [01/10/2001]
In the birthday problem, what if the distribution were a normal one instead of uniform - for example, trying to find the probability that any two years had the amount of rainfall?

Employee Turnover Rate [09/19/2002]
What is the formula to calculate employee turnover rate?

Estimators of Statistics Variables [11/17/1999]
Can you prove whether s^2 (variance) of a sample, sigma^2 of a sample, and the median of a sample are unbiased estimators for s^2, sigma^2, and the arithmetic mean of the population, respectively?

Example of Dependent but Uncorrelated Random Variables [01/25/2006]
One reads often that two independent random variables are always uncorrelated but that the converse is not always true. Can you provide an example of two random variables that are uncorrelated but NOT independent?

Expectation and Hypothesis Testing [08/24/1999]
Four problems related to expectation and hypothesis testing in statistics.

F Distribution: E(x) and Var(x) without Beta Distribution Transformation [07/07/2010]
A student struggles to find the expected value and the variance of the F distribution using its probability density functions. Acknowledging the messiness of the integrand, Doctor George suggests a change of variables, explains the new degrees of freedom -- then re-visits his approach, offering up another substitution that avoids the beta distribution transformation all together.

Finding Covariance and Expectation [12/02/1999]
If x is the number of 1's and y is the number of 2's that occur in n rolls of a fair die, what is the Cov(x,y)? Also, how many times would you expect to roll a fair die before all 6 faces appear at least once?

Fitting Equation to Data with Regression Techniques [04/20/2007]
I have a set of data and I'm trying to find a best-fit equation. I've used linear regression with little success, and I don't know much about how to do other non-linear regressions. Can you get me started?

General Comments on Standard Deviation [01/15/2004]
Answers to general questions about standard deviation including vocabulary, interpretation, calculation, and history.

Generating a Random Field with Normal Distribution [08/07/2005]
I am working with OpenSource GIS, and in this application I would like to generate a random field n*m matrix (within the range -x to +x) with mean as zero and standard deviation as x, as in a normal distribution.

Interpreting a Correlation [08/06/2004]
Does a correlation of 0.60 between teacher attire and student academic performance indicate that encouraging teachers to be properly attired will increase academic performance?

Interpreting Chi-Squared Test Results [10/26/2004]
The critical values for chi-squared increase as the confidence level increases. My question is why does a distribution "pass" this test if the calculated value is less than the critical value and not vice-versa?

Lagrange Interpolation [08/20/2003]
I am trying to learn Lagrange interpolation.

Least Squares Regression for Quadratic Curve Fitting [02/27/2008]
A derivation of the general formulas needed to fit a quadratic curve to a set of data points by the least-squares regression method.

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