







A pie chart 
20161205 

From vickie: Determine the central angle needed to form a pie chart for the following housing characteristic data: 63% owner occupied, 27% renter occupied, and 10% vacant Answered by Penny Nom. 





Brokenline graphs and histograms 
20060216 

From George:
1. What is the main difference between a brokenline graph and a histogram? Both represent continuous variables.
2. What is the correct way to read a multiplication array: xaxis first and then yaxis, other way around or it doesn't matter?
Answered by Penny Nom. 





A normal distribution problem 
20060215 

From Mary: In a certain normal distribution, find the mean when the standard deviation is 5 and 5.48% of the area lies to the left of 78. Answered by Penny Nom. 





The median 
20060127 

From Wael: " median"; what does it mean and how do we calculate it? Answered by Penny Nom. 





Coefficient of variation 
20051019 

From Jan: I am currently teaching the coefficient of variation and am wondering if there are some guidelines as to the interpretation of this statistic. I understand that it measures the variation in a variable relative to the mean  but what is the cut off for "too much" variation expressed in this way???
Answered by Andrei Volodin and Penny Nom. 





Linear regression 
20020116 

From Murray: If you have a set of coordinates (x[1],y[1]),(x[2],y[2]),...,(x[n],y[n]),find the value of m and b for which SIGMA[from 1 to m=n]AbsoluteValue(y[m]m*x[m]b) is at its absolute minimum. Answered by Harley Weston. 





Dual spaces 
20011126 

From Hoda: In the book "Linear Functional Analysis" from Epstein there is a proof (page 116) of the following theorem: The dual space of L^{p} is equal to L^{q}. Later, it is stated as a theorem without proof that for 1 <= p < +infinite, The dual space of l^{p} is equal to l^{q}. Answered by Doug Farenick. 





Box and Whisker plots 
20011119 

From Rod: In our Prealgebra course, we have been studying Box and Whisker plots. Recently, we learned how to decide whether a data point is an outlier or not. The book (Math Thematics, McDougall Littell) gave a process by which we find the interquartile range, then multiply by 1.5. We add this number to the upper quartile, and any points above this are considered to be outliers. We also subtract the number from the lower quartile for the same effect. My question: where does this 1.5 originate? Is this the standard for locating outliers, or can we choose any number (that seems reasonable, like 2 or 1.8 for example) to multiply with the Interquartile range? If it is a standard, were outliers simply defined via this process, or did statisticians use empirical evidence to suggest that 1.5 is somehow optimal for deciding whether data points are valid or not? Answered by Penny Nom. 





e^pi > pi^e 
20010727 

From Dusty: What book(s) contain a proof that e^{Pi} > Pi^{e}? I think it might be in Problems in Analysis published by SpringerVerlag but I have not been able to check. Answered by Chris Fisher. 





A confidence interval 
20010628 

From Murray: An investigator wants to find out of there are any difference in "skills" between full and part time students. Records show the following:
Student Mean Score Std Dev Number
   
Full time 83 12 45
Part time 70 15 55
Compute a 95% confidence interval for the difference in mean scores. Answered by Andrei Volodin. 





What is the difference between Mean and Average? 
20001213 

From Julie: What is the difference between Mean and Average? My thinking is the average, is the equal to the sum of all numbers divided by the number of numbers added together. But the mean, I think should be calculated by adding the largest and smallest numbers in the set and them dividing by 2. (which is the point where 1/2 the numbers are higher and 1/2 the numbers are lower) Answered by Patrick Maidorn and Penny Nom. 





Mode 
20000922 

From James Barton: I have always been told that a mode is the "one" number that appears most in the set of numbers: ex.{1,3,4,6,3,2} the mode is 3. What if you have {1,1,3,4,5,5}is there a mode. I was taught long ago that there is no mode, Not i am having to teach there is two modes. 1 and 5. If this is the case if we have {1,1,2,2,3,3,4,4,5,5} that every number is the mode. True or false. This is being ambigiuous if we say all are the mode. Because no one number is used more than the others. Answered by Claue Tardif and Harley Weston. 





Central Limit Theorem and Law of Large Numbers 
20000626 

From Jonathan Yam: The Central limit Theorem states that when sample size tends to infinity, the sample mean will be normally distributed. The Law of Large Number states that when sample size tends to infinity, the sample mean equals to population mean. Is the two statements contradictory? Answered by Paul Betts and Harley Weston. 





Sample variance 
20000416 

From Jonathan Freeman: I was just reading your article entitled "A Note on Standard Deviation" I'm now teaching a unit on s.d. and my students were wondering why one uses a denominator of n for a population and n1 for a sample. I saw in your article that this is because "[the quantity] tends to underestimate sigma... and other technical reasons." To which my students again asked... "Why?" Could you please elaborate a bit on the "other technical reasons" perhaps in terms a high school senior (or their teacher...) could understand? Answered by Harley Weston. 





Estimating the population mean 
19991113 

From John Barekman: Statitistics: Estimating the population mean when the standard deviation is known: I am not sure which n to use in the formula for the confidence interval equation: x +/ z*(standard deviation/sqrt(n)) If we have data of ten people, and if we have the data of ten sets of ten people each, what is the difference in the n that we use? What is the difference between the standard deviation and the standard error? Are we using the number of sampling means or just the number of samples? Answered by Harley Weston. 





Stem and Leaf Plot 
19990914 

From Jeanette Sovick: My 5th grade son brought home a math paper, the title of which reads, Reading StemandLeaf Plots...can you explain this so I can explain it to him...There is no book, his teacher just sent this practice sheet home for him to complete and I have no clue! Answered by Penny Nom. 

