







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. 





The range in grouped data 
20120827 

From maria: Question from maria, a student:
how to find range from group data.?i know that it is the difference between largest and smallest value.but confuse to find range of group data e.g
class interval 
frequency 
05 
6 
510 
7 
1015 
9 
1520 
4 
Answered by Robert Dawson. 





The average age of 300 cars 
20111122 

From Jason: I have 300 used cars built from 1970 to 1980, I would like to know the average
age by total volume. If I provide the qty built per year, can I determine the average age of the lot (300) by total volume?
Total built 
50 
56 
30 
10 
30 
25 
64 
9 
12 
14 
Year built 
1971 
1972 
1973 
1974 
1975 
1976 
1977 
1978 
1979 
1980 
Thanks Answered by Penny Nom. 





Economic data 
20101224 

From Le: I'm student in economics. I have to read some research of test of financial model (test of Black, 1972, Fama et McBeth, 1973, Fama et French, 1993, about the CAPM or APT model). And I really want to redo these tests with the same data to understand them better. But I don't know where and how I can have these data. I hope to have some recommendations from you.
Thank you,
Le Thi Bich Hanh Answered by Robert Dawson. 





Accuracy of Data 
20090625 

From Bill: If say, a predictin is 20 and the actual is 35 how do you work out the accuracy of the prediction Answered by Janice Cotcher. 





The range of a set of numbers 
20081119 

From krista: hi, i was working on a math problem for homework and it asked me to
find the range out of these numbers:
1,15,16,16,19,25,27,28,28, can you help me? Answered by Penny Nom. 





A decision based on data 
20071204 

From manny: You have administered a standardized test of manual dexterity to two groups of 10 semi skilled workers. One of these two groups of workers will be employed by you to work in a warehouse with many fragile items. The higher the manual dexterity of a worker the less likelihood that worker will break significant inventory. Because of a unique contract you must hire all 10 employees from one of the two groups and none of the employees from the other.
You must decide which group to choose. Choose at least two measures of central tendency and at least one measure of dispersion for each group and use those to make your choice. Be sure to justify your choice with at least one page of discussion and analysis. Answered by Penny Nom. 





Normal distribution 
20070524 

From Paula: Consider a data set that is normally distributed.
The mean of the data set is equal to 10,000.
a.) Suppose that, for this data set, 10,625 has a
"zvalue" = 2.5. Solve for the standard deviation of
the data set.
b.) Solve for the "zvalue" of 9,900. Answered by Penny Nom. 





Outliers in a box and whisker plot 
20060219 

From A student: i need help on determining if their is an outlier...i know how to find the median and the lower quartile and the upper quartile..but i don't understand about the outliers....please tell me if their is an outlier in this problem....the numbers are...63,88,89,89,95,98,99,99,100,100 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. 





The range of a data set 
20051004 

From Carmen: What is the range of this data? 36,64,37,45,53,60. Answered by Penny Nom. 





Statistics from grouped data 
20031009 

From Rebecca:
I have to use a suitable computer package (ie. Excel) to work out the mean and standard deviation of the following:
Price Range No of Houses No of Houses
£`000 Area 1 Area 2
45 and under 50 4 5
50 and under 55 7 12
55 and under 60 14 16
60 and under 70 19 18
70 and under 80 8 3
80 and under 100 5 2
I have used excel to work out mean and standard deviation before, but not in a more complicated example like this. Any advice on where to start would be greatly appreciated. Answered by Penny Nom. 





Variance 
20021029 

From Ade: I am trying to solve a standard deviation question, I have 30 data points to use, should I group the data before solving for variance or should I just use the raw data. Answered by Andrei Volodin. 





On which assignment did I do better 
20020517 

From Denise: I have 2 writing assignments in class. The first assignment, which had a mean of 10 and a standard deviation of 2, I got a score of 12. The second assignment had a mean of 18 and an s.d. of 3, I got a 21. I need to know which assignment did I do better, relative to my classmates? Answered by Andrei Volodin. 





The Dugout, Don's Basement, Cd Corner,... 
20020430 

From A student: The Dugout, Don's Basement, Cd Corner, Harry's Deli, Bill's Software, Anne's Footwear, and Joanne's House cleaning. The gift certificates are each in multiples of $5. There is a $100 range in the value of the gift certificates, which start at $25. The mean value of all seven gift certificates is $80, and the median and mode are both $70. The certificate from The Dugout is worth the most and the one from Joanne House cleaning is worth the least. The total value of the gift certificates from CD Corner, Harry's Deli, and Anne's Footwear is $270, but Anne's Footwear certificate is worth $50 more than the one from Harry's Deli. The Cd Corner gift certificate is equivalent to the mean for this group of three. What is the value of the gift certificates from each store? Answered by Penny Nom. 





Range of values for standard deviation 
20020322 

From Susan: What is the range of values for standard deviation? Is it between 0 and +3? Is it between +1 and +3? Answered by Andrei Volodin. 





Testing a hypothesis 
20020314 

From A student: A large distriutor of cosmetics has kept his outstanding accounts receivable to a mean age of 18 days over the past year. This average is considered a standard by which to measure the efficiency of the credit and collections department. Management wishes to check if receivables in the current month is over standard and will do this at a significance level of 0.50. A random sample of 100 accounts yields an average of 20 days with a standard deviation of 9 days. what should management conclude? Answered by Andrei Volodin. 





The median with ties 
20020227 

From Marcel: What, exactly, is the proper way to determine the median of a set of numbers when doubles or triples of a number are part of that set? Do the doubles count as two and the triples three, or does each count only as one toward determining the median. Answered by Harley Wston. 





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. 





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. 





Column doesn't add up to 100% 
20011017 

From A student: why don't some tables I'm studying in a column add up to 100%? Example: N=338, but responses to questions asked in survey I'm studying equal of 24.3, 9.8, 43.8, DON'T add up to 100%. I'm assuming that some people surveyed out of the 338 didn't bother responding, but is there another problem related to proportion or ratio being used, but improperly labeled on graph?. Note at bottom of table says: "number in parenthesis are numbers of cases" and 338 was in parentheses. I'm lost. Answered by Penny Nom. 





Ciefficient of variation 
20010923 

From Carmen: I have a question from my OAC finite class. I've come across a problem with the coefficient of variation. I have taught my students that there are no units for coefficient of variation and it can be expressed as a percent. So, for example, a set of data with mean of 5 and standard deviation of 100 would have a CV of 5%. But what happens in this situation: the mean is 4meters and the standard deviation is 0.7mm. Is the CV 1.75% or 0.00175% or 0.0175%? I've had some students change leave the units as is, change them both to mm or change them both to meters...so which is it and why? Answered by Penny Nom. 





Double bar graphs 
20010909 

From Leslie: My daughter has a homework problem in which she is graphing data from two frequency tables onto a double bar graph. The graph shows how many students worked in a program in two different years, grouped by age. In the first age group, one of the years has no students working, while there were students in that age group in the other year. Answered by Penny Nom. 





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. 





Probability and odds 
20000505 

From Leah: The chances of rain on friday, saturday, and sunday are 20%, 30%, and 50% respectively. what are the odds it will rain all three days? Answered by 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. 





Box and whisker plots 
20000309 

From Brett Blake: Do you have any information on Box and whisker graphs? Answered by Harley Weston. 





Bar graphs and histograms 
20000111 

From Raeluck: What is the difference between a bar graph and a histogram? Answered by Harley Weston. 





Mean, median and mode 
19991207 

From J William Morning: Using the data values 2,2,10,6,5, determine the median, mode and mean. Answered by Penny Nom. 





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. 





Body part measurements 
19991110 

From V Bailey: I am a kindergarten teacher and mother of a 6th grader who wants to do a science project on the correlations of body part measurements. We heard this on the radio and it sparked our interest, but now I cannot find any information about it. Examples are: your height is supposed to equal the distance from fingertip to fingertip when your arms are outstretched. Your foot size is supposed to equal the distance from your wrist to your elbow. Please help me find more information on this topic. Answered by Penny Nom. 





A pictograph 
19991028 

From Ali: Please tell me how to make a pictograph.I am 2 grade student. Answered by Penny Nom. 





Predictions 
19990922 

From Joesph Dana: How do u find the results of an unbiased sample of 100 students that are shown on the table. For example the school has a total of 1,150 students prdict how many students would chose cereal(46) pancakes(15) eggs(20) and sandwich(19) Answered by Haeley 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. 





Three dice 
19981117 

From Ryan Allinson: Rolling three regular dice how many different ways could a sum of 10 be rolled? Hope you can help. Can you please show me how this is done? Answered by Penny Nom. 





Rolling a seven 
19980611 

From Bruce Thompson: What is the probablity of rolling two dice and it coming out as seven? a) 1/6 b) 1/36 please give me the correct awnser and explain please. Answered by Harley Weston. 





Histograms. 
19970926 

From David Wilson: I need some help to teach my daughter the functions and the techniques involved in solving histograms. She is in the 7th grade and is in a prealgebra class. She was give these as homework, however there is no section in her book explaining what a histogram is or how to solve them. Thanks! Answered by Penny Nom. 





15 films 
19991109 

From Hebert: Un touriste revient de vacnces avec 15 films:  2 films de photos d 'Italie
 8 films de photos de Grèce
 5 films de photos de Turquie.
Aucune marque distinctive ne permet d'identifier les films. Pour des raisons financières le touriste ne fait développer à son retour que 11 de ces 15 films qu'il choisit au hasard.NB : on donnera les résultats sous forme décimale approchée à 104 près.  Combien y a t il de choix différents possibles de 11 films parmi les 15 ?
 Quelle est la probabilité que , parmi les 11 films développés, il y ait:
 ...
Answered by Claude Tardif. 

